A Proof for the Existence of God
Let’s start by clearing up some confusion. (1) While some people may think of God as an old man in the sky, that is not the notion of God in the Judeo-Christian-Islamic tradition, nor that addressed by Aristotle or the Buddhist Logicians. For us, God is an Infinite being. (2) “Infinite Being” does not mean, “really big and powerful being.” It means completely unlimited being.
Dynamic Ontology
Dynamic ontology is built on the notion of being can be explicated as the capacity to act. A finite being can act limited ways, and an Infinite Being can do any possible act. Finite beings can act in this way, but not that; here, but not there; now, but not then. Infinite being can act in all possible ways in all possible places at all possible times. So we are not God and have forgotten it, because forgetting is a limitation on our ability to think. Nor is the universe God because it is constrained by the laws of nature, which are more restrictive than what is logically possible.
Dynamic ontology helps us understand the distinction of essence and existence. Essence, what a thing is, is the specification of its possible acts. But, a specification does not normally entail that what we specified actually exists. Existence adds a new note of comprehension: that the thing we are talking about can act in reality. Not only does it have a specification, but that specification is operational. Perhaps an analogy will help. Essence is like a photographic slide. It specifies the picture on the screen, but there is no picture on the screen until the slide is illuminated. Existence is like the light illuminating the slide. It makes the projected picture actual.
Background
To prove existence we need to show the capacity to act. We can only show this by pointing out a concrete act that must be attributed to the being in question. We know concrete acts only through experience.
Thinking something does not make it exist. So “proofs” such as St. Anselm’s ontological argument fail because they only prove that if we define God as the greatest possible being, then we must think of God as existing. But, thinking of God as existing does not make God exist. We can think something in two ways – with commitment to the thought and without commitment. The ontological argument does not show that we must be committed to the thought that God exists, but only that to be consistent, in the context of the definition, we must think of God as existing.
We can only prove what we know implicitly. Proofs show us how to assemble facts we already know to see something we may not have noticed. So, we can only prove God's existence if knowledge of it is implicit in experience. People with good intuition can see it directly, but may not be able to articulate it for others. Those of us who are less intuitive, or who trust intuition less, need step-by-step guidance to come to the same conclusion. A proof will make the connections needed for us to be aware of God in our experience.
Finally, this proof assumes a working knowledge of logic that not all may possess. For example, the Principle of Excluded Middle tells us that complete disjunctions like “A is either B or not B” are always true if they are meaningful.
The Proof
Premise 1: Something exists.
This is a fact of experience. At least I exist (cogito ergo sum), so let’s take our self to be concrete.
Premise 2: Whatever exists is either finite or infinite.
This is a complete disjunction. Remember that “finite” means limited in ability. I am finite because I can’t do everything that's logically possible, but only what is physically possible for me.
Premise 3: Any collection of finite beings, including the universe as a whole, is finite in being.
Again, finite does not mean quantitatively finite, but limited in its ability to act. Even the whole universe is limited in its ability to act. If it were not, logical possibility would be the same as physical possibility and physics identical to logic. There are logically possible acts that the universe cannot do. Since it has finite dimensionality, the directions in which its parts can move are limited. It is logically possible to move in more directions, and so the universe is at least limited in this way. Even if the universe were spatially or numerically infinite, it would still have a limited capacity to act. Since the universe (or multiverse if you subscribe to it) is the largest possible collection of finite beings, any smaller collection will also be finite.
Premise 4: If a being exists, its explanation must exist.
If this were not true, science would be impossible. If things "just happened," the observations would not be underlying dynamics, and could neither confirm nor falsify hypotheses. Note that “explanation” has two senses: (1) the fact(s) that make some state of affairs be as it is. (We may or may not know these.) This is the sense I am using. (2) Our attempt to articulate our understanding of (1). This is not the sense I am using here.
Premise 5: If something exists, its existence is explained either by itself or by another.
Given that explanations exist, this is a complete disjunction: the explanation is the thing in question, or not the thing in question.
Premise 6: A finite being cannot explain its own existence.
Why? Because whatever can be explained by a being, viz. whatever a being can do, results from its essence, the specification of its acts. For a finite being, existence, the unspecified power to act, is logically distinct from its specification. I am human and I exist. Being human explains my ability to think, because that is part of what it is to be human. But, being human does not imply that I exist. If it did, no human could cease existing.
A thing is finite because its specification or essence limits its capacity to act, its existence. What limits is not what is limited, viz. existence, the bare capacity to act – just as a slide limiting light differs from the light it limits. Logically, limits negate specific acts, while existence does the opposite, making acts operational. When essence limits existence, existence is more comprehensive. Something less comprehensive, a finite essence, cannot entail something more comprehensive – existence. Thus, a finite essence cannot entail existence -- a finite being cannot explain its own existence.
The distinction of essence from existence does not apply to an infinite being, if it exists. Why? Because an infinite being’s capacity to act is not limited by what it is. For it, no possible act is negated by its specification. So for an infinite being, what-it-is would be identical with that-it-is.
Further explanation of Premises 4, 5, and 6:
A being is necessary when it is. (Once it is now, it is no longer possible for it not to be now.) Since finite beings have a history of coming into and going out of existence, the necessity of their present existence is not intrinsic. (It is possible for them not to be.) So it must derive something extrinsic – their explanation. Therefore, every actual thing has an explanation even if we are ignorant of it and say, “It just is.” Our verbal explanation is not true unless there is it reflects reality.
Conclusions
Conclusion 1: The existence of a finite being implies the existence of another being, its explanation. P4, P5, P6.
Conclusion 2: This other being cannot ultimately be finite. P3, P6
Any collection of finite beings, taken as a whole, is itself finite and so requires a further explanation.
Conclusion 3: So, the existence of a finite being implies the existence of an infinite being, as its explanation. C2, P2.
Conclusion 4: Therefore an infinite being exists, which we call “God.” C3, P1.
We are free to name things as we wali, but calling the infinite being “God” corresponds to common usage.
All of the commonly ascribed attributes of God (almighty, omniscient, etc.) follow from God's unlimited capacity to act. For example, if God were not omniscient, then there would be a logically possible act, reflecting on an item of information, which God could not do. If God knows, God thinks and so is personal in the sense of being aware, etc.
Note that this does not show God as existing and acting in only the past, but as the present and on-going explanation of all existence.
Dynamic Ontology
Dynamic ontology is built on the notion of being can be explicated as the capacity to act. A finite being can act limited ways, and an Infinite Being can do any possible act. Finite beings can act in this way, but not that; here, but not there; now, but not then. Infinite being can act in all possible ways in all possible places at all possible times. So we are not God and have forgotten it, because forgetting is a limitation on our ability to think. Nor is the universe God because it is constrained by the laws of nature, which are more restrictive than what is logically possible.
Dynamic ontology helps us understand the distinction of essence and existence. Essence, what a thing is, is the specification of its possible acts. But, a specification does not normally entail that what we specified actually exists. Existence adds a new note of comprehension: that the thing we are talking about can act in reality. Not only does it have a specification, but that specification is operational. Perhaps an analogy will help. Essence is like a photographic slide. It specifies the picture on the screen, but there is no picture on the screen until the slide is illuminated. Existence is like the light illuminating the slide. It makes the projected picture actual.
Background
To prove existence we need to show the capacity to act. We can only show this by pointing out a concrete act that must be attributed to the being in question. We know concrete acts only through experience.
Thinking something does not make it exist. So “proofs” such as St. Anselm’s ontological argument fail because they only prove that if we define God as the greatest possible being, then we must think of God as existing. But, thinking of God as existing does not make God exist. We can think something in two ways – with commitment to the thought and without commitment. The ontological argument does not show that we must be committed to the thought that God exists, but only that to be consistent, in the context of the definition, we must think of God as existing.
We can only prove what we know implicitly. Proofs show us how to assemble facts we already know to see something we may not have noticed. So, we can only prove God's existence if knowledge of it is implicit in experience. People with good intuition can see it directly, but may not be able to articulate it for others. Those of us who are less intuitive, or who trust intuition less, need step-by-step guidance to come to the same conclusion. A proof will make the connections needed for us to be aware of God in our experience.
Finally, this proof assumes a working knowledge of logic that not all may possess. For example, the Principle of Excluded Middle tells us that complete disjunctions like “A is either B or not B” are always true if they are meaningful.
The Proof
Premise 1: Something exists.
This is a fact of experience. At least I exist (cogito ergo sum), so let’s take our self to be concrete.
Premise 2: Whatever exists is either finite or infinite.
This is a complete disjunction. Remember that “finite” means limited in ability. I am finite because I can’t do everything that's logically possible, but only what is physically possible for me.
Premise 3: Any collection of finite beings, including the universe as a whole, is finite in being.
Again, finite does not mean quantitatively finite, but limited in its ability to act. Even the whole universe is limited in its ability to act. If it were not, logical possibility would be the same as physical possibility and physics identical to logic. There are logically possible acts that the universe cannot do. Since it has finite dimensionality, the directions in which its parts can move are limited. It is logically possible to move in more directions, and so the universe is at least limited in this way. Even if the universe were spatially or numerically infinite, it would still have a limited capacity to act. Since the universe (or multiverse if you subscribe to it) is the largest possible collection of finite beings, any smaller collection will also be finite.
Premise 4: If a being exists, its explanation must exist.
If this were not true, science would be impossible. If things "just happened," the observations would not be underlying dynamics, and could neither confirm nor falsify hypotheses. Note that “explanation” has two senses: (1) the fact(s) that make some state of affairs be as it is. (We may or may not know these.) This is the sense I am using. (2) Our attempt to articulate our understanding of (1). This is not the sense I am using here.
Premise 5: If something exists, its existence is explained either by itself or by another.
Given that explanations exist, this is a complete disjunction: the explanation is the thing in question, or not the thing in question.
Premise 6: A finite being cannot explain its own existence.
Why? Because whatever can be explained by a being, viz. whatever a being can do, results from its essence, the specification of its acts. For a finite being, existence, the unspecified power to act, is logically distinct from its specification. I am human and I exist. Being human explains my ability to think, because that is part of what it is to be human. But, being human does not imply that I exist. If it did, no human could cease existing.
A thing is finite because its specification or essence limits its capacity to act, its existence. What limits is not what is limited, viz. existence, the bare capacity to act – just as a slide limiting light differs from the light it limits. Logically, limits negate specific acts, while existence does the opposite, making acts operational. When essence limits existence, existence is more comprehensive. Something less comprehensive, a finite essence, cannot entail something more comprehensive – existence. Thus, a finite essence cannot entail existence -- a finite being cannot explain its own existence.
The distinction of essence from existence does not apply to an infinite being, if it exists. Why? Because an infinite being’s capacity to act is not limited by what it is. For it, no possible act is negated by its specification. So for an infinite being, what-it-is would be identical with that-it-is.
Further explanation of Premises 4, 5, and 6:
A being is necessary when it is. (Once it is now, it is no longer possible for it not to be now.) Since finite beings have a history of coming into and going out of existence, the necessity of their present existence is not intrinsic. (It is possible for them not to be.) So it must derive something extrinsic – their explanation. Therefore, every actual thing has an explanation even if we are ignorant of it and say, “It just is.” Our verbal explanation is not true unless there is it reflects reality.
Conclusions
Conclusion 1: The existence of a finite being implies the existence of another being, its explanation. P4, P5, P6.
Conclusion 2: This other being cannot ultimately be finite. P3, P6
Any collection of finite beings, taken as a whole, is itself finite and so requires a further explanation.
Conclusion 3: So, the existence of a finite being implies the existence of an infinite being, as its explanation. C2, P2.
Conclusion 4: Therefore an infinite being exists, which we call “God.” C3, P1.
We are free to name things as we wali, but calling the infinite being “God” corresponds to common usage.
All of the commonly ascribed attributes of God (almighty, omniscient, etc.) follow from God's unlimited capacity to act. For example, if God were not omniscient, then there would be a logically possible act, reflecting on an item of information, which God could not do. If God knows, God thinks and so is personal in the sense of being aware, etc.
Note that this does not show God as existing and acting in only the past, but as the present and on-going explanation of all existence.
Comments (248)
Your concept of "explanation" seems under-defined to me. You reference science, but that's a method that generates a specific kind of explanation. It's hard to judge your premises 4 to 6 without a clear definition of "explanation".
The way your argument is structured right now, I cannot see how premise 4 is justified. Having an explanation is certainly nice, but I fail to see how it would be necessary.
Similarly, your justification for premise 6 does not convince me. For one, it seems contradictory to state that:
Quoting Dfpolis
When you earlier (and correctly, I think) noted that existence is always distinct from essence. But regardless, your premise doesn't really follow from the justification. The existence of a finite being might still be unlimited in time, for example. Or finite beings might explain the existence of each other. These possibilities remain unexplored.
Moving on to the conclusions, you never specify why the explanation for a being needs to be another being, nor why finite beings cannot explain each other. So your conclusions seem to hang in the air.
Ultimately, it looks to me like you are reformulating the "first cause" argument, but I cannot see the advantages of your take.
The OP is quite lengthy and complex. My off the cuff response is that there are a number of things in your proof that do seem problematic to me. The stand-out would be:
Quoting Dfpolis
It is to your credit that you state this premise explicitly. But this does not mean that it is unproblematic.
Science does not require that literally everything have explanation. Science only requires that some things have explanation.
Much of physics, as an intellectual project, has been an attempt to determine the fundamental laws of the universe. If there are fundamental laws, by definition they are unexplained. They are simply "brute facts." Today's brute fact may be tomorrow's well explained phenomena (witness what Einstein did for Newtonian gravity), but at any one time there is a base level of explanation. Acceptance of the idea that explanation has to end somewhere is quite widespread among both scientists and philosophers, and science works perfectly well on this level.
I am not going to say that there are brute facts. I am going to say that it is not a self evident truth that there are not - and since you're the one offering the proof, the burden is on you.
If brute facts are not for you, you also do not seem to consider the possibility of antifoundationalist infinite regress, in which every finite explanation has another finite explanation... and so on forever. "Turtles all the way down," as it were.
Another unconsidered possibility here is that of an Escher-esque universe that is ontologically circular. To provide a concrete example of this, consider the following extract from the SEP's entry on time travel:
Quoting Smith, Nicholas J.J.
So you can pick up the collected works of Shakespeare from Amazon, go back in time, and hand them to Shakespeare, who is then spared of the chore of ever having to actually write them. It may or may not be allowed by the laws of physics. It may be mind-bending. But it is generally accepted that there is nothing incoherent in this. It is not a priori clear that it is not possible. And bear in mind, of course, that this is just a concrete, physical example of what I'm talking about.
Finally, the logical possibility of this kind of circularity brings us to premise six. You argue:
Quoting Dfpolis
I'm afraid I can't agree. To be human (or to be anything at all) is to exist. You can't be human if you don't exist. So to be human does imply that you exist. To imply existence is not to imply unceasing existence. If it did, everything that existed would exist forever, which is clearly not the case.
These are just off the cuff thoughts, of course.
3 is contrary to what most cosmologists believe, which is that the universe is infinite.
4 and 5 are assertions of the existence of explanations, for which there is no logical need. The universe doesn't need an explanation.
Further, I find the insistence that God must be omnipotent unnecessarily limiting, given the well-trodden logical problems with the notion of omnipotence. In my view, no god worth believing in is omnipotent (problem of evil, logical paradoxes regarding heavy stones and so forth) and, if there were such a god, humans would certainly not be in any sense in Her image.
Advaita Vedanta has a pretty mind-blowing conception of God as a sort of cosmic consciousness (the 'We are God' path), but it doesn't need any gimmick as trite and MarvelUniverse-ish as Omnipotence to impress people.
Nor is the attempt to rule out the universe as being God (pantheism), because of the 'laws of nature' convincing. The 'laws of nature' are regularities we have discovered that explain to a pretty good degree of accuracy what we see happening in our part of the universe, in the time periods we can observe. They say nothing about what might be happening elsewhere, or what might happen later. Since the universe is likely infinite, regularities discovered in this tiny finite part of it say nothing about what its nature and capabilities might be. It's quite possible that there are no universal laws of nature, and that everything that can be imagined (plus even more that can't) is happening somewhere (Tegmark's hypothesis)
Yes, even if one accepted this proof (which I don't) one must be careful about the implicit leap from
Quoting Dfpolis
to any other characteristics traditionally assigned to God. To hand wave over this with a simple assurance that we are not talking about
Quoting Dfpolis
seems... problematic.
Quoting Dfpolis
...is that as an explanatory concept, it's completely bankrupt. You have a theory that can explain literally anything. It's the absolute antithesis of falsifiable.
So by being able to explain literally anything, your theory predicts nothing, and therefore explains nothing.
I think this is the most fundamental problem with your proof.
I don’t think you ought to appeal to Buddhism for support of this kind of argument. Buddhists only generally address the existence of God in order to dispute it (regardless of what universalists are inclined to say.)
1. A finite entity can't explain itself
So,
2. There exists an infinite entity (God) that explains all finite entities
I thought much of our knowledge framework is a work in progress. If history is researched we can see an ever increasing list of explanations, all finite, that make sense.
In other words your argument depends on a premise (finite entities can't explain themselves) that is shaky because it rests on the mistaken certainty that the finite can't explain itself. Look at the progress science has made. In fact it looks like your argument is simply a revamp of the God of the gaps argument.
On the basis that 'proof', 'existence', 'thinghood', 'limit' and 'God' are all concepts with contextual utility, I suggest the main reason believers have for these (incestuous) word games is a 'belief reinforcement exercise' to shore up weaknesses in their 'utility insurance policy'.
I’m not overall in agreement with the OP, BUT I think this claim is deeply questionable. Yes, science has made progress in some respects - certainly in terms of technological and medical invention, of which there can be no doubt. But scientific cosmology and even the basic nature of matter itself is often and widely said to be in a state of crisis, and there are raging controversies over the reality or otherwise of many universes, parallel universes, and so on, none which seem remotely solvable in our lifetime. Now of course that is not in itself an argument for theism, but you can’t gesture towards science as an argument against it, either!
Correct. I was just pointing out the flaw in the OP argument which is that the finite can't explain itself; it's an open question that has no satisfactory answer at the moment. If you look at how religion has lost ground to science you'll notice the point I was trying to make.
Anyway thanks for the gentle warning.
Harking back to my previous post, I would say that only that which is limited in at least some respect is capable of offering any explanation at all.
Sure, whatever happens the completely unlimited can allow you to tell some kind of story about it. But to call this story an "explanation" is a semantic sleight of hand.
Because the completely unlimited is equally capable of "explaining" literally anything, it predicts nothing. It's the absolute antithesis of falsifiable. It has literally no ability to tell you why any particular thing exists or occurs, as opposed to any other particular thing - or indeed, no particular thing at all.
Why does the sun continue to shine in the sky rather than waft gently down to Earth, offer you a Vienna coffee, and then begin discussing logical positivism? The completely unlimited can't tell you.
Zero explanation.
To choose my words a little more carefully so as to avoid the apparent paradox inherent in my previous formulation, in its superficially apparent ability to explain literally anything, the completely unlimited actually explains nothing.
A finite being outside of time has no need to explain its own existence, it is beyond causality, it just 'IS'.
Quoting Theologian
A finite being outside of time is a brute fact. This I believe is the actual nature of God.
Quoting Dfpolis
I would argue that infinite (unlimited ability to act) is self-contradictory in a finite universe.
'square circles exist or they don't' - complete disjunction so true.
'square circles exist ' - contradictory
'Whatever exists is either finite or infinite' - complete disjunction so true.
'The infinite exists' - contradictory (could a completely unlimited being exist in a finite universe?)
The rest of the proof assumes that an infinite being is possible; it needs to be demonstrated that an infinite being is not a logical contradiction.
Finite things have NOT been known for a history of coming into and going out of existence. At all.
I am a human; I have come into existence, will pass out of existence. But my component parts, matter, have not gone in-and-out of existence. I, the human, am a complex configuration of matter; the configuration may and does change, matter never perishes or or comes into existence (other than changing forms, and changing to-and-fro energy to matter, matter to energy).
I call you out on this assumption. In my opinion it is wrong.
several problems with this paragraph.
All existing humans exist.
I am a human.
Therefore I exist.
I don't know how you can conclude, from the same premises
All existing humans exist.
I am human.
Therefore I don't exist.
Your reasoning is wrong in he sense that humans exist in a temporal fashion. But they do exist when they do. Therefore your premise fails on this turn:
"Being human explains my ability to think, because that is part of what it is to be human. But, being human does not imply that I exist. If it did, no human could cease existing."
Being human implies that you currently exist. It does not exclude the possibility that you came into being or that you will exit into nihil. But the current state of affairs is that you exist. Therefore your conclusion in this premise, or the reason you argue for us to accept the premise, is wrong.
You are using the QED as your premise. It's called "begging the conclusion" or something like that fallacy.
If specifications exist, then there is a creator. So you assume there is a creator. You use this assumption to say there is a creator. But the assumption is random, it is not well-grounded; and more importantly, the assumption pre-requires the object of your proof to exist.
In other words: you use something that you accept as a premise, to prove that it exists. That is wrong.
I don't personally buy either your theology or that of @Dfpolis. My own chosen moniker is a kind of private joke, and essentially ironic. But that said, I do think there is a problem with this argument.
Specifically, that the "God" philosophers have traditionally talked about is not seen as existing inside the universe, but as beyond it: eternal and uncreated, as it were. In keeping with this tradition, you yourself describe God as a
Quoting Devans99
Yet placing God, or at least God's ability to act, wholly inside this universe seems to be a premise of your argument. Remember: post Einstein, time is very much a part of the fabric of this universe. So it is difficult to say that God exists outside of time and yet is somehow constrained by the limits of the universe.
I think the same goes for people who try to disprove God. I think it stems from a fear that there may really be a God that punishes those who do not believe in It, so they attempt to keep the fear at bay by proofs.
Personally I just rely on faith. My faith is that
(1) most of us (including me) will be unable to ever know whether there is a God - at least in this life;
(2) most of us (including me) will be unable to know what God is like if She is there; and
(3) if there is a God, and She has anything remotely like personal characteristics, She is wise and kind, and nothing at all like the cruel, vain, childish, violent personality described in the holy books of the three Abrahamic religions. Like all good friends, She is not to be feared, obeyed or worshipped. But She may be loved.
Given the nature of the universe in which we find ourselves, why on Earth would you conclude that?
The Abrahamic God, whatever else you might say of Him, is surely infinitely more plausible than that.
Although personally, I think the most plausible theology is Lovecraft's. Ironic, considering he never represented his own writings as anything other than fiction.
One problem with this is that all of the major religions have a god that not only has the feelings of a person--the god is pleased or displeased, it has preferred states or preferred behavior for others, and so on--but usually it even speaks so that we can quote things it said.
So what sort of thing is it supposed to be if it has those characteristics? It's natural to think of it as a person, because persons are the sorts of things that have those qualities.
What are we supposedly quoting if not a person?
lol. no comment. i'm going to be accused of trolling for this post but it might be best for me to get kicked off at this point. Have fun Theologian, but not too much fun :)
Quoting Theologian
I agree with what you wrote but you might want to expand on it to fill in the holes. I'm going to put in my journal and analyze it line by line.
you are one of the most intelligent people i've come across on an online forum. Certainly much more intelligent than me. Do you know how to fix a car? I don't.
But I'm afraid I wouldn't have the foggiest notion of how to go about fixing a car. Does that cost me virtual IQ points in your estimation?
A few. Like i said, i can change oil but other than that i can't fix a car essentially. I just think in the day and age we live in fixing a car is a person's greatest asset. (top 10 atleast).
Just my opinion.
You mention lovecraft. The author was born in the same city where i had my first memory in life. I lived in providence Rhode Island at a young age. I love coincidences. This is pertinent to the OP because you mentioned Lovecraft.
i had a manual transmission (delivering pizzas) and i burned up two clutches in two years. I don't drive a manual transmission any more unless in the future its for a truck company.
50 cents on amazon. consider it done.
In real life his views were more complex and nuanced than you may suspect from his writing alone: he did ultimately marry a Jewish woman.
Anyway, if you can get past that, there is a lot there that's worth experiencing. Any time we explore authors from outside our own time and culture, we almost inevitably encounter values at odds with our own. But I think on balance it's better to have such encounters than not.
If for no reason other than that seeing all the crazy and stupid things that highly intelligent people from other times and places have believed may make us at least a little more inclined to ask which of the things that we ourselves believe are no less crazy and stupid.
Well, but what is acting? Are we talking about shape-shifting, or? If so, then we are talking about an old man in the sky sometimes. It would just be that we're not only talking about that.
i agree with that.
I can't speak for @Dfpolis, but I'm guessing he might draw a distinction between actually acting, vs simply having the ability to act. So God can act as an old man in the sky, but probably just doesn't on account of the whole thing being... kinda stupid really... :razz:
First, "not being able to do things that are logically impossible" would be a limitation. So if a god can't do things that are logically impossible, then the god isn't infinite, either.
If, instead, we say, "'infinite ability' refers to 'no limitation of ability within the scope of abilities that are possible'," then we invite discussion as to why we should consider logical-but-not-physical possibilities as within the scope of abilities that are possible, because we seem to be conflating what "ability" refers to.
Or otherwise, with a nod to the Euthyphro problem, it suggests that logic is prior to any god. That would need to be explained (how is that the case ontologically for example), and it would need to be justified why god should be given an exalted position in that case rather than logic, since god would be logic's lapdog so to speak.
Of course, the points about logic also have problems depending on one's ontology of logic. The comments about logic do not work if one isn't a platonist on logic.
I think that the term universe is the source of your confusion:
- If we define the universe as everything then God must be within it by definition
- Everything must also be finite
- Hence we cannot have an unlimited God in a limited universe
- So God exists outside of spacetime but he still exists within the context of a larger, finite, timeless universe
But then we need to alternatively explain the major religions, who supposedly had their god(s) speaking to them.
Or is this supposed to be a proof for a god that bears no resemblance to the god of any major religion?
Quoting Devans99
Okay, I follow you there. But...
Quoting Devans99
Still not entirely sure how you get to that. I'm not saying it isn't, but I'm not at all sure how you justify that claim in a positive sense.
Proving a theorem amounts to demonstrating that it necessarily follows from the explicitly-stated axiomatic construction logic of the abstract, Platonic world in which it is provable.
God is defined as the creator of the real, physical world.
Therefore, to prove the theorem, we would need access to the axiomatic construction logic of the real, physical world, also called, the theory of everything (ToE).
In his lecture, Gödel and the End of Physics, Stephen Hawking quite successfully argued, however, that we cannot possibly discover the ToE. Gödel's incompleteness theorems prevent us from achieving that feat.
This implies that it is not possible to prove anything at all about the real world. It is not possible to prove that anything exists, and science does not prove anything about the real world.
Since you cannot prove anything about the real, physical world, you cannot prove anything about its creation.
This does not mean that God exists or does not exists. It only means that our knowledge methods fail to reach the answer to this question. Hence, the belief that God exists or does not exist is necessarily the result of something else than knowledge.
There is nothing special about that, actually.
For example, access to existing knowledge is insufficient for the purpose of discovering new knowledge. Therefore, the most important ingredient in the discovery process of new knowledge is something else than knowledge. Otherwise, our existing knowledge would allow us to enumerate all possible knowledge theorems, and use that to discover new knowledge. That is exactly, however, what Gödel's incompleteness theorems disallow.
You can also prove this impossibility from Turing's halting problem. In fact, that is how you can trivially produce an alternative proof for Gödel's incompleteness theorems from Turing's halting problem (for the weaker form).
GIven @Dfpolis's background, I doubt the latter. But I really shouldn't speak for him.
You don't have to buy anything a la platonism to do proofs.
Quoting alcontali
That's not necessary in a proof. You can define something any way you like in your proof, really.
Quoting alcontali
How are you arriving at that conclusion?
There is a separate thread:
https://thephilosophyforum.com/discussion/5791/musings-on-infinity/p1
In summary I would say:
- Reality is constrained to what is logical
- Actual infinity comes with a bunch of illogical behaviours (see Hilbert's Hotel etc...)
- So Actual infinity does not feature in reality
I hesitate to ask, but how are we arriving at "everything must also be finite"?
https://thephilosophyforum.com/discussion/comment/303825
And if the second premise is true, how would you be arriving at the first premise?
Proof is context-sensitive.
It is only valid in the abstract, Platonic world in which it necessarily follows from its construction logic.
For example, you can prove a theorem from number theory, or from set theory, or from the lambda calculus (and so on). These are three different axiomatizations, i.e. abstract Platonic worlds, with each their own set of theorems.
None of their theorems prove anything about the real, physical world. The real, physical world has another (unknown) construction logic.
Furthermore, none of the theorems of one abstract, Platonic world (=axiomatization) proves anything about another abstract, Platonic world.
In the thread you're linking to you're talking about finite/infinite quantitatively. Dfpolis stresses that he's not talking about finite/infinite in this sense, but in the sense of limited vs unlimited abilities.
I've yet to see you not (keyword not) say something, brilliant. You would impress me more if you threw in something dumb. Watching you is glorious. Please show some humanity. lol.
So part of the background assumptions you're working with is that the physical world has different (and unknown) logic?
You'd need to support that claim.
Contrast to actual infinity. ?+1=?. IE something that when you change it, it does not change. How is that logical?
I consider the existence of actual infinity in reality as likely as a teapot orbiting Jupiter.
Not to worry: it's bound to happen sooner or later!
And you know, some folks here might say that it's happened already. Some might even say that it's happened more than once! :gasp:
Okay, but again, Dfpolis stresses that he's not talking about finite/infinite in this (quantitative) sense, but in the sense of limited vs unlimited abilities.
At least criticize his argument from the perspective of his argument. Not from what you'd rather talk about re infinity.
your probably right, simply because different backgrounds and chosen mind sets effect our perception of reality. For my own sanity i won't reply to what you say too much. I can't stress this enough, you are brilliant!
I've always thought so...
But, it's adios from me for now. 'Night all!
But then you're supporting that with arguments about infinity in the quantitative sense.
Logic does not operate on real-world observables. It operates on statements, which are not real-world, but language objects that live in their own abstract, Platonic world.
Logic are not statements about the real-world. Logic consists of statements about other statements.
Since when is a language expression a real-world phenomenon? Does it have energy, mass, gravity, or an electrostatic charge? What could there possibly be physical about a language expression? Hence, a language expression cannot possibly be an object in the real, physical world.
How is a language expression not a real-world phenomenon? The essence of ostensive definition is language binding itself to the real world. If I utter the phrase "Pick up that stone" and you pick it up, how is that not a real-world phenomenon? Does language have energy? Does thought? I would argue that it does, yes.
In fact, the term "Platonic" is just a figure of speech to refer to an abstraction, i.e. a mere language expression. I just use it to distinguish them from physical, real-world objects. So, a chair is a physical object, but the language expression "chair" is not.
There is a simple litmus test for platonicity of the target of a language expression.
If you can translate it into other languages, then it must be a language object. For example, "5" is a language object, because you can also write "five", "cinque", "fünf", or "101" (binary). Therefore, it has nothing to do with the real, physical world. It is an idea instead of something physical.
Till this very day, Platonist philosophy is the core of the philosophy of mathematics. It is not literally Plato, though. It is just highly Plato-like, and it is clearly inspired by Plato's work.
My own take is somehow related to Edward Zalta's Platonic abstract object theory.
In my opinion, however, Zalta fails to mention explicitly the fact that mathematical (abstract-Platonic) objects do not exist outside the context of the axiomatic system ("axiomatization"), i.e. the construction logic, in which they are defined.
Proof theory requires the prover to supply the axiomatization in which the proof is derived.
Therefore, I do not say that this would be an error in Zalta's theory, but I consider this certainly to be an omission (or a lack of emphasis) in his otherwise excellent characterization of abstract objects as encoded language.
I don't know that I see Cthulhu as a potential deity. But if you want to start a thread to discuss it, that should be great fun!
I can only disagree.
What about Game of Thrones? Doesn't the television series bathe in language? Does it even pretend to be about the real world? It is obviously completely imaginary!
Therefore, language has generally nothing to do with describing the real world.
Some subset of the set of language expressions does indeed attempt to be isomorphic with the real, physical world, but that is just a subset. You can do much, much more with language than merely describing the real world!
Quoting Pantagruel
Yes, in that particular case, the language expressions are about real-world, physical objects, situations, events, and other observables.
I have never said that language cannot attempt to describe the real world. It sometimes even moderately successfully does so, even though it always remains a simplifying abstraction, albeit one that is somehow isomorphic with the real, physical world.
I have only said that not all language expressions attempt to do that. Language does not need to refer to the real world. For example, a language expression can trivially refer to other language expressions.
That's just one view. Another view is that there is no separate "abstract, platonic world," yet we still have logic, here in the real world
And re this:
Quoting alcontali
There is a view that the linguistic expression "chair" most certainly is physical, as is everything else. That view is called "physicalism."
Quoting Terrapin Station
Ok, understood.
I can only say that it is not the dominant view in mathematics, which is staunchly Platonic. There is a fringe philosophy, called constructivism, in mathematics that goes in that direction, but it is generally considered to be a heresy.
[i]Traditionally, some mathematicians have been suspicious, if not antagonistic, towards mathematical constructivism, largely because of limitations they believed it to pose for constructive analysis. These views were forcefully expressed by David Hilbert in 1928, when he wrote in Grundlagen der Mathematik [...]
Even though most mathematicians do not accept the constructivist's thesis that only mathematics done based on constructive methods is sound, constructive methods are increasingly of interest on non-ideological grounds.[/i]
I tend to follow David Hilbert's view on (real-world) constructivism, for similar reasons, and I am therefore also very negative about it. I think that the constructivist mentality is unproductive. Therefore, I consider it to be a heresy.
I'm basically a constructivist on mathematics and logic, by the way.
I'm also a physicalist and what's called a nominalist, where part of my nominalism is a rejection of there being any real abstracts.
Not being able to establish an existence claim through a proof by contradiction really sucks.
This assertion worries me. It doesn't ring true. Why "must" every being have an accompanying explanation? Is this knowledge that has escaped me thus far? Do *I* have an explanation, and if so, what is it? You seem to be saying that every being has a purpose. That may be so, but do we know it for a fact, or is it wishful thinking?
Yes, but since contradictions cannot be instantiated, (by the ontological principle of contradiction) they are not possible. So, the formulations mean the same thing.
Quoting tim wood
I do not follow your thinking here. Things that come to be cannot act before they come to be and so have limited being. The point I was making is that the necessity things have once they come to be is not intrinsic.
Quoting tim wood
What is contradictory is outside the scope of being and so not a limit on being. Having limited non-being (not being able to instantiate contradictions) does not entail having limited being.
Quoting tim wood
Again, this is a confusion. The non-existence of a necessary being is not possible. So a necessary being ceasing to be is not a possible act.
.
Quoting tim wood
In a way and in a way not. Yes, God is not limited to the physical multiverse. Still, that does not preclude God from acting in the cosmos.
There is something deeper here, viz. the identity of action and passion. The act of an agent operating on a patient is identically the passion of the patient being operated on by the agent. Thus, the cosmos being held in being by God is identically God holding the cosmos in being. This identity, however, applies to the operation, not to the beings involved. So, while God is immanently active in the cosmos, He is not identical with it.
Quoting tim wood
This assumes that God is extended (has parts outside of parts). Since God is infinite, you argument shows this is a false assumption. To be able to act at many points does not imply intrinsic extension. The laws of nature, for example, act throughout the cosmos, but have no parts outside of parts.
Quoting tim wood
For the count of Gods to be more than one, we need to be able to differentiate the second from the first. Since God is infinite, this is impossible. Any differentiating factor would imply the existence of an act one could do and the other could not (i.e. that of properly eliciting the concept of the differentiating factor). That implies that at least one is not an infinite being.
Quoting tim wood
No, because having a location mean that God would exist (and act) at one place and not another, and so not be an infinite being.
Quoting tim wood
No, because any "there" needs be defined relative to a finite existent, which would necessarily imply that God was active in maintaining its existence -- and so "there" operationally.
OK, an explanation in this sense is an agency that effects what is to be explained.
Quoting Echarmion
Knowing the explanation is nice. Having an explanation is necessary. I can think of three arguments for this.
1. Practically, if we allow any phenomenon to be a "brute fact," we undermine the logic of the scientific method. Unless we hold that the need of an explanation is universal, no observation, however carefully made, can be taken as evidence of an underlying dynamics. Instead of definitely confirming or falsifying a hypothesis, our observation could merely be something that "just happened" with no relation to the relevant hypotheses.
2. Phenomena come to be and pass away. That means that they have no intrinsic necessity, for it they did, they would necessarily be as they are -- always. Yet, once they are, they necessarily were then -- they no longer cannot not have been. So, they have a retrospective necessity. As this necessity is not intrinsic, it must be derivative and extrinsic -- implying the existence of an explanatory agency.
3. Finally, nothing can act prior to its actual existence, so anything that is transitory must have been brought into actuality by something already operative/actual -- its explanation.
Quoting Echarmion
Could you say why you are not convinced? What you see as a lacuna? Or a counterexample?
I do not see how a limited specification of acts can entail an indeterminate capacity to act, or how what a finite the is could entail that it is. At the very least all finite things we know seem to have come to be -- so what they are cannot necessitate that they are.
Quoting Echarmion
No, I said it was distinct for finite beings: "What limits is not what is limited, viz. existence, the bare capacity to act."
Quoting Echarmion
Possibly, though we know of no examples. Still, infinite duration is not infinite capacity to act. The argument is existence has no intrinsic limitations -- to exist means that a thing can act in some indeterminate way in reality. A finite being's essence (the specification of its possible acts) limits this inderminate capacity, making it determinate. Since it is a limitation on existence, it can't entail existence. (If it did, every possible kind of thing would necessarily exist, and no finite being could cease to be.)
Quoting Echarmion
I addressed this by noting that any collection of finite beigns is finite.
Quoting Echarmion
An explanation acts to effect the explans, and whatever acts, exists.
I gave more arguments for this in my previous post to Echarmion. There I argued, inter alia, that if we allow exceptions to the universality of this postulate, the logic of science collapses. It is irrational to say that a foundational principle applies when I want it to apply and does not apply when I do not want it to apply.
Quoting Theologian
Something being fundamental and unexplained within a science is not the same as having no explanation or not being explained simpliciter. The foundations of mathematics are examined in metamathematics and the foundations of physics by metaphysics. So, your point relates to how humans choose to structure their inquiries rather than to the nature of reality.
Quoting Theologian
This is not the sense in which I am using "explanation." I said:
Quoting Theologian
As noted earlier, I expanded on this in my response to Echarmion above. I gave two additional arguments there.
Quoting Theologian
I considered any collection of finite beings, which includes infinite regresses. Also, in my book, I show by mathematical induction that an infinite regress cannot give a complete explanation. I did not repeat that proof here as regresses do not arise in the argument. If you feel they do, please say at what point.
Quoting Theologian
(1) My argument uses exhaustion of possibilities by applying the Principle of Excluded Middle. If you feel that an Escheresque universe provides an alternative not covered by my application of excluded middle, please point out how I missed it.
(2) Time travel, by whatever means, may relate to accidental or Humean-Kantian time-sequenced causality, but my argument makes no appeal to that type of causality. Rather, it deals with concurrent explanations. As such explanations (e.g. explanations by the laws of nature) deal with simultaneous operations, they are not susptible to temporal paradoxes or even the fact that time may not be defined at scales beyond the Planck time.
Quoting Theologian
Yes, to be is to exist. That is a fact, not an explanation of the fact. What you have done is shift the emphasis (and so the meaning) from humanity to being. So, let me rephrase: My humanity explains my ability to think, but not my existence.
Quoting Theologian
I am providing an existence proof, not a manual of natural theology. I did indicate how one can proceed to a number of divine attributes.
Quoting Theologian
Falsifiability is a requirement applicable to the scientific or hypothetico-deductive method, not to strict deductions. It is no criticism of Godel's work to say that his conclusions are unfalsifiable. While it is irrational to posit a hypothesis that cannot be adequately tested, it is equally irrational to require falsifiability where it does not apply. We have a different, but well-defined method of examining deductions. We consider the truth of the premises and the validity of the logical moves. If both pass muster, the conclusion is true.
While belief is not evidence, granting that the universe has an infinite extent, does not mean that it has infinite being, viz. the ability to do any possible act.
Quoting andrewk
I find that strange in that you based your first objection on what cosmologists believe and all the cosmologists I know seek to explain the universe. I gave three reasons why phenomena need explanations in my response to Echarmion, above. Please explain why you object to them.
Quoting andrewk
The proof shows that there is an infinite being. What you call the infinite being is up to you. If you think that an infinite being is problematic, we can discuss that in an other thread, as this one is too busy for that digression. The same applies to the imago dei.
As to the universe, what is changing can't be necessary.
I suggest you look at F. Th. Stcherbatskv, Buddhist Logic.
No, it rests on a proof, (not an assumption) that a finite being cannot explain its own existence. If you want to reject my argument, show why that proof fails.
Look around you.
Plausible, no?
Believers do not need proofs. They are quite content without them. Thinkers need to examine beliefs rationally because, as Aristotle says at the beginning of his Metaphysics, "All humans, by nature desire to know."
Quoting fresco
Why would a rational person another's motives instead of their argument? Is truth no longer valued?
Assuming there is one, if it is timelessly, it is necessarily. This necessity is either intrinsic (in which case it is self-explaining), or it is derived (in which case it is explained by another). In either case, it has an explanation.
Quoting Devans99
I make no claim that the universe has infinite being.
Quoting Devans99
Sentences need to be meaningful to be true or false. Non-referential sentences are neither.
Quoting Devans99
I made no claim that God is "in" (limited to) the cosmos.
Quoting Devans99
Proving that x exists shows that it is not contradictory as one cannot instantiate a contradiction.
There is no reason why everything explainable ultimately must be explained by somebody. That is a weakness in the argument. In other words, because an entity can't explain itself, it is not NECESSARY that something else be able to explain it.
There is also the possibility that another finite thing can explain a certain finite thing, which is not itself. The argument does not allude to this very real possibility.
You are a being, (an ostensible unity). Your parts are potential, not actual unities.
Further, Greek atomism is long dead. There are no immutable atoma. The quanta constituting you came into being, most of them shortly after the big bang. If our present understanding of cosmology is correct, they will cease to be in a future big crunch. In the meantime, they are subject to quantum creation and annihilation processes.
Quoting god must be atheist
Quite true. Now that we agree on the fact, by what dynamics do you exist?
Quoting god must be atheist
I do not deny, but affirm, that humans exist when they exist. I went even further, saying that once they begin to exist, it is necessary that they exist then. So, I have no idea what point you're trying to make.
The question is not about the fact, which we agree on, but on the dynamics behind the fact.
Quoting god must be atheist
This sentence seems to be causing some confusion. What I mean is that our humanity entails our capacity to think, but humanity does not entail that we exist. Of course being means that we exist, but being human does not entail existing.
Quoting god must be atheist
I do not mean "specification" in the sense of prior design. I mean it as a list of the powers we have -- as something that can be known, not as something used as a blueprint.
Yes, religious texts use anthropomorphic language. I think that is natural, but I do not think that God is a person in the same way humans are, or that God has fits of emotion. I think most theologians in the Judeo-Christian-Islamic tradition would agree.
Yet, if God can do every possible act, God must be aware, for many possible acts require awareness. So, God is personal in the sense of being aware of reality.
This is where you should have started and ended. Positing an unexplained God as an explanation of what cannot be explained is conjuring.
By "being" I mean what has the capacity to act in any way. Still, as I said to Terrapin Station, being aware is required to perform many possible acts, so we can conclude that infinite being entails some kind of awareness.
There is a lot of stuff in this post I could (and may later) take issue with. But right now I want to cut to what I consider the heart of the matter.
You argue that:
Quoting Dfpolis
But to go back to your OP, your fourth premise states that:
Quoting Dfpolis
And you clarify that by explanation, you mean:
Quoting Dfpolis
When I said that the completely unlimited was the antithesis of falsifiable, I did not simply mean that it could not be falsified scientifically.
My point was and is that the completely unlimited is logically incapable of being the fact that makes some state of affairs be as it is. It is incapable of being that fact because by definition it is equally of making the same state of affairs not be as it is.
Therefore, if there is something that makes the state of affairs be as it is, the completely unlimited is not it.
Therefore we have only two logical possibilities:
1. There is nothing that makes the state of affairs be (no explanation)
2. There is always something other than the completely unlimited that makes the state of affairs be (other explanation).
In either case, your proof falls apart.
Thank you. Posting it is a means of eliciting criticism.
Quoting Dfpolis
:Being human: is present tense affirmative (nominative). Human is being, and therefore the human exists.
At one point you say that being human means the human exists, at another point you say being human means that the human does not exist.
Would it be not easier to say "a being that had been does not exist, even if it had been a human when it had existed"? I exaggerated the tenses to make this obvious (although grammatically not totally cool.)
Quoting Dfpolis
I'm not sure how much formal philosophical education you've had (I'm just a beginner myself), but the term "metaphysics" is just a historical accident. It is not "meta" in the way that modern academics generally use the term. I'm not sure if you're aware of that or not. Forgive me if I'm just belaboring the obvious.
I think I should log off for a bit. Otherwise I'm going to spend the entire day on this forum, and I do actually have other things I should be doing! :razz:
Not to worry: I will be back. And probably sooner than I should! :wink:
...what cannot be explained by itself. It can be explained, by another... be it another finite being or be it an infinite being. But either way, the assumption that something necessarily can explain a finite being IS, like you said, not a necessary consequence. And the existence of that something is the second assumption that is wrong, as you say conjuring, because its existence is not necessary, either.
So Dfpolis piled one not necessarily following consequence on top of another not necessary consequence, and insisted that they are both necessary.
I defined "infinite being" as being able to do any possible acts. If you want to see being unable to instantiate contradictions, be my guest. Such labels do not change the content.
Quoting Terrapin Station
This is because logical possibility is based on the nature of being, not on contingent restrictions as physical possibility is. For example, the reason for the logical principle of noncontradiction is that it is impossible to instantiate a contradiction in reality. On the other hand, the laws of nature are contingent and need to be discovered empirically.
'Rationality' is merely a mental exercise with a particular 'coherence' claim, 'logic' being merely one such exercise. And you appear to be using 'truth' in an absolutist sense which for me begs the question of dubious status of any 'absolute' including 'God'.
IMO, debates about 'existence of God' are futile. As an atheist, the 'God concept' has no utility for me, whereas for believers it does. As a pragmatist any concept stands or falls on the basis of its utility. Hence I'm quite happy with 'God's existence' for believers provided that belief doesn't impinge on my well being. Atheists who engage in debate on the basis of 'evidence' or 'logic' are wasting their time since 'evidence' lies in the eye of the beholder, and 'logic' has limited applicability even in physics.
Timeless things should be able to exist without an explanation (as a brute fact). I believe the first cause is of this nature. Asking for an explanation is like asking what engine size an elephant has; the first cause simply does not have a 'why' property.
Quoting Dfpolis
So there must be a wider (timeless) container that contains God and the cosmos. The wider container cannot just be 'nothingness' - nothing can exist in nothing - no dimensions. It must be something, and if it is something, then it is finite (infinity has the property ?+1=? which implies it can be changed without being changed which is a straight contradiction).
But your definition of infinite seems to be omnipotence which I think is defined as ability to achieve anything possible. God must clearly be benevolent, so how do you account for the problem of evil? Having a deist view of God myself, the problem of evil is simply not relevant; the universe is a good as God could make it which is not perfect. It seems obvious to me that a first cause must exist. Omnipotence complicates logical / scientific justifications unnecessarily.
I think you're considering the wrong realm of discourse. As metamathematical proofs do not belong to mathematics, so metaphysical proofs do not belong to physics. So progress (or lack of progress) toward a physical ToE is entirely irrelevant.
I think that Godel's work has little to say about a ToE, because the method of physics is not the method of mathematics. Physics is not built on a closed axiomatic foundation, but an open experiential foundation. That does not make a ToE possible, but it does make the analogy with mathematics highly questionable.
Quoting alcontali
Again, you are confusing methodologies. Natural science uses the hypothetico-deductive method, while metaphysical proofs often use strict deduction. We can know with certitude that finite beings exist, that there is change and other facts which provide an adequate foundation for sound metaphysical conclusions.
Quoting alcontali
If by this, you mean its historical origin, this is a standard Aristotelian-Thomistic position. Nothing in my OP depends on the detailed history of the cosmos, and nothing in it draws any conclusions about its historical origin. So, while I disagree with your premise, I agree with your conclusion.
Quoting alcontali
"Not proven." You've done a lot of hand waving, but provided little evidence-based argument. In fact, your entire line of thought seems self-contradictory. On the one hand, you claim we can prove nothing about reality, and, on the other hand, you seem to claim to have proven that we can prove nothing about reality -- which is proving something about reality.
Quoting alcontali
This shows a fundamental misunderstanding of the nature of knowledge as awareness of present intelligibility. Knowledge is new if previously unactualized intelligibility is actualized by awareness. Yes, what is new may have been implicit in existing knowledge, but that only means that it was intelligible, not that it was actually known.
Quoting alcontali
This is a complete non sequitur. Just because what we already know can be the basis of some new knowledge, does not mean that it can be the basis for all possible knowledge. New knowledge can come both from reflection on what we already know and from new types of experience, e.g. the kinds of observations and experiments that have informed science since antiquity.
Quoting alcontali
Let's consider the second incompleteness theorem, which rules out self-proofs of consistency. If we have a set of axioms that are not merely posited, but properly abstracted from reality, we do not need to prove that they are consistent, because no contradstictions can be instantiated in reality. That means that simultaneously instantiated axioms have to be mutually consistent. It is only if one restricts the knowledge base to an abstract system that there is a problem. Opening ourselves to reality can often resolve such problems.
Further, with respect to the first incompleteness theorem, while our axiom set may not allow us to prove that theorem is true, if it is true, it may be instantiated and if it is, we may be able to see and abstract it as new knowledge.
I suggest you read Roger Penrose, The Emperor's Mew Mind, in which he shows that human minds are able to solve uncomputable problems.
I'm talking about efficient causality or actualization, not final causality or purpose (we can discuss that later). Since you came to be, you need to have been actualized by something already operational. Since you continue to have your potential for further existence actualized, you need an operational on-going source of actualization.
I have not said that God is unexplained, but self-explaining.
Still. Where does god enter the picture? Just because something is not explained, (the finite to his self) AND assuming an explanation is possible, it does not necessarily follow that there is someone or something that can and will explain it.
THAT is the conjuring in your failed proof.
Dfpolis, your wording lends itself to all kinds of fallacies, this time I believe it's a strawman.
Alcontali claimed (I wasn't there, but I believe you) that we can prove nothing about reality
Alcontali SEEMED to have claimed (so he did not claim... you put words in his mouth, which he did not say, and you defeat his argument based on something he did not say... hence the strawman) to have proven (which he did not) that we can prove nothing about reality.
Therefore no contradiction exists, therefore your counter-argument is invalid.
Dfpolis, you are a shifty arguer. You remind me of somebody on another website, but he was not as lucid as you are.
This is actually not true. A lower-level movement can create a higher-level movement, and there need not be, there is no, actualization process.
Your counter-argument fails, Dfpolis.
Then your "proof" would be superfluous. And yet the only explanations I have ever come across are failed human explanations, including yours. Your appeal to intuition is a dodge and circular - God is only self-explaining to those to whom this is intuitively evident. I would assume that your infinite God could explain itself to everyone without your help!
With regard to your distinction between essence and existence, what is the essence of what is not?
How do you explain the claim that if a being exists, its explanation must exist? There is nothing self-evident about this claim. Science does not explain existence in toto. It explains some things in terms of others. That there is anything at all is not something that science explains. Your claim that an explanation means the fact(s) that make some state of affairs be as it is does not explain those fact(s). To claim that the fact(s) are self-explaining because without the fact(s) we can't explain anything does not show that the fact(s) exist. It may be that at some point we reach the limit of explanation.
If you think that you have not posited an unexplained God then you have failed to follow your own failed proof.
The terminology is confusing in this regard, because metamathematics is defined as a subdivision of mathematics, while metaphysics is defined as non-physics.
Metamathematics uses the same axiomatic method as mathematics. The reason for the meta is because the objects studied are mathematical theories themselves. It concerns axiomatic theories about other axiomatic theories.
Metaphysics does NOT use the same scientific method (of experimental testing) as physics. Hence, physics is a subdiscipline of science, but metaphysics is not.
Quoting Dfpolis
The ideal of the ToE is to discard the scientific method, i.e. experimental testing, and be able to do science using the axiomatic method, i.e. proving by axiomatic derivation. The reason why science is not axiomatic, is because the axiomatic base for physics is lacking.
Hence, science would like to be like mathematics, but does not have the instruments available to do so. Science and its method of experimental testing is therefore some kind of poor man's mathematics. Science does not use the scientific method because it wants to, but simply because the desired alternative, i.e. axiomatic provability, is not attainable.
Quoting Dfpolis
The ToE is exactly about replacing the scientific method by the axiomatic one. Stephen Hawking explores this possibility at length in his lecture, Gödel and the End of Physics.
About the ToE, i.e. the ultimate (mathematical) theory of the universe in terms of a finite number of principles (=axioms), Hawking said: [i]What is the relation between Godel’s theorem and whether we can formulate the theory of the universe in terms of a finite number of principles? One connection is obvious. According to the positivist philosophy of science, a physical theory is a mathematical model. So if there are mathematical results that can not be proved, there are physical problems that can not be predicted.
Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind.
[/i]
Hawking believed that the ToE is not attainable because of Gödel's incompleteness theorems.
Quoting Dfpolis
Well, the ToE is exactly about replacing the one by the other, and the very reasons why this is not possible. In the discourse on the ToE, the confusion is simply deliberate.
Quoting Dfpolis
This impossibility does not prove anything about the real world, but about the relationship between us and the real world. It just means that we do not have access to a copy of the axioms from which the real world has been/is being constructed.
Quoting Dfpolis
The nature of knowledge as a justified (true) belief, JtB, requires that it has the shape of an arrow. If Q can be justified from P, then Q is knowledge. Having access to Q is insufficient. It is not knowledge, until the necessity of the arrow, i.e. the justification, has been demonstrated.
You consider Q to be knowledge in and of itself. That is contrary to the Platonic definition, i.e. JtB, which places knowledge in the arrow between P and Q. If knowledge cannot be written in arrow format, P=>Q, then it is not knowledge. In that case, Q is merely a conjecture.
Quoting Dfpolis
Well, this is exactly what Gödel tries to achieve in his incompleteness theorems. He maps encoded knowledge statements onto numbers, and their justification, i.e. proof, onto other numbers. Then, he investigates if he could enumerate all numbers that constitute formally valid language and verify if it has a corresponding number representing proof.
The simplest way to figure out if it could work, is to try to solve Turing's halting problem by enumerating all possible programs, and verify if they actually halt, i.e. if their computation stops:
Assume that we have a consistent and complete axiomatization of all true first-order logic statements about natural numbers. Then we can build an algorithm that enumerates all these statements. This means that there is an algorithm N(n) that, given a natural number n, computes a true first-order logic statement about natural numbers such that, for all the true statements, there is at least one n such that N(n) yields that statement.
We already know that such procedure cannot exist. Therefore, if Gödel's procedure exists, then it would solve Turing's Halting problem too. That is exactly what is not possible. Hence Gödel's procedure cannot possibly exist. In other words, even though you can represent all knowledge theorems as numbers, you cannot just enumerate all possible numbers to discover all possible knowledge.
Quoting Dfpolis
That is a very constructivist remark (constructivism).
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists.
[i]Traditionally, some mathematicians have been suspicious, if not antagonistic, towards mathematical constructivism, largely because of limitations they believed it to pose for constructive analysis. These views were forcefully expressed by David Hilbert in 1928, when he wrote in Grundlagen der Mathematik [...]
Even though most mathematicians do not accept the constructivist's thesis that only mathematics done based on constructive methods is sound, constructive methods are increasingly of interest on non-ideological grounds.[/i]
Constructivism is a long debate. To cut a long story short, I consider constructivism to be heretical.
I assume that the book is copyrighted, but I have still found a summary.
Gödel's procedure is actually just a special case, i.e. merely an example, of the fact that human minds are able to solve uncomputable problems. Gödel proves that there is no knowable procedure possible to discover new knowledge. Still, humanity obviously did it. So, yes, just the discovery of new knowledge is already one such uncomputable problem.
In other words, it will indeed never be possible to explain (as in knowledge) why humanity has managed to discover its existing stock of knowledge. If the human brain were just some kind of biological computer, it would not have been possible at all.
Furthermore, there is something in that human brain that allows us to decide the otherwise (computationally) undecidable problem whether God exists or not. At the same time, there is absolutely no input that you could ever feed to a computer, short of the undiscoverable ToE (Theory of Everything) that will allow it to decide this question.
I object to your claim that "explanation must exist". First, I'll note that this contradicts your definition of existence (" Existence adds a new note of comprehension: that the thing we are talking about can act in reality"): an "explanation" cannot act, and therefore explanations don't exist. Explanations "exist" (in a broadened sense of "exist") in minds, but only after theory has advanced to do so, and theory depends on the prior existence of minds that are capable of articulating it. The universe operated without existing explanations for quite a long time (and we obviously don't understand every aspect of material reality even now). I expect you're actually referring to the fact that mind-independent laws of nature exist, rather than semantic/mathematical descriptions of these laws. However, this can't suit your argument: laws of nature exist, but this provides no grounds for extrapolating beyond the universe (i.e. the totality of material reality) as you're trying to do. Everything within the universe is causally connected to everything else; it is these causal connections that constitute the laws of nature. But the existence of these intra-universe causal connections does not imply there is a causal connection to something external to the universe - there's no basis for assuming that to be the case.
.
If you're saying that unlimited being has free will, I agree, but having free will does not preclude causal efficacy. Nor does the prior co-possibility of contrary states preclude the actualization of either possibility. Power need not be actualized to be power. For example, I may choose to go to the store or not, but if I choose to go to the store, I am the agent effecting my going to the store -- even though it was in my power to choose not to go.
You need more far more argument to show that that a free-willed being can't be causally effective. All you have actually shown is that God must have free will to be truly infinite.
I hope that you are not wasting my time, but have a sincere inability to make the distinction between what a thing is and that it is. If you can't see that what a human is does not make it exist, I can see that following the OP would be difficult. As I do not see how to overcome that difficulty, there is no point in our continuing.
Thank you for your consideration.
Yes, I know that it is because of the placement of Aristotle's work on first philosophy after his work on nature; nonetheless, there was a reason for the placement, viz. because the Metaphysics examines issues fundamental to, but outside of the scope of, the Physics -- just as metamathematics does with math.
I appreciate the thought you and other commenters are expending on my post.
No... that's not really it. Although I do agree that -
Quoting Dfpolis
- at least as you have defined your terms for the purposes of this proof. But that wasn't really my point.
My point was purely and simply that completely unlimited being, by which you seem to mean completely unlimited capacity to do, cannot be the fact that makes some state of affairs be as it is.
It is logically incapable of being that fact because it is incapable of rendering any specific state of affairs necessary. Or perhaps to make things more concrete, I could say that it is incapable of rendering any specific state of affairs inevitable.
That's because completely unlimited being as you define it could equally well lead to any other state of affairs. Therefore it does not "explain" - in any sense of the word - any specific state of affairs.
So if you ask "Why did completely unlimited being produce this state of affairs and not a different one?" you will never have an answer.
Never.
It's unexplained - again, in any sense of the word.
Either there is no explanation - the LORD thy God is a capricious SOV - or there is some other explanation. Those are your only choices.
I see "truth" not as an absolute, univocal term, but as analogously predicated. Following Isaac be Israel and Aquinas, I see truth as the approach to equality (adaequatio) between intellect and reality. This leads me to reflect on how near an approach need be. I key my response off the English cognate "adequate." What is adequate to the needs of one realm of discourse may be entirely inadequate in another. Still, respect for truth is due because it is a means of human self-realization.
I see logic as the art and science of correct thinking, where by "correct" I mean truth-preserving, not power preserving. So logic is not merely one exercise among many, but an indispensable means of dealing with reality -- and even more so in an era in which POTUS has told over 10,000 public lies since coming to office. Those who attack and belittle truth support, knowingly or ignorantly, the atrocities that such lies minimize.
So, while you are free to proceed irrationally, I choose to proceed with the greatest respect for truth, evidence and the kind of thinking that preserves them.
I might as well admit that I don't know enough about this topic to have an intelligent opinion of my own. But my understanding - based solely on the pronouncements of others - is that it's not quite that straightforward.
The intro and section 1 of this article are quite readable and on point:
https://plato.stanford.edu/entries/metaphysics/
From section 2 onwards it descends into one of the worst pieces of explanatory writing I have ever had the misfortune of attempting to read, but... that's already been discussed on another thread.
Oh, PS
Speaking only for myself, you're welcome. I quite enjoyed it. Though I may have to bow out of the discussion. As I was saying on yet another thread, this forum has the capacity to eat pretty much ALL of your time and energy if you let it. Since I arrived I've been struggling to find the right forum-life balance. :meh:
"Should"? Why? What is the force of this "should"? And, what is the error of my analysis?
Quoting Devans99
On what do you base this admitted belief?
The way I see it, I've presented a sound argument that shows the existence of an infinite, self explaining being. You object that you do not believe my conclusions. I give arguments you do not reply to. That is your privilege, but its not very persuasive.
Quoting Devans99
It's a category error to think an infinite being can be confined to a location. If a being is contained, it can act in the container, but not outside of it, and so is limited.
Quoting Devans99
This argument fails because we are not speaking of numerical but ontological infinity -- the capacity to do any possible act. An infinite being cannot change because an infinite being is a necessary being, and whatever is necessary cannot possibly be different.
Quoting Devans99
I agree that it is a real problem, but having a problem does not mean that the proof is unsound. I think the problem is that what might be good for other things need not be good for humans. If dinosaurs could think they would have thought the asteroid that ended their era was evil, but it was good for us.
The question I have is, if language objects have nothing to do with 'the physical world', then how come instructions, specifications, formulas, recipes, architectural designs, programming languages, and many other symbolic systems actually produce real changes in the physical world? How can we communicate information about the world using language, if language has 'nothing to do' with the 'real world'? Because we plainly do communicate information and produce changes.
I agree that ideas are not physical, but I rather prefer a dualist interpretation, whereby humans are able to interface between the Platonic realm of abstractions, and actual objects, to produce neat things like:
Say that L is the set of all possible expressions in language, then Lr is a subset of L in which the language expressions seek to be isomorphic with the real, physical world R.
I agree that:
Lr ? L and Lr ? R
Let's call Lr "the map" and R "the territory".
One major problem is, of course, that R is actually unknown. As Immanuel Kant famously quipped: Das Ding an sich ist ein Unbekänntes. (The thing in itself is an unknown).
We often use Lr and R interchangeably, and that is often no problem, but in the cases in which it is a problem, we may soon run into an abstraction leak, because ultimately the map is not the territory:
The map–territory relation describes the relationship between an object and a representation of that object, as in the relation between a geographical territory and a map of it. Polish-American scientist and philosopher Alfred Korzybski remarked that "the map is not the territory" and that "the word is not the thing", encapsulating his view that an abstraction derived from something, or a reaction to it, is not the thing itself. Korzybski held that many people do confuse maps with territories, that is, confuse models of reality with reality itself. The relationship has also been expressed in other terms, such as Alan Watts's "The menu is not the meal."
As coined by Joel Spolsky, the Law of Leaky Abstractions states:
All non-trivial abstractions, to some degree, are leaky.
Not only do abstract models not represent reality at all, unless you painstakingly expend effort to maintain such isomorphism, they do not even need to do so, in order to be useful. Mathematical axiomatizations, for example, never represent reality, while theorems must not be considered to be mathematical unless they belong to such axiomatization. They could be something else, however; such as scientific, for example.
In other words, a theorem can be mathematical or can be scientific, but can never be both at the same time.
There must be at least one timeless thing without at explanation and it must be capable of acting as a causal agent - the pyramid of causality within time requires a first cause.
So I think the difference of opinion is that I have God as a timeless brute fact which clashes with your premise 4 - you have God as a 'self explaining being'. I also have God as a non-omnipotent being.
I do not understand the concept of 'self explaining being' and I am not sure it hangs together logically.
As I mentioned before, nothing can exist 'forever' in time so the concept of timelessness seems to be required, which leads to the existence of brute facts.
Quoting Dfpolis
To be a being is to be composed of information - otherwise we have null and void. That information must have a representation. That requires some form of container. Maybe not a physical container as we understand it, but a container none the less and containers are finite. A belief in spiritualism does not escape this requirement (unless we also dispense with common sense - assume that nothing can be something).
Quoting Dfpolis
How is it possible to do anything possible and not be changed by the doing? I can only think of future real eternalism - God would have done everything already (in a sense) so would be completely static from the perspective of 4D spacetime. Maybe this is the way things are but it is a lot to swallow (no free will for example).
I must admit this is a challenge for my point of view too - how can a timeless being effect change? Possibly essential causality might help? Maybe change is possible without time. Maybe God has something like time within him (it cannot be without him - cannot exist 'always' in any form of time).
Quoting Dfpolis
There are things in the universe that are just plain bad for all intelligent beings. Black holes for example are purely destructive. But they are a necessary consequence of gravity which is necessary for life. I would have thought an unlimited God would have gravity and also somehow intercede to prevent the negative consequences?
If a proof leads to a conclusion that clashes with reality, one has to question the proof. One or more of these has to give:
- Omnipotence
- Omnipresence
- Omnibenevolence
Personally I belief none of the 3 hold - leading to a deistic God - which is much easier concept to prove and defend.
I think your proof is an excellent effort but you are trying to prove something that is impossible.
I think you are confusing the two meanings (verbal and effective) of "explanation" I distinguished. the proof deals with what makes things so, not with our articulation fo what makes things so. Things work in a certain way whether or not anyone tells us they do.
Quoting god must be atheist
It is not just that he claimed we can prove nothing, but that he did so in the context of proof theory, which is a highly logical structure. I acknowledged that he provided no actual proof, but the claim being made in that context, and with appeals to Godel's incompleteness theorems, strongly hinted at the existence of a proof. My post was designed to elicone if he had one. It was intended to be a challenge awaiting response, not the final word.
Quoting god must be atheist
Then no potential ever becomes actualized and there is no change,
Your conclusion is a non-sequiteur, and it does logically not follow. You said something completely incongruent to my statement. You made an absolutely false claim because it does not pertain to my claim.
My criticism stands both ways. Both if you consider explanation verbal, and if you consider explanation effective.
You more and more resemble someone I know from another site. He makes claims out of the blue, and he says it so that it is hard to notice he is saying falsehoods.
The Euthyphro problem in a nutshell here is that either God could do things that are "logically impossible" if He were to choose to do so, or logic is primary/prior to God, who must obey it.
Quoting Dfpolis
You avoid Aristotle's causal language but do not side-step the problem. What distinction do you make between the fact(s) and some state of affairs? You said:
Quoting Dfpolis
Your argument is that there are these facts because of some other fact(s). There are finite beings because there is an infinite being, that the infinite being is the "explanation" of finite beings, and that the infinite being needs no explanation because it is infinite. In Scholastic terms you make the distinction between contingent beings and a necessary being. A first cause. An uncaused cause.
The same tired old argument.
This is silly, As most people are unaware that what God is entails that God is, it is quite worthwhile explaining this fact.
Quoting Fooloso4
My actual claim is quite the opposite. It is that a proof is possible because most people know, via ordinary experiential means, all that they need to know to prove that God exists, but lack the extraordinary intuitive insight to see the connections. Fortunately some (e.g. Aristotle, ibn Sina, and Aquinas) have had the insight to point the way.
Quoting Fooloso4
It does not help you case to equivocate on the two meanings of "explanation" (verbal vs effective) that I carefully distinguished. A careful reading of my OP may refresh your memory.
Quoting Fooloso4
As I explain earlier, essences specify possible acts, while existence makes powers operational. Knowing what a thing is, is convertible with knowing what it can do. But, knowing what a thing could do if it existed is not the same as knowing that a thing actually exists. So, essence and existence are distinct concepts.
Quoting Fooloso4
I already answered this in a response to Echarmion on p.3, giving three reasons. I did not claim it was self-evident, but a requirement of scientific thought.
Quoting Fooloso4
Agreed, That is why we need to study metaphysics.
Quoting Fooloso4
Definitions of terms are only intended to explain how the relevant terms are used.
Quoting Fooloso4
If there are facts with no underlying dynamics/explanations ("brute facts" that "just are"), then the logic of science fails. Once you allow exceptions to avoid a consequence you do not like, a principle is no longer universal, and there is no reason to think it applies when you like its consequences. If the principle is not universal, any scientific observation may be a "brute fact" with no underlying dynamics -- and not evidence confirming or falsifying a hypothesis. Thus, denying the universality of the principle converts science from an objective search for truth into an enterprise ruled by subjective whim.
I know that this is a practical, not a theoretical argument, but it shows the grave implications of your line of thought. Since it is only practical, I gave two theoretical justifications in my response to Echarmion,
A clear similarity that you both use is to hide behind jargon when cornered. There are other similarities, such as not getting emotional. Everyone gets emotional when under a lot of fire. Except BOTs and those participants who 1. have nothing at stake because 2. they know themselves they are not putting forth their own sweet convictions although 3. they don't play the devil's advocate either, but instead 4. are trolling in haute vogue for whatever their reason is.
There must be an explanation for everything that is not a brute fact. Brute facts can only exist outside of time. So I assume the quantum system you refer to exists outside of time and is somehow responsible for the creation of time. What is the mechanism by which time is created? I doubt a dimension could be created by evolution of a quantum system. The start of time would seem a discontinuous, unnatural process.
I grant that they don't seem to exist WITHIN spacetime, but that doesn't necessarily have bearing on spacetime itself. Spacetime doesn't exist "within" spacetime, so our intra-universe observation/intuition doesn't apply.
Anything that exists within time must have a start. It is impossible to exist 'forever' in time - forever has no start. If something has no temporal start, then it has no start+1, start+2 and so by induction it does not exist. So a brute fact cannot exist in time. Everything in time is subject to causality and requires an explanation. Spacetime itself must also have an explanation.
The sort of thing that clearly has had a "start" are merely configurations of fundamental stuff. The fundamental stuff itself has no apparent "start", and I see no justification for believing it necessary had one.
Or we could consider the collision history of a particle to be represented by a temporal/causal infinite regress. Infinite regresses are impossible.
I'd also argue that time has a start so everything within time must have a start. If time did not have a start, we would have already passed through all possible states of the universe and some of those states must be equilibrium states - in which case we should still be in equilibrium - we are not.
Causality requires a brute fact to be the base of the pyramid of causality and brute facts are timeless - this is also strongly suggestive of time having a start.
No, mathematics has quantitative relations as its subject matter, and metamathematics has mathematics as its subject matter. the fact that it may use mathematical methods does not make it mathematics anymore than the fact that physics uses mathematical methods makes physics a branch of mathematics. Metaphysics deals with the foundational assumptions of physics, among other matters.
Quoting alcontali
This is simply false. There are many fields that are not physics, and most to not deal with metaphysical issues. What we now call "metaphysics" was called "first philosophy" by Aristotle because it deals with issues fundamental to all other areas of research, including physics.
Quoting alcontali
If you're restricting "science" to disciplines using the hypothetico-deductive method, metaphysics is not that sort of science. Neither are mathematics and metamathematics. Still, all three are sciences in the more traditional sense of rigorous systematic fields of study.
Quoting alcontali
As a physicist, I that is not my understanding of a ToE. A ToE is just like any other hypothetical construct in physics, but its targeted range of application spans all physical phenomena. It is absurd to think that any competent physicist would accept a proposed ToE absent rigorous experimental testing.
There are axiomatic formulations of a number of fields in physics, e.g. quantum theory and quantum field theory.
Quoting alcontali
I am not sure an axiomatic approach is the "desired alternative" in natural science. You'd need to make a case for that. It seems to me that many physics like the method of discovery they signed up for.
Quoting alcontali
I don't think that Hawking's view is widely shared. Sir Arthur Eddington tried a similar approach in the 30s and 40s, famously predicting that the fine structure constant was exactly 1/136, then exactly 1/137. (It is neither.)
Quoting alcontali
While it is not, let us assume that it is. It is still irrelevant as the subject matter of physics is the measurable behavior of nature (which has intrinsic uncertainties, even in the absence of quantum uncertainty), while metaphysics is concerned with being as being, which is not subject to the vagaries of measurement.
Quoting alcontali
While I'm happy to admit that knowledge is a subject-object relation, I do not see that the admission precludes proofs about reality.
Quoting alcontali
I am sorry, but I do not see nature as an axiomatic construct. Rather, I see it as a complex, intelligible whole from which we may abstract some universal truths. At the simplest level, we understand being well enough to see that (1) Whatever is, is, (2) that a putative reality must either be or not be, and (3) that nothing can be and not be at one and the same time in one and the same way. These ontological insights, informing our thought about reality, give us the logical principles of identity, excluded middle and non-contradiction. Thus, we are able to abstract principles of absolute certitude which can advance our inquiries.
Quoting alcontali
I reject the thesis that knowledge is any form of belief. To know is to be aware of present intelligibility, and is an act of intellect (awareness). To believe is to commit to the truth of some judgement, and commitment is an act of will, not intellect. If knowledge were a species of belief, we would necessarily be committed to the truth of anything we knew. Clearly, this is not the case. One can be certain that one cannot afford a purchase and buy it anyway, showing no commitment to the known truth. So, knowledge cannot be a form of belief.
Quoting alcontali
This, is true, but a non sequitur. Mathematical relations are possibly instantiated in nature, not assuredly instantiated. So, it is possible that we could deduce all actually instantiated relationships. The reason your conclusion is true is that we already know from nonlinear math in general (e.g the 3-body problem and chaos theory in particular (e.g. turbulence and neural processing) that there are predictive calculations we will never be able to carry out.
Still, I fail to see the relevance of this, as mathematics is not the basis of metaphysical thought. We know the consistency of metaphysical premises from the fact that they are instantiated in reality and one cannot instantiate a contradiction.
Quoting alcontali
This analysis precludes any knowledge, for it leads to an infinite regress (How do we know P?). It has been known to be errant since Aristotle examined the foundations of knowledge. We know when our neurophysical system presents intelligible contents to awareness (Aristotle's agent intellect). Then, the intelligibility of the encoded contents is converted to actual knowledge by an act of awareness. Thus, there is no need for an infinite regress of Ps and Qs. We know by being aware of presented contents. We judge by abstracting concepts from those contents and grasping relations between those concepts. We can then deduce further justified relations.
Quoting alcontali
I am not a Platonist. I counted 17 errors in Plato's epistemology pointed out by Aristotle in his Metaphysics.
Also, doxa in Plato means opinion, not belief. So JtB is not Plato's definition, but a modern misreading of the text.
Quoting alcontali
No. Godel was working in the context of Hilbert's program, which it effectively destroyed. Hilbert's model was one of a priori consistency, with no connection to empirical reality. Godel's work showed that this approach is doomed to failure. Aristotelian metaphysics, on the other hand, is built on a posteriori, empirical foundations. Its concepts are abstracted from sensory experience and its judgements result from analyzing such experience. Because the relationships it builds upon are abstracted from reality, which is necessarily self-consistent, they are guaranteed to be self-consistent.
Quoting alcontali
Yes, we do, but that is entirely irrelevant to the present discussion. Metaphysics does not even aspire to a physical description of the cosmos or a complete enumeration of all possible theorems in any axiomatic system. It deals with being qua being, abstracting away from both quantifiability and the detailed laws of nature.
Quoting alcontali
So?
Quoting alcontali
That is not what I am saying. I am speaking of the epistemological basis of noetic systems, not their rules of application. Also, I do not consider philosophy to be a closed axiomatic system, but an open one -- always open to new, experientially based knowledge.
Quoting alcontali
Please don't burn me!
Quoting alcontali
He does no such thing. He only considers closed, formal systems, not empirically open systems. If your claim were true, we would never have made progress in any science.
Quoting alcontali
Your conclusion is Penrose's point. However, I think we can explain how we come to know if we do not confine ourselves to a priori, axiomatic ways of thinking, but work out the implications of such facts as those we are discussing -- which is a point i develop at length in my book.
Quoting alcontali
I never thought there was. It is easy to show that the mind cannot be purely neurophysical. The neural representation of seeing a ball and the retina being modified by the image of a ball are identical, but their conceptual representations are not.
Matter and energy (which are interchangeable) are just configurations of fundamental stuff. The intuition (which is not a proof) is rooted in our experiences with configurations of stuff having a "start." This leads to the conclusion there is a past infinite series of configurations (every configuration "started", having been caused by a prior configuration), but even so - this doesn't entail a beginning for the fundamental stuff itself - just a beginning for any particular configuration.
The 'fundamental stuff' must of had a start in time. Else how did it come about? A quanta of energy remains a quanta of energy even if its form can change. So that quanta requires a start in time - 'always' existing is not the answer because that explicitly rules it out from starting to exist - leaving only wishful thinking to explain its existence.
The situation with space is analogous - think about an object with no spacial start point(s) - it would be nothing. Time works like space - a quanta of energy with no temporal start does not exist - it would be exactly analogous to an object in space with no spacial start. Its worldline in spacetime would be length zero.
Quoting Relativist
That leads to a causal/temporal infinite regress - which is impossible - for example: imagine a pool table. The cue hits the white ball. The white ball hits the black ball. The black goes in the pocket. Would the black ball go in if the cue did not hit the white? No - if we remove the first element in the time ordered regress, the rest of the regress disappears. So the first element is key - it defines the whole of the rest of a regress. If it is absent, as in the case of an infinite regress, then the regress does not exist - temporal/casual infinite regresses are impossible. So this chain of configurations requires a temporal start.
There is also impossibility of the actually infinite to consider. There are many arguments for the start of time (and the start of everything within it) based on this, here is one: imagine an ever-lasting time traveller travelling backwards in time whilst counting. From our perspective, the past is completed, so the time traveller must have counted every number if the past is infinite. But there is no largest number, so that is impossible - time must be finite.
Then there are other arguments like entropy (it is too low for infinite time), the measure problem, the BB, BGV theorem. All of these point to a start of time and a temporal start for all 'fundamental stuff' within time.
Why believe the fundamental stuff required a start in time? Your intuition about the need for a start is based on experience with configurations of the fundamental stuff, and when you extrapolate this to the fundamental itself, you commit the fallacy of composition.
Quanta are disturbances in a quantum field. Fields are fundamental (or at least, MORE fundamental), so quanta are just configurations of the more fundamental field.
I have given you arguments based both on the 'fundamental stuff' and its composition. If the fundamental stuff exists then its composition exists as well. So both basis are covered and I am not committing the fallacy of composition.
Also, It is not intuition; it is logic: things must first come into existence in order to exist - the alternative is just a belief in magic. You cannot have something like a particle existing as an infinitely long world line in spacetime with one end missing - it would be nothing. It would also be fundamentally partially defined - which means it is undefined - meaning it cannot exist. I have already given adequate proof of this IMO, all I can do is reiterate:
1. Assume a particle does not have a temporal start point (IE its existed ‘forever’)
2. If the particle does not have a start, then it cannot have a ‘next to start’ (because that would qualify as a start and 1 says that it does not have a start)
3. So particle does not have a next to start (by Modus Ponens on 1 and 2).
4. etc… for start+2, start+3…
5. Implies particle does not have middle
6. etc… unto start+? (now)
7. Implies particle does not have a (temporal) end
8. Implies particle never existed
Quoting Relativist
If you prefer to view it that way, then I would say those fields and the disturbances in them need a temporal start too. One configuration of the field is caused by a previous configuration of the field. If there is no first configuration of the field, there is no second configuration, no third, and by induction, no configurations at all.
And say we find X is actually fundamental (be it a string or whatever). X will have innate properties. That will require a temporal start at which these innate properties are acquired. Else X has no innate properties and X is null and void.
What is self-explaining (meaning 1) but cannot be explained (meaning 2) is a conjuring act. What is self-explaining but by which you cannot explain anything is empty. It amounts to saying that nothing in the universe can explain itself (1) and so there must be something else that explains what is in the universe, but can't be explained (2) and does not need explanation (1 and 2).
You claim that:
Quoting Dfpolis
All that is actual is possible, and our concern is with what is actual, that is, the universe as it is, was, and will be. Any imagined possible acts that are impossible within the universe have no bearing on the universe as it is.
In addition, we do not know the limit of what is possible within the universe. We cannot extrapolate from our limited acquaintance with limited things to a universe that is limited.
Quoting Dfpolis
The "logic of science" works quite well without recourse to an a priori first cause, or in your terms, without something that does not require an explanation because it is self-explaining.
Quoting Dfpolis
This is what you said:
Quoting Dfpolis
A thing cannot be what it is if it is not. Nothing is possible for what is not. Essence separate from existence is an abstract fantasy.
Number theory is no longer the dominant axiomatization in mathematics, and has not been for over a century (Dedekind-Peano). Nowadays, it is set theory that is considered the dominant axiomatization in mathematics (ZFC, aka, Zermelo-Fränkel-Choice).
In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.
Number theory is not even Turing-Complete, and hence, considered to be a relatively weak and incomplete axiomatization.
Besides set theory, there are numerous other Turing-complete axiomatizations such as function theory (lambda calculus), type theory, combinator theory, and so on. Every Turing-complete axiomatization is capable of expressing all possible knowledge in its associated language.
Numbers are just one type of building brick in mathematics. Sets, functions, types, combinators, and so on, are other types. You can trivially express numbers as sets, with e.g. Von Neumann ordinals:
0 = { }, 1 = {{ }}, 2 = {{ }, {{ }}}, 3 = {{ }, {{ }}, {{ }, {{ }}}}, and so on. Therefore, numbers are not a separate building brick in set theory -- that would be unnecessary -- but are just set expressions.
Hence, mathematics is not just about quantities, or numbers, which are not even essential in math. Mathematics is the set of all theorems that you can derive using the axiomatic method from any consistent axiomatic system. Number theory is merely one such axiomatization.
Mathematics, science, and history are not subject matters.
They are epistemic domains, i.e. the sets of knowledge statements -- with knowledge a justified (true) belief (JtB) -- that you can legitimately justify using their associated epistemic justification methods.
There is no mathematical subject matter, nor a scientific subject matter, nor a historical subject matter.
If you can justify a claim using one of these methods, then the claim legitimately belongs to that epistemic domain. For example, any claim that you can justify using the scientific method, is part of the science epistemic domain.
Furthermore, these epistemic domains exclude each other. It is not possible that a proposition can be justified by one epistemic method and also by another.
It's bad logic. If the past is finite, then something existed without "coming into existence" because that would entail a state prior to its existence, and this is logically impossible.
The following two quotes appear to reflect the same point: Quoting Devans99
Quoting Devans99
If there is fundamental stuff, it is metaphysically impossible for it not to exist (i.e. its existence is metaphysically necessary). A finite past implies the fundamental stuff was in an initial state (configuration) and perhaps this state could have been different (i.e. the specific state is contingent), but why think that it impossible for an initial, uncaused, contingent state to be impossible? You need to provide a justification for this that is not based on the subsequent temporal states and the composition fallacy.
The formal argument you gave is inconsistent with a finite past. A finite past implies an initial state, and I see no reason to think an initial state cannot have some contingent properties.
Quoting Devans99
I don't follow your argument. It appears you're treating particles as fundamental. What do you mean by "next to start"? An eternal particle doesn't start to exist (nor cease to exist) but it exists in contingent relations to other eternal particles that collectively configure into higher level objects. These higher level objects are what come into existence.
Quoting Devans99
Again, you just seem to be asserting (without support) that contingent things cannot exist uncaused. My response is the same: any initial state will necessarily have contingent properties. This is true even if there is a God. A God that exists in an initial state would have had had an uncaused plan for a universe in his mind - i.e., an intent to create THIS contingent universe rather than all other metaphysically possible universes.
Things came into existence/time at the point time started - either by creation ex nilhilo (see zero energy universe hypothesis) or because these things existed timelessly already (and they entered time at the start of time). This explains how matter/energy came about - your explanation of things existing 'forever' is impossible - everything in the universe would be null and void.
Quoting Relativist
I do not think an initial uncaused state is impossible - it is possible, but only possible outside of time. The justification is causality - everything must have a cause - unless it is beyond causality (IE beyond time).
Quoting Relativist
By 'next to start', I mean if we label the temporal start as t=0, then next to start is t=1. The argument then continues with induction out to infinity to establish that the particle cannot exist without a start.
Everything, including fundamental stuff, must be accounted for. IE it must either be created or exist permanently. As I've pointed out, it is impossible to exist permanently/'forever' in time - you simply cannot have a brute fact within time because causality (which is a feature of time) requires everything to have a both a prior and ultimate cause. So only possible conclusion is that at a timeless brute fact exists and it is the ultimate cause of everything in time/causality.
Quoting Relativist
I have excellent support for 'things in time cannot exist uncaused' - it is causality - everything in time must have both a prior and ultimate cause. Things that exist outside of time however can clearly be uncaused.
I am not sure precisely how the state of timelessness works beyond the fact that it required. Without timelessness, there are no brute facts. Without brute facts, there is nothing. God may exist within what is referred to as the 'eternal now' - all is simultaneous - causes do not precede effects. God's plan is part of God (a brute fact) so it can exist uncaused.
No, mathematics has quantitative relations as its subject matter, and metamathematics has mathematics as its subject matter. the fact that it may use mathematical methods does not make it mathematics anymore than the fact that physics uses mathematical methods makes physics a branch of mathematics. Metaphysics deals with the foundational assumptions of physics, among other matters.
Quoting alcontali
This is simply false. There are many fields that are not physics, and most to not deal with metaphysical issues. What we now call "metaphysics" was called "first philosophy" by Aristotle because it deals with issues fundamental to all other areas of research, including physics.
Quoting alcontali
If you're restricting "science" to disciplines using the hypothetico-deductive method, metaphysics is not that sort of science. Neither are mathematics and metamathematics. Still, all three are sciences in the more traditional sense of rigorous systematic fields of study.
Quoting alcontali
As a physicist, I that is not my understanding of a ToE. A ToE is just like any other hypothetical construct in physics, but its targeted range of application spans all physical phenomena. It is absurd to think that any competent physicist would accept a proposed ToE absent rigorous experimental testing.
There are axiomatic formulations of a number of fields in physics, e.g. quantum theory and quantum field theory.
Quoting alcontali
I am not sure an axiomatic approach is the "desired alternative" in natural science. You'd need to make a case for that. It seems to me that many physics like the method of discovery they signed up for.
Quoting alcontali
I don't think that Hawking's view is widely shared. Sir Arthur Eddington tried a similar approach in the 30s and 40s, famously predicting that the fine structure constant was exactly 1/136, then exactly 1/137. (It is neither.)
Quoting alcontali
While it is not, let us assume that it is. It is still irrelevant as the subject matter of physics is the measurable behavior of nature (which has intrinsic uncertainties, even in the absence of quantum uncertainty), while metaphysics is concerned with being as being, which is not subject to the vagaries of measurement.
Quoting alcontali
While I'm happy to admit that knowledge is a subject-object relation, I do not see that the admission precludes proofs about reality.
Quoting alcontali
I am sorry, but I do not see nature as an axiomatic construct. Rather, I see it as a complex, intelligible whole from which we may abstract some universal truths. At the simplest level, we understand being well enough to see that (1) Whatever is, is, (2) that a putative reality must either be or not be, and (3) that nothing can be and not be at one and the same time in one and the same way. These ontological insights, informing our thought about reality, give us the logical principles of identity, excluded middle and non-contradiction. Thus, we are able to abstract principles of absolute certitude which can advance our inquiries.
Quoting alcontali
I reject the thesis that knowledge is any form of belief. To know is to be aware of present intelligibility, and is an act of intellect (awareness). To believe is to commit to the truth of some judgement, and commitment is an act of will, not intellect. If knowledge were a species of belief, we would necessarily be committed to the truth of anything we knew. Clearly, this is not the case. One can be certain that one cannot afford a purchase and buy it anyway, showing no commitment to the known truth. So, knowledge cannot be a form of belief.
Quoting alcontali
This, is true, but a non sequitur. Mathematical relations are possibly instantiated in nature, not assuredly instantiated. So, it is possible that we could deduce all actually instantiated relationships. The reason your conclusion is true is that we already know from nonlinear math in general (e.g the 3-body problem and chaos theory in particular (e.g. turbulence and neural processing) that there are predictive calculations we will never be able to carry out.
Still, I fail to see the relevance of this, as mathematics is not the basis of metaphysical thought. We know the consistency of metaphysical premises from the fact that they are instantiated in reality and one cannot instantiate a contradiction.
Quoting alcontali
This analysis precludes any knowledge, for it leads to an infinite regress (How do we know P?). It has been known to be errant since Aristotle examined the foundations of knowledge. We know when our neurophysical system presents intelligible contents to awareness (Aristotle's agent intellect). Then, the intelligibility of the encoded contents is converted to actual knowledge by an act of awareness. Thus, there is no need for an infinite regress of Ps and Qs. We know by being aware of presented contents. We judge by abstracting concepts from those contents and grasping relations between those concepts. We can then deduce further justified relations.
Quoting alcontali
I am not a Platonist. I counted 17 errors in Plato's epistemology pointed out by Aristotle in his Metaphysics.
Also, doxa in Plato means opinion, not belief. So JtB is not Plato's definition, but a modern misreading of the text.
Quoting alcontali
No. Godel was working in the context of Hilbert's program, which it effectively destroyed. Hilbert's model was one of a priori consistency, with no connection to empirical reality. Godel's work showed that this approach is doomed to failure. Aristotelian metaphysics, on the other hand, is built on a posteriori, empirical foundations. Its concepts are abstracted from sensory experience and its judgements result from analyzing such experience. Because the relationships it builds upon are abstracted from reality, which is necessarily self-consistent, they are guaranteed to be self-consistent.
Quoting alcontali
Yes, we do, but that is entirely irrelevant to the present discussion. Metaphysics does not even aspire to a physical description of the cosmos or a complete enumeration of all possible theorems in any axiomatic system. It deals with being qua being, abstracting away from both quantifiability and the detailed laws of nature.
Quoting alcontali
So?
Quoting alcontali
That is not what I am saying. I am speaking of the epistemological basis of noetic systems, not their rules of application. Also, I do not consider philosophy to be a closed axiomatic system, but an open one -- always open to new, experientially based knowledge.
Quoting alcontali
Please don't burn me!
Quoting alcontali
He does no such thing. He only considers closed, formal systems, not empirically open systems. If your claim were true, we would never have made progress in any science.
Quoting alcontali
Your conclusion is Penrose's point. However, I think we can explain how we come to know if we do not confine ourselves to a priori, axiomatic ways of thinking, but work out the implications of such facts as those we are discussing -- which is a point i develop at length in my book.
Quoting alcontali
I never thought there was. It is easy to show that the mind cannot be purely neurophysical. The neural representation of seeing a ball and the retina being modified by the image of a ball are identical, but their conceptual representations are not.
"Ex nihilo" = from nothing, implies a state of "nothingness" existed, a self-contradictory term ("nonexistence exists"). If x exists at all times, and the past is finite, then x did not "come into" existence - that would entail a prior existing state of affairs into which x appears, which is impossible because x exists at all times. Further, the scenario assumes x is fundamental to everything that exists - everything in existence is composed of x.
Quoting Devans99
What is your justification for believing something causally efficacious can exist outside of time, and can somehow reach into time and interact?
Quoting Devans99The fundamental stuff is necessary for all existence, since everything is composed of it. It therefore exists permanently. It can't have been caused, because all possible causal factors (like everything else in existence) are composed of this fundamental stuff. That's what it means to be fundamental. Your only optiob is to deny that there can exist some fubdamental stuff.
You have provided no justification for believing this.
I almost agree. Which is to say that I agree with some of your formulations, but not with others. Clearly, being capable of any possible act does not necessitate any specific act, because it is equally capable of a contrary act or no relevant act at all. That is why we agreed that an infinite being must have free will.
It further follows that any state of affairs it effects must be intrinsically contingent, not necessary. Thus, I agree that "it is incapable of rendering any specific state of affairs [intrinsically] necessary." I agree further that the mere existence of an infinite being does not logically imply the inevitability of any further state of affairs. That is why theologians in the Christian tradition, at least, consider creation a free act, not one necessitated by the nature of God.
I further agree that many, and specifically pagan neoplatonists such as Plotinus, have seen this as highly problematic, as they believed that the One, being intrinsically complete had no need to act outside of its own being.
The problem with this line of argument is that we know more than "there exists an infinite being." So our fact base is not confined to this alone. We also know that there are contingent beings, a whole universe full of them. This logically entails that the infinite being does, in fact, act outside of itself.
So, it is not necessary that the existence of infinite being logically (a priori) necessitate finite beings. They are logically necessitated a posteriori by our experience.
Further, infinite being's lack of logical necessity to act outside if itself, in no way precludes it from freely acting outside of itself, nor does it preclude it from being the agent effecting (the dynamical explanation of) such effects.
It has been my experience that most contemporary philosophers have a hearsay acquaintance with Aristotle.
I also know what you mean about time management. That is why I have been absent for some time. We will miss your reason.
I agree with your conclusion, but not your time-based reasoning.
Quoting Devans99
The problem with this is that if you allow one brute face, one exception to the need for adequate dynamics, one thing with no intelligible explanation, then there is no reason not to allow others -- and once you do that, your entire line of reasoning breaks down. If one arbitrary finite being can have no explanation why can't any arbitrary finite being have none, be a brute fact? So I see your reasoning self-refuting.
The genius of Aquinas's insight that God's essence is His existence is that it gives us an intelligible reason why God requires no extrinsic explanation.
Quoting Devans99
I see no reason to accept this definition. Information is the reduction of possibility, while every new existent makes more acts possible. I agree that finite beings have an intelligible/informative essence that specifies what they can do, but the essence of infinite being does not limit possibility, and so is utterly uninformative. (This is confirmed by trans-cultural reports of mystical experience -- see W. T. Stace's works.)
Common sense is based on the common experience of finite being and does not conform to reports of mystical experience.
Quoting Devans99
It is possible if the change terminates outside the agent. If an agent is fully actualized intrinsically, it has no unactualized intrinsic potency and so cannot change intrinsically. That does not preclude acts terminating extrinsically.
Quoting Devans99
There seems to be a black hole at the center of each galaxy, hinting that they may be essential to the formation of galaxies and the possibility of life.
Quoting Devans99
I've rebutted many such arguments in my book. If you have a new one, please state it.
Peace, Dennis
Yes, sorry, I should have been more specific. The zero energy universe hypothesis (which I don't necessarily buy) has some sort of 'seed' causing a chain reaction that then generates the rest of the matter/energy in the universe in exchange for negative gravitational energy. So I agree something permanent must exist (at least a seed, maybe all matter/energy if the hypothesis does not hold). But permanent existence is only possible outside of time so whatever existed permanently has its origin outside of time.
Quoting Relativist
There is no other option; the start of time need a timeless cause:
- I gave several justifications for the start of time above. You did not respond to my argument regarding gravitational equilibrium which I feel is particularly strong.
- A second instance of time causing our time leads to an infinite regress of nested times - which is impossible - there must be something timeless - a brute fact - as the root cause.
Quoting Relativist
I am saying that the fundamental stuff must of originated outside of time because of the requirement for things in time to have a start, IE: 'It can't be X if it never started X' - substitute any action for X and the statement is always true: counting, walking, sitting, spinning, vibrating (eg a string), existing.
The BB is consistent with this view of matter/energy coming into time at the start of time.
Quoting Relativist
I feel I have justified that permanent existence within time is impossible. Here is another justification:
1. A system has a state (be it a particle or a universe)
2. The state is determined by the previous state
3. If it existed forever in time, there is no initial state
4. So all the states of the system are undetermined (because there is no initial state to make any of the other states 'real' - they form an endless chain of undetermined states)
An example using a pool analogy: Imagine a frictionless perfect pool table. The balls are all wizzing around. We know they cannot have been wizzing around eternally - we can infer an initial state of the white being set in motion by the player. If that initial state did not exist, then there would be no motion (and no balls either - the balls are part of the initial state within time).
Physics does not use the axiomatic "method". Physics uses mathematical formalisms to maintain consistency in its theories, but has actually nothing to do with mathematics. Maybe I did not express myself clearly. With the term "method", I meant "epistemic method", i.e. knowledge-justification method, as in axiomatic "method", scientific "method", and historical "method". I did not mean algebra or mere symbol manipulation. It was an epistemic concern only.
Quoting Dfpolis
Well, we will have to agree to disagree here.
Mathematics is not (Dedekind-Peano) number theory, which is no longer the dominant axiomatization nowadays. Contemporary mathematics defaults to Zermelo-Fränkel-Choice (ZFC) set theory as its dominant axiomatic context. The switch dates back to 1905. So, this has been the case for over a century now.
Quoting Dfpolis
Metaphysics does not establish the epistemic method for any area or research, including physics. It is epistemology that does that job.
Mathematics is what you can justify using the axiomatic method, science using the scientific method, and history using the historical method.
That is not a metaphysical but epistemic concern.
Quoting Dfpolis
According to Karl Popper's 1963 "Science as Falsification", which has in the meanwhile become the dominant view in the philosophy of science, science consists of the theories that you can justify by experimental testing. Mathematics never does that. Hence, mathematics is not science. Mathematics is not empirical and uses the axiomatic method instead. Therefore, it does not make sense to count mathematics under the nomer science. Furthermore, mathematics and science exclude each other. It is not possible to justify a theorem with both methods. It is the one or the other. Metamathematics is just a subdiscipline in mathematics, i.e. one particular axiomatization amongst many.
Quoting Dfpolis
According to the late Stephen Hawking, the problem will never even occur. According to him, there simply won't be anything to test.
Quoting Dfpolis
Well, the ToE is an axiomatic system, and physicists seem to dream of finding it. The late Stephen Hawking clearly did, but then he eventually concluded that it cannot be done.
Quoting Dfpolis
Well, I do not think that Hawking was infallible. He was just influential in his circles, and with a rare connection, say, even fascination from the general (layman) public. Especially because of his debilitating disease, people admired his tenacity, willpower and willingness to do some real work in spite.
Quoting Dfpolis
Well, metaphysics seems to have very little influence nowadays on the practice of physics. This is not true for metamathematics, which thoroughly dominates the discourse in mathematics.
Quoting Dfpolis
It is otherwise an epistemic view widely shared by lots of mathematicians and scientists. If it is provable, then it is not about the real world. If it is about the real world, then it will not be provable. It harks back to the definition of the term "proof" as the derivation path between a theorem and its underlying axioms. Without axioms, no "proof".
A mathematical proof is an inferential argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms, along with accepted rules of inference.
You can clearly see that this is not possible in science. Science is backed by experimental testing. So, science cannot provide us with such derivation path to something that does not even exist in science, i.e. axioms.
Quoting Dfpolis
Well, you will always be right, because according to Stephen Hawking, nobody will ever be able to supply you with the axiomatic construct that will prove you wrong. The ToE is just an unattainable pipe dream anyway.
Quoting Dfpolis
Well, these "truths" -- I would rather say experimentally-tested "theories" -- have only been tested at best against observations in the visible part of the universe. I do not see how it would be possible to justify with observations anything about the non-visible part of the universe. Hence, it is very local knowledge, the visible part of the universe being deemed just a small fraction of the complete universe, most of which is merely being conjectured about.
Quoting Dfpolis
Well, there seem to be physics theories that do not abide by this, such as Schrödinger's cat and the entire concept of entanglement.
But then again, these theories are too physical-world to my taste. That is why I do not know particularly much about them. I personally prefer the abstract, Platonic worlds of mathematics, for which you only need pen and paper. In fact, I actually, actively avoid physics, because I do not want to end up needing a gigantic particle accelerator or anything of the sort.
Quoting Dfpolis
The mainstream view is that knowledge is a justified (true) belief:
Justified true belief is a definition of knowledge that gained approval during the Enlightenment, 'justified' standing in contrast to 'revealed'. There have been attempts to trace it back to Plato and his dialogues.
Quoting Dfpolis
P does not need to be knowledge. For example, axioms are not knowledge, because they are not justified. Therefore, there is no infinite regress in axiomatic knowledge. There is no infinite regress in scientific knowledge, because the final justification is provided by experimental test reports, which are historical knowledge, and justified by the historical method (Did they really take place?).
Quoting Dfpolis
I agree. It is obviously not. Otherwise, it would be mathematics. Still, you have to start somewhere. It will initially, and possibly even never, be possible to turn a philosophical idea into a rigorous system.
Quoting Dfpolis
Yes, of course. However, with access to the ToE -- which will never happen -- the distinction between axiomatic and empirical would disappear. Furthermore, knowledge of science is not enough to discover new science. There is another ingredient than mere knowledge that is needed for such discovery.
Quoting Dfpolis
Agreed. If it were, it would not even work.
I responded as I did because I assumed that you were talking about a point I made about the actualization of potency. If your not talking about that, it's hard to see what you are driving at.
Let's go back to what you said.
Quoting god must be atheist
Lower level movements do not create higher level movements, they are the same movement thought of in two distinct ways. I can think of a whole as a whole, or I can think of a whole in terms of its parts, but my way of thinking about the whole is purely subjective and does not change the objective reality of the whole in any way. So, lower-level movements do not create higher-level movements.
You can also see this in terms of priority. Temporally, lower and higher level movements simultaneous, and so neither can be a temporally prior event leading to the other (an accidental cause). Logically, one think of wholes without thinking of decomposing them into parts, but one cannot think of parts without reference to the whole of which they are parts. So, wholes are logically prior to parts and high level changes to low level changes.
Even if we completely forget about the relation of wholes and parts, your argument proves nothing. Why? Because it admits that there are low-level changes, which are still changes -- still the actualization of a potential insofar as it is still in potency -- and the union of all the lower level potencies is the higher level potency.
If you say that there's no potential for the relevant change, that is equivalent to saying that there is no possibility of the relevant change, which denies experiential reality of observed change.
Now, what point are you trying to make?
Quoting god must be atheist
First, I did not assume that anything is unexplained effectively, so your premise ("Just because something is not explained") is not mine, and consequently your criticism does not apply to my argument.
Second, I did not assume "an [effective] explanation is possible," but showed that it is necessary. Again, you are criticizing an argument I did not make.
In my understanding, logic is consequent on the nature of being, and all being is traceable to God. So, logic is posterior, not prior, to God.
Right, so then God could presumably make anything He desired logically possible.
I do not see more than one brute fact as a problem; all that is required is a brute fact to act as the first cause for causality/time. It maybe that God and matter/energy are both brute facts and God injected the matter/energy into time with the BB. I cannot rule out the possibility of more than one timeless being - all I seek to justify is the cause of the universe - which I believe is the timeless being I refer to as God.
Quoting Dfpolis
I think we have a very different conception of what God is. I have a pseudo-materialist outlook on the world. God has to play by certain common sense axioms - he exists in reality (possibly an unfamiliar / non-material reality) and reality follows certain common sense axioms - so must God. I cannot imagine anything that is not composed of information.
I think we are not likely to agree on this or the remaining points.
But thanks for the discussion and peace to you also!
You might think it genius but as you said in the OP, thinking something does not make it exist. So too, for the same reason, one cannot define something into existence . Aristotle saw that the cause of being cannot be a being. Aquinas, in line with the belief in a Creator, avoids the problem by simply declaring that there is an uncaused being that is the cause of other beings. A being that is (existence) because to be is what it is (essence).
You are attempting to put old wine that has turned to vinegar into new bottles. Once again:
Quoting Fooloso4
You have some particular (unprovable) ontology in mind, and dismissing other possibilities because they are inconsistent with the (unprovable) assumptions of your ontology. For example, the notion that something with causal efficacy can exist "outside of time" is pure assumption - there's no basis for thinking such a thing can exist. If such a thing can exist, then your scenario is fine. But if it can't exist, then we're stuck with the sort of scenario I've described - along with the assumptions it entails. We've been down this road before, so there's no point in going down it again. Thanks for the discussion.
I avoided "cause" because I'm not writing in ancient Greece. Modern philsophy ignores essential causality and takes "causality" to mean Kant's "time sequence by rule." as I am not speaking of temporally prior events, but of concurrent agency, I carefully avoided the term "cause." I am perfectley happy with either "fact" or "state" of affairs as long as no confussion arises.
Quoting Fooloso4
That is a complete misstatement of my position that everything that is, has some underlying dynamics/explanation. It you are going to criticize, criticize what I actually say.
Quoting Fooloso4
Thank you for illustrating why I did not use "cause" -- by misstating of my position.
Aquinas did not write in ancient Greece
Quoting Dfpolis
The point is you are using the term in two fundamentally different ways - (1) fact(s) that are not dependent (God/infinite being) and (2) all other facts which are dependent on (1).
Quoting Dfpolis
What you said is that God, i,e., the infinite being is self-explaining.
Quoting Dfpolis
How does your argument for a self-explaining God differ from Aquinas' first cause, an efficient cause, an uncaused cause?
Imagine an eternal god who has always been counting - what number would he be on? Forever has no start, so the god could not have even started counting - so the lack of an initial state invalidates all subsequent states - 'forever' is impossible.
I have no idea what you're talking about. I said precisely how God is self-explaining. Please read what I posted.
Quoting Fooloso4
First, you are begging the question by assuming that all reality is part of the universe. Most cosmologists, even though they are naturalists, believe that there may be other universes, with other laws (the multiverse). Second, you are confusing logical possibility with physical possibility. The laws of nature restrict what is physically possible, but they do not restrict what is logically possible. Third, things that happened in the past are possible in virtue of having actually happened, but they are not actual because they no longer exist.
Quoting Fooloso4
Yes, we can. Because whatever changes has to be limited. If it were not, it would be all that it could be, and so there would be nothing for it to change into.
It is really quite simple. You have not provided an explanation (2) for the existence of God, you simply assert that God is self-explaining (1). You are claiming that an explanation (1) is:
Quoting Dfpolis
and that in the case of God:
Quoting Dfpolis
and:
Quoting Dfpolis
This is not an explanation (2) it is an unsubstantiated claim, creatio ex nihilo, of an infinite being made to explain (2) what cannot be explained - being. It amounts to saying it must be because otherwise there is no explanation for what is (2).
Quoting Dfpolis
The question is whether the universe requires God. It seems evident to me that what is part of the universe is actual. If you are going to claim that there is something that is not that is the explanation for what is in the universe then the burden is on you to demonstrate its existence.
Quoting Dfpolis
Is the multiverse infinite in the sense you are using the term? If not, then the same problem holds - it would not be self-explanatory. If the multiple universes are separate then the existence of one has no effect on the others.
Quoting Dfpolis
And what do you think follows from that? If something is logically possible that does not mean that it is actual or has any bearing on what is actual.
Quoting Dfpolis
This is muddled. If something were not possible it would not have happened. There are things that are possible that are not actual, but what is actual cannot be impossible.
Quoting Dfpolis
The inability to change is a limit.
I did not confine my definition to number theory, which does not include geometry and its subdisciplines, topology, analysis, calculus, distribution theory, chaos theory, etc., etc.
Still, a sincere thank you for stating the role of set theory in the minds of contemporary mathematicians. I knew many in grad school and discussed these topics, so I should have included set-theoretic relations in my description of the subject matter of mathematics (defined as what mathematicians study).
If you take mathematics to mean what mathematicians study, then you can say metamathematics is part of mathematics. If you take the position that fields of study are defined by what is studied (their material object) and the aspect under which it is studied (their formal object), then metamathematics is not mathematics, even if we include set theory in mathematics.
It does not matter that one can represent meta-mathematical relations mathematically, for if it did, mathematical physics would be subalterned to mathematics, and it is not. The use of mathematical representations is a tool, and tools do not define the subject matter they are used on. The material object of mathematical physics is the dynamics of natural processes, and its formal object is being viewed from a mathematical perspective. Similarly, the material object of metamathematics is the fundamental structure of mathematics and its formal object is being viewed from a mathematical perspective. Who undertakes such studies, and whether they also study other things from other perspectives is completely immaterial.
Quoting alcontali
This is a sweeping, and over-reaching, claim. How would one express, without circularity that lavender is not orchid? Of course, one could say that L ? O, but will not adequately express this fact to one who does not already know what lavender and orchid are. Or did you mean that one can [inadequately] express all possible knowledge in a Turing-complete axiomatization's associated language?
This is not a fatuous observation, but points to critical issues. Natural languages are not purely formal systems. They are not merely sign-sets following syntactic rules. In order to function they need the power to instantiate meaning in other minds, and to do so they need reference, which relates signs to certain aspects of reality. Formal languages lack determinant reference, and in order to provide such reference, one must employ natural language. I have yet to see a mathematical proof not contextualized by natural language text.
So, your claim is either false, of vacuous. (It is vacuous if you mean that what is wholly indeterminate can receive any determination.)
Quoting alcontali
Did I say they were????
Quoting alcontali
If you want to say "epistemic domains" instead of "fields of study," be my guest. They are not, however sets of knowledge statements. Why? Because:
(1) Sets are well-defined collections of distinct objects, while accepted science is indeterminate because it varies over time. Newtonian physics was unquestioned for centuries, but is now known to be inaccurate.
(2) The definition of a science cannot change with the discoveries it makes. When Aristotle, Archimedes, Jean Buridan and other early physicists applied mathematics to the study of natural processes they were as much physicists as those struggling today to find a theory of quantum gravity. Yet, in their day little of what we now accept was or could be justified. What defines a science is what is studied (its material object) and the approach to studying it (its formal object) -- not what is actually known at any time.
(3) Your definition suffers not only from indefiniteness, but from being closed. As sets have to be well-defined, they cannot adequately represent fields that are open to new data and theoretical revision.
Also, while I agree that scientific findings can be justified beliefs, in many cases we have no way to determine whether they are true in any absolute sense. So, your definition of knowledge cannot be applied to scientific findings in general.
Quoting alcontali
Unless you are willing to argue a case, this claim is to absurd to be worth rebutting.
Quoting alcontali
Why is that?
Quoting alcontali
Physics is not subalterned to math, but that does not mean it has nothing to do with math. (1) Many mathematical concepts were discovered as part of physics before being formalized by mathematics. For example, medieval physicists developed the concept of instantaneous velocity, which is the basis of the concept of a derivative. The first examples of chaos theory were discovered by physicists. Dirac's delta function gave rise to distribution theory. (These examples also show that same finding can be discovered by diverse methods -- rebutting your claim above.) (2) Routinely, the observable implications of physical theories are mathematically deduced.
Quoting alcontali
I do not see that there is an axiomatic method. There is deduction, which can be applied as much to deducing the consequences of axioms as those of hypotheses.
Axioms can be abstracted from reality, in which case abstraction is the method, or they can be hypothesized (like the parallel postulate or the axiom of choice), in which case we are dealing with an instance of the hypothetico-deductive method -- and one that it epistemically problematic, as unfalsifiable hypotheses are suspect. (Of course, we can confirm many consequences.)
Quoting alcontali
I did not say that metaphysics established the epistemic method for any area. I said "it deals with issues fundamental to all other areas of research." This means that it deals with foundational issues of logic and epistemology as well as physics.
Quoting alcontali
This is an absurd claim. How does the so-called "axiomatic method" justify its axioms? Clearly, it does not, for it takes them as given. Similarly, the scientific method takes takes observations and the logic involved in working out the implications of hypotheses as given, and provides no justification for either.
Quoting alcontali
You are equivocating. I said "science in the traditional sense," and you're discussing only sciences that use the hypothetico-deductive method. I have no problem with the concept of falsification in the context of the hypothetico-deductive method, but I hope we can agree that it is not the only method that can be applied to come to a rigorous systematic understanding. If it were, mathematics would not be scientific.
Quoting alcontali
This is obviously wrong. Newton did not develop fluxions in a rigorous, axiomatic way, but in a hypothetical way that was justified by its successful application to, and confirmation by, empirical findings. His empirically justified discovery was later "cleaned up" (axiomatically formalized) by mathematicians. The same is true of Dirac's discovery of the delta function and its later justification with the development of distribution theory. There are many other counterexamples I could cite.
Quoting alcontali
First, this doesn't rebut my point, but only makes the claim that it's counterfactual. Second, it is an argumentum ab auctoritate from an unreliable source. Hawking, despite many admirable traits, has been wrong on fundamental matters much more central to his area of expertise. (See Leonard Susskind , The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics.)
Quoting alcontali
While physics can be and has been axiomatized (e.g. quantum theory and quantum field theory), the axioms remain hypothetical, and so do not change the nature of the science. The justification for the axioms is that, so far, they seem to work. A ToE would be the same. Its axioms would not be deduced (or otherwise justified) on a priori grounds, but hypotheses that seem to work with respect to the available data.
Quoting alcontali
I agree. Still, what is rational and what is in vogue are rarely the same. E.g., the interpretation of quantum theory is plagued by irrational and manifestly false beliefs.
Quoting alcontali
So, a bowl that holds only one apple and one pear cannot be proven to hold two pieces of fruit? Or, if Jane is actual, we can't conclude that Jane must be possible? You really believe that? I see such claims as in the same category as Daniel Dennett consciously denying that he is conscious.
Quoting alcontali
Think logically, please! Scientists routinely assume statements to be true. Such assumed truths are called "hypotheses" (h) and they can yield conditional predictions (p) true about the real world, viz. h => p. Scientists also take observations to be true and deduce implicit facts from observed facts and "self-evident" "axioms."
Of course, no proposition is truly "self-evident." All truths derive from experience. It is just that some judgements can be seen to be universally true after a single experience.
Quoting alcontali
So, 2 objects and 2 more objects might not yield a total count of 4 objects outside the visible universe? Sehr interessiert!
To be continued...
Science is a growing collection of theories that can be justified by the scientific method. At any point in time it is a set, but over time it is a changing collection. I concede that sets are immutable. In fact, I only wanted to refer to the fact that scientific theories are enumerable.
Quoting Dfpolis
That is probably true for "a science" but not for "science", which is simply any proposition that can be justified by experimental testing.
Quoting Dfpolis
Yes, agreed. I do not think that knowledge is necessarily a "true" belief, with the term "true" as in the correspondence theory of truth. Knowledge as a "justified belief" should be sufficient.
Quoting Dfpolis
Math justifies by axiomatic derivation, while science is does that by experimental testing. Experimental testing always occurs in the real, physical world, of which we do not have the axioms. Therefore, we cannot axiomatically derive that what can be experimentally tested. The converse is also true. If a proposition is derived axiomatically from a set of axioms that construct an abstract, Platonic world, you cannot experimentally test it, because that would require the objects to be part of the real world and not the Platonic world in which they have been constructed.
Quoting Dfpolis
The axiomatic method is defined and discussed in numerous places, such as here and here.
In mathematics, the axiomatic method originated in the works of the ancient Greeks on geometry. The most brilliant example of the application of the axiomatic method — which remained unique up to the 19th century — was the geometric system known as Euclid's Elements (ca. 300 B.C.).
After Euclid's Elements introduced the axiomatic method, Socrates got the idea that philosophy had to be approached in a similar manner. The approach did not entirely succeed, and it was not a good idea for science, as would later become clear from Aristotle's now outdated scientific publications, but it works for mathematics and morality.
Quoting Dfpolis
That is how axioms were originally understood:
Axiomatic method, in logic, a procedure by which an entire system (e.g., a science) is generated in accordance with specified rules by logical deduction from certain basic propositions (axioms or postulates), which in turn are constructed from a few terms taken as primitive. These terms and axioms may either be arbitrarily defined and constructed or else be conceived according to a model in which some intuitive warrant for their truth is felt to exist.
Nowadays, axioms are deemed to be arbitrarily defined. They are unrelated to the real, physical world. Axioms are not true nor false, in terms of the correspondence theory of truth. Axioms are the building bricks of a new, abstract, Platonic world.
Quoting Dfpolis
It doesn't. In fact, that is even forbidden, because in that case, they are not axioms. In a knowledge statement P => Q, you can see that Q is justified by P. We do not care how P is justified, or if this is even the case. It does not change anything to the fact that Q necessarily follows from P. The knowledge expressed by P => Q, as a justified belief, is not P nor Q, but the arrow between both.
Quoting Dfpolis
In science, the observations are the P (justifying statement) and the theory (knowledge statement) is the Q, in P => Q:
(P) justifying statement => (Q) knowledge statement
There is no need to justify P, because the status of P does not affect the arrow, which is the real knowledge.
Quoting Dfpolis
Mathematics is not justified by experimental testing, and is therefore, not scientific.
Quoting Dfpolis
In his lecture, Gödel and the End of Physics, Hawking spent quite a bit of effort justifying his views. For me, it works.
Quoting Dfpolis
If it is physics, it is about the real, physical world, and in that case, you can test it. Therefore, it will not be accepted, as a matter of principle, that it does not get tested.
Quoting Dfpolis
If "they seem to work" is about what they observed in the real, physical world. That amounts to again to testing.
Quoting Dfpolis
No. It will undoubtedly be true, but it will not be provable. To cut a long story short, there are numerous articles in the search results that explain why not.
Quoting Dfpolis
Yes, agreed, in the correspondence theory of truth, the real, physical world is the benchmark for truth.
Quoting Dfpolis
Doesn't matter, because you cannot observe it. Therefore, without observations in an experimental testing fashion, such claim about the non-visible universe is unscientific.
Quoting Dfpolis
Metamathematics is the axiomatic system about (other) axiomatic systems. It is an abstract, Platonic system that produces theorems about other abstract, Platonic systems. Mathematical physics, on the other hand, is still about the real, physical world. Therefore, it is not part of mathematics.
Mathematics requires you to painstakingly construct the world in which you will derive your mathematical theorems. We did not construct the real, physical world. Therefore, we are not allowed to derive mathematical theorems in it.
Quoting alcontali
Yes, some irrational minds hold such views. That does not establish them as facts, or even good physics.
As I recall, Schrödinger proposed his thought experiment as a way of rebutting the Copenhagen Interpretation, not as a way of rebutting the foundations of logic. It should be clear to any physicist who approaches the collapse of the wave function at a fundamental level, that physics already accepts an understanding of bulk matter that entails the failure of superposition (e.g. the measurement problem, Schrödinger's cat, and the quantum-classical transition).
As I recently explained to David Hand on my YouTube channel, the wave function collapses because electron-electron interactions are nonlinear. Electrons interact via the electromagnetic field, represented by the 4-potential, A. The source of A is the 4-current j (charge density + current density), which is quadratic in the wave function, ?. The interaction is represented by a jA term which is quartic (quadratic in two different ?s).
Superposition requires linearity. Before detection, we can treat a quantum as isolated, so its dynamics is linear to a good approximation. Once it starts to interact with a detector or any other form of bulk matter (which is bound by atomic electron-electron interactions) the system becomes nonlinear, and any superposition must collapse. So, Schrödinger's cat is physically impossible.
Turning to entanglement, Bell's theorem, spooky action-at-a-distance, etc., the issues raised attack neither the principles of being nor the foundations of logic, but a certain misunderstanding of physics. It is well-accepted that ERP/Aspect-type experiments imply no violation of the relativistic principle that no signal can travel faster than the speed of light. So, there is no violation of accepted physical principles, only a concern that a local, realistic, deterministic interpretation of quantum theory may not be possible. I assure you that is possible, as an assumption critical to Bell's proof (viz. detector independence) is false (it ignores accepted physics,i.e. the antisymmetry of multi-fermion wave functions under coordinate interchange aka the Pauli exclusion principle.)
The underlying error in most quantum mythology is Whitehead's fallacy of misplaced concreteness. It consists in treating abstractions as though they were actual, contextualized reality. The more formal and abstract, the more axiomatic, one's thinking, the more prone one is to this fallacy. One way of spotting such errors is that those making them are often forced to question fundamental metaphysical principles.
Quoting alcontali
There's no point in being bound to reality.
Quoting alcontali
And the experience of being as quantifiable, from which to abstract the relevant concepts.
Quoting alcontali
Ah! How powerful is the need for social acceptance! Still, I prefer to examine the foundations of "accepted" views, however common. Clearly, we may not believe (accept) what we know, which would be impossible if knowledge were a species of belief. As a historical example, Descartes knew he was in his chamber (an act of intellect = his awareness of present intelligibility), but chose to suspend belief that he was in his chamber (an act of will = the suspension of commitment to the truth of what was known).
Quoting alcontali
Before the so-called Enlightenment. there was a clear distinction between experientially known reality (what is known by reason) and what was accepted by faith. So, this is a solution to a problem that did not exist. You can confirm the by reading the beginning of the Summa Theologiae, or by reading about the doctrine of the two books (the book of revelation and the book of nature) in James Hannam, The Genesis of Science: How the Christian Middle Ages Launched the Scientific Revolution.
In point of historical fact, the Enlightenment was an intellectually retrograde movement, in which ancient origins were thought more important to judging truth than rational reflection on empirical evidence.
Quoting alcontali
If you do not assume that the axioms are true, then one cannot assume that anything derived from them is true. If we only need begin with unjustified axioms, we can start with any assumptions and prove anything. That may satisfy you, but it certainly does not satisfy the general desire of humans to know.
In my view, axioms can be justified by abstraction, and most mathematical axioms are. A few, like the parallel postulate, are hypothetical, and are justified (confirmed) empirically because the sum of the measured interior angles of triangles is invariably two right angles to within the error of the measurements. If such measurements did not confirm this prediction, we would reject the parallel postulate -- as we do for non-Euclidean metrics.
Since we know the axioms are true any valid deduction from the axioms must be true (logic is salve veritate.)
Quoting alcontali
Thank you for the unargued faith claim. You have made no case that we cannot come to a certain knowledge of fundamental principles (of being, mathematics, and even physics) by abstraction. Until[ you do, all you have is unjustified belief.
quote="alcontali;304563"]Yes, of course. However, with access to the ToE -- which will never happen -- the distinction between axiomatic and empirical would disappear.[/quote]
Your recurring appeal to what we both agree is an impossibility is an annoying and pointless distraction.
Good physicist that I am, I've been studying entanglement for years and have found the flaw in Bell's proof. It is quite possible to have a local, realist and deterministic account of quantum theory -- where realist is to be understood in the Aristotelian, not the Platonic sense. I have discussed this possibility for a long time and my explanation has become better defined over time.
Axiomatic thinking is meant to be used for abstract, Platonic worlds. It is not a tool for justifying statements about the real world, which are supposed to be backed by experimental testing.
Quoting Dfpolis
In mathematics, indeed, no.
Quoting Dfpolis
Mathematics does not seek to be an abstraction of the real world. That is what physics seeks to be.
Quoting Dfpolis
If you know it, it means that you can justify it. So, why would you not believe it?
Quoting Dfpolis
Mathematical theorems are not "true" in a correspondence theory (CT) sense. Theorems are merely provable from axioms, which themselves are never "true" in a correspondence theory (CT) sense.
Provable is never CT true --> because a provable theorem is part of an abstract, Platonic world
CT true is never provable --> because we do not have the axioms of the real world, i.e. the ToE.
Hence, CT true and provable exclude each other.
Quoting Dfpolis
No. A system becomes trivialist because it contains a contradiction, for example.
Quoting Dfpolis
Axioms do not need to resemble the real world in any way. That is simply not a requirement. Axioms can best be considered to be arbitrarily chosen.
Quoting Dfpolis
Justification by experimental testing, is not mathematics, but physics. Math does not justify axioms by experimental testing. In fact, Math does not justify axioms at all. If you justify axioms by experimental testing, then it is simply not math. In that case, you are doing something else.
Quoting Dfpolis
Axioms are not correspondence-theory true, and any theorem proven from such axioms is not correspondence-theory true either.
Mathematics does not seek to model the real, physical world. Physics tries to do that. Mathematics and physics are different disciplines that are in many ways diametrically opposed.
I personally do not believe that a good physicist could ever be a good mathematician, nor the other way around. That what is mandatory in the one, is strictly forbidden in the other. The one's virtues are the other one's heresies.
Changing hats is really hard, because if you wear the same hat, day in day out, it becomes a second nature. The more advanced you become in the one, the less suitable you become for the other.
The real, physical world is something that will always be systematically eliminated from mathematics:
Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.
In mathematics, the real, physical world is treated as an unwanted impurity that needs to be cleaned away, until it is finally gone. Good riddance!
Give this a little thought. As I said, logic, as correct thought about existents, is based on the nature of existence. You are suggesting that existence is limiting, but it can't be. Existence is not a predicate like other predicates. If something is red, for example, it is limited, because the opposite of red is not-red and not-red things can exist. But, if, as you think, something were limited by being, what is excluded is not other kinds of things, but non-being. So, "everythng that is logically or ontologically possible" only excludes non-being, which is nothing. Clearly excluding nothing is not a limitation.
The idea is much simpler in a way:
If God exists (something like the typical ideas of God re the Judeo-Christian God), then either:
(a) God created logic, or it's at least part of His nature, and God could make logic however He'd want to make it--He has control over His own nature,
or
(b) Logic is more fundamental than God, and God can't buck it any more than we can. God must conform to it. It supersedes Him in its regard.
I apologize if you addressed this already, but could you clarify what you mean by any possible act? Could an infinite being eat a ham sandwich for lunch at my dining room table today?
Interesting point, a few notes:
- The act of the creation (of logic or anything else) requires logic. So God cannot of created logic.
- Logic constrains God just as it does us. God cannot make a square circle - he is limited to non-contradictions only.
- A world without logic (like X and ~X = true) is a world without information so no being could exist without information.
- So logic would appear to preexist God and be an unchangeable part of his nature.
I am not claiming that the contradictions can inhere in things as accidents, i.e.,as what Aristotle calls secondary beings. I am claiming that they cannot exist, and so do not exist. As they do not exist, they do not inhere, and as they do not inhere, they have no need of something to inhere in.
If you're asking how we can form/justify this judgement given that what we are talking about does not exist, I respond that the judgement is not based on any experience of non-existence (which is impossible), but on our experience of being. Everything we encounter exists, and this allows us to abstract a notion of existence. (I say "notion" because it is not a concept like other concepts.)
When we do so, we see that existing utterly excludes not existing, and so we grasp the ontological principle of non-contradiction (A putative thing cannot both be and not be at one and the same time in one and the same sense.) It is this principle that is applied here.
Quoting tim wood
I answered your definition question in the OP, saying that "Dynamic ontology is built on the notion [s]of[/s] [that] being can be explicated as the capacity to act." I see now that I made a typo, which I just corrected. As de-finition limits, and being is intrinsically unlimited, it cannot be de-fined, but it can be explicated and this is what I have done. Existence and the ability to act are convertible.
I am happy to accept your distinction between mental reality and extra-mental reality, but I don't think you've thought it through properly. Mental existents may be thought of in two ways: as they are in themselves, and as possible objects of thought. As they are in themselves, they are intentional beings, which is to say that their very nature is to be about something. The concept of red is about possible red objects, and the hope for happiness is about attaining a happy state. So, they are not monadic, but relational -- always beyond themselves to something that may or may not be real.
As possible objects of thought, mental realities are in the same class as any other possible object of thought. So, I don't see mental reality as disjoint from extramental reality, because I do not see knowing thought as any different than knowing beach balls. In order to be known, each must do something intelligible that existentially penetrates us -- that is presented to our awareness. To know is to be aware of present intelligibility -- and reality makes itself present by acting on us, by existentially penetrating us.
Why do I say "penetrating"? Because things are where they act. My seeing a ball is identically the ball being seen by me. This identity is only possible if we both act at the same time and place.
Now, let's discuss some of the abstactions you've mentioned. We are not born with the concept seven. We learn it in learning to count extramental objects. A collection of seven objects has a cardinality of seven -- i.e. it has a note of intelligiblity with a determinate relation to the concept seven. So, again, the concept is not monadic, but bears relational. It is applicable to any collection with a cardinality of seven, because any such collection is properly able to evoke it.
Truth also has a foundation in reality. We come to the concept when we realize that some thoughts and locutions are adequate to reality and some are not. So, again, we could not have the concept of truth independently of experiencing reality.
Because all of our concepts have a similar story, no concept is monadic. The ontogenesis of each is based on our experience of reality. So, while they may appear monadic when considered abstractly, their genesis is inexorably grounded in our experience of reality. The same applies to God. Sound proofs are based on experiences that implicate an infinite being.
Quoting tim wood
No, it does not. Contrary to Boole, logic is not about the laws of thought. It is about rules we must follow if we want our thought to reflect reality -- to be salve veritate, truth preserving. I have no trouble thinking "square circle," "five-sided triangle," or "infinite wealth." Nothing in my mental constitution, no "law of thought," precludes such thoughts. It is only when I wish my thought to reflect the nature of reality, of being, that I realize that such concepts should be excluded. Why? Because my understanding of being entails that no contradiction can be instantianted.
Quoting tim wood
No, as I just argued, they reflect the nature of being. Our experiential grasp of being is such that we know that it is utterly incompatible with non-being.
Quoting tim wood
That is why I have avoided it.
Quoting tim wood
Yes, I would say "concurrent."
Quoting tim wood
That is why I have outlined the relation between thought and reality. First, wrt traditional logic, that it reflects the nature of existence, and second wrt to concepts that ideogenesis is the result of our awarenss of present intellibility -- of the object existentially penetrating (acting within) us. For example, the neural modification that represents a sensed apple is identially the modification of my neural system by the apple acting on me. This identity is real, but partial. The modification of my neural system is not all of me, but it is still part of me. The modification of my neural system is not all the apple can do, but it is still the apple doing it. So, part of me is identically an act of the apple. That means the apple is really present (via its act) in me. We are not separate, but one and, as you say, coterminus.
Quoting tim wood
This is a very Kantian view, and, to my mind, wholly unjustified. I hope the little I've said will help you rethink it, but really, it deservfes a thread of its own.
But, there is no objective reason for such a limitation. It is all very subjective. Whenever you do not like where a line of explanation is leading, you can stop it by pulling the "brute fact" cord.
Quoting Devans99
I agree.
Thank you for your reflections.
No, because that would entail the contraction of Its being limited, but It could create a finite being capable of doing so. Am I invited?
What you may regard to be the relationship between thought and reality is simply your thoughts on that relationship. A clear example of why your simplistic bivalent logic fails:
Quoting Dfpolis
What is the opposite of red? Is blue the opposite of red? Is green or yellow? All of them are not-red but are all of them the opposite of red? You are not-red, so are you the opposite of red? A car is not red even if it is a red car. Cars and colors are not the same and are not opposites.
Sure, if you like ham sandwiches.
Quoting Dfpolis
Wait, so an infinite being cannot engage in any possible act? You seem to be saying that there are certain acts that only a finite being can accomplish. This seems problematic. You said that the difference between infinite being and finite being is that the latter can only engage in some possible acts whereas the former can engage in any possible act. If that's no longer true then your distinction between finite and infinite being collapses.
That is why I provided a proof.
Quoting Fooloso4
Do you have a citation for Aristotle?
No, Aquinas did not make a faith claim. He provided a proof. Also, my use of "explanation" is not the same as Aquinas's use of "cause" in "uncaused cause." Aquinas's "causes" must be extrinsic, while my "explanation" can be intrinsic or extrinsic.
Quoting Fooloso4
I agree that my argument uses insights due to Aristotle, ibn Sina and Aquinas. Still, being old is not a fallacy. Do you have an objection other than the ancient roots of my thought?
Quoting Fooloso4
Aquinas wrote for a more philosophically literate audience -- one that knew the distinction between essential and accidental causality.
Quoting Fooloso4
Has that caused you any difficulty?
Let's clarify the "dependence" of facts. There is epistemological dependence. We need not know God before we know empirical facts. And, there is ontological/dynamical dependence. Contingent facts cannot explain themselves.
Quoting Fooloso4
I think you can work that out for yourself. The question is irrelevant to the soundness of my argument.
Yes, it can. An infinite being acting as only a finite being can is not a possible act.Quoting Theorem
Why is it problematic? Truly eating requires a number of operations that imply finiteness: changing in the course of chewing means that the eater has unrealized potencies. Using and requiring nutrients to maintain one's being implies contingency. and so on. So, you must see the acts, not in abstraction (which would be Whitehead's fallacy of misplaced concreteness), but in the context of being done by an unlimited being.
Using this line of reasoning, we could say that a finite being acting as only an infinite being or as only any other finite being can is also not a possible act. Therefore, finite beings can engage in any possible act.
Quoting Dfpolis
That's not the issue. The issue is that your distinction between infinite and finite beings is made in terms of an ambiguous definition of "possible acts". See above.
Call it what you like but it is nothing more than a claim for the existence of a being whose existence you assert but cannot prove or demonstrate exists.
Quoting Dfpolis
No. Aristotle requires us to think if we are to understand him. Claiming that a being is the cause of being leaves unexplained the existence of that being. Here I am using explanation in the ordinary sense as Aristotle did. An explanation is discursive. Claiming that there is self-explaining being is not to provide a discursive explanation.
Quoting Dfpolis
I have no objections at all to the ancient roots of thought. I have made my objections clear. You simply posit what you cannot explain or demonstrate. It is just kicking the can.
Quoting Dfpolis
You should not underestimate your own audience. There may be some here who do not know the difference but some who do.
Quoting Dfpolis
No, no difficulty at all. The difficulty is with your "proof".
Quoting Dfpolis
Positing a necessary being or, facts as you would have it, explains nothing. It is a misuse of the term explanation. I think you might know this and that is why you called you assertion a fact.
Quoting Dfpolis
While there are some who still attempt to defend Aquinas' argument others, including theologians, have rightly moved on. Your argument fares no better than his.
In Book Book 1, 2:
He does not pursue this, however. There are some who suggest that Aristotle like Socrates was as skeptic, possessing human wisdom - knowledge of his ignorance, rather than divine knowledge
12:6:
Why must it be asserted? Aristotle is a careful writer. If it is something known of could be demonstrated to be true then he would say so
Is there anything that we have knowledge of that is not destructible? If all things are destructible, as the available evidence indicates they are, then the assertion that it is necessary that there should be an eternal unmovable substance is questionable.
12:10:
Of course what one says and what has been demonstrated to be true is not the same thing.
I am not claiming that the contradictions can inhere in things as accidents, i.e.,as what Aristotle calls secondary beings. I am claiming that they cannot exist, and so do not exist. As they do not exist, they do not inhere, and as they do not inhere, they have no need of something to inhere in.
If you're asking how we can form/justify this judgement given that what we are talking about does not exist, I respond that the judgement is not based on any experience of non-existence (which is impossible), but on our experience of being. Everything we encounter exists, and this allows us to abstract a notion of existence. (I say "notion" because it is not a concept like other concepts.)
When we do so, we see that existing utterly excludes not existing, and so we grasp the ontological principle of non-contradiction (A putative thing cannot both be and not be at one and the same time in one and the same sense.) It is this principle that is applied here.
Quoting tim wood
I answered your definition question in the OP.
Perhaps Lovecraft derived this idea from the Gnostic's own "idiot" creator God, Yaldabaoth.
"In one of the ironies of mythic history, Yahweh himself became guilty of self-deification. In the book of Isaiah, the Jewish deity declares: “I am God and there is no other!” (46:9). In gnostic sources, this declaration becomes the mantra of the foolish creator, Yaldabaoth. This chapter examines three versions of Yaldabaoth’s myth (all found in Nag Hammadi codex II) in (1) The Apocryphon of John, (2) The Nature of the Rulers, and (3) The Origin of the World. It is argued that Gnostic Christians created the character of Yaldabaoth not to subvert Judaism itself but to criticize fellow Christians who adopted Yahweh’s superiority. By fitting the Jewish deity into the typology of self-deification, gnostics showed how foolish it was to believe in a jealous god who tried to prevent the deification of others."
From here: https://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780190467166.001.0001/acprof-9780190467166-chapter-4
I'm not enough of a Lovecraft scholar to say (actually not a Lovecraft scholar at all :wink: ). Although he was quite erudite, I'm also not entirely sure how many of the sources your article references would have been available to him.
It's also important to be aware that in describing Azathoth as a "blind idiot God" Lovecraft was telling us (as he more explicitly explains elsewhere, I think) that Azathoth was not sentient. So not quite a "blind idiot" in the usual sense.
~The Dream Quest of Unknown Kadath
Sentences are enumerable, but I don't think theories are as they may contain unspecified constants that are indenumerable. Also, it is unclear that the judgements sentences express are enumerable, as concepts can be analogously predicated. So there is not a one-to-one mapping of concepts to words.
Quoting alcontali
I see no need to restrict systematic knowledge to what can be justified by the hypothetico-deductive method. What is so justified is not known to be true, only known to be justified. Since we do not know it to be true in any absolute sense, it does not even meet the JtB definition of "knowledge."
Quoting alcontali
I am willing to agree with this in the context of experimental/observational science; however, we can do better wrt to math, being and certain mental topics.
My preferred approach is to use an analogous definition of truth as adequacy to the needs of a particular discourse. Then, for example, Newtonian physics is true with respect to many engineering needs.
Quoting alcontali
While it is quite true that we do not have an exhaustive knowledge of reality, that is not the same as having no knowledge of absolute real world truths. We can and do have axioms applicable to the real world. Recall that the root meaning of "geometry" is "land measure" and many of its axioms are true of real-world geometric relations relations. Number theory derives from counting real world objects, and applies to such operations. We also know some of the principles of real-world existence. No real thing can be and not be in one and the same way at one and the same time, and so on.
Quoting alcontali
Of course we can. We can measure the interior angles of plane triangles and see if the results agree with the prediction that they will sum to two right angles. Then, the result is both axiomatically derived and experimentally confirmed.
Also, as I have mentioned earlier, physicists have axiomatized quantum mechanics and quantum field theory. Special relativity rests on two axioms. So, in al of these fields, we have the ability to proceed axiomatically, but that in no way prevents us from testing our deductions experimentally.
Quoting alcontali
I agree that this is true with respect to justification, if are restricting yourself to sciences that use the hypothetico-deductive method.
Quoting alcontali
I hate to break it to you, but there is no Platonic world. There is the real world and there are mental constructs that exist in the minds of people living in the real world.
Historically, most axioms have been abstracted from our experience of reality. For example, the Dedekind–Peano axioms are all derived from our experiences of counting and dealing with equal quantities. A very few (principally Euclid's parallel postulate) were not derived from experience. The fact that neither the parallel postulate, nor any equivalent to it (such as the sum of the interior angles of a triangle) could be abstracted from experience has been recognized as a problem from the very beginning of axiomatic geometry. So, from the beginning, we've had axioms that could be abstracted from reality and hypothetical axioms, such as the axiom of choice.
We use the same logic in deducing both predictions from physical hypotheses and mathematical theorems. In fact, many of the axioms used in mathematical physics are identical to axioms used in mathematics. So, the only methodological difference is that physics has a much greater percentage of hypothetical axioms and so makes greater use of experimental confirmation. (While it is not part of the canonical procedure, many geometry students have measured the interior angles of triangles.)
When we test conclusions, we do not test them in abstract, universal form, but as they are instantiated in real-world particulars. So, the fact that we have no experimental access to abstract forms is irrelevant.
Quoting alcontali
I am not denying that. I meant that there is no clear distinction between the methods you mentioned. The axiomatic method is no different than the method used in rigorous papers in physics. One states one's premises/axioms and then deduces consequences. The main difference is that in mathematics, hypothetical axioms need not be falsifiable. Those of us trained in the natural sciences do not see unfalsifiable as an advantage, especially given that Godel work ruling out consistency proofs in systems representable in arithmetic.
So, the only way to insure consistency is to abstract one's axioms from reality, which cannot instantiate a contradiction.
Quoting alcontali
Socrates died in 399 BC, Euclid flourished about 100 years later, c. 300 BC. If you read the history of Greek science, you'll learn that Euclid modeled his method on the logical approach developed by Aristotle.
Quoting alcontali
While science moves on, it is hardly a failure to found a number of fields, including political science, logic, mathematical physics and marine biology. Aristotle was a tireless researcher, reading all the works of his predecessors. He was also a thorough observer and empiricist, insisting that his students dirty their hands with dissections and keeping informed on advances in mathematical astronomy. He knew more about viscous fluids than Newton and his work on Aegean fish is still a valuable reference.
Aristotle's approach to empirical science was empirical, not axiomatic. His approach to philosophy was fundamental and logically, but not axiomatic in the sense of positing unexamined assumptions. Instead, he saw the role of metaphysics to be the examination and justification (but not deduction) of first principles.
As a passing note, the axiomatic method does not work for morality, nor did Aristotle claim that it did.
Quoting alcontali
I am glad to find some agreement. Those not so abstracted are, then, hypothetical. If they cannot be tested, they are unfalsifiable hypotheses and highly suspect.
Quoting alcontali
This is utter nonsense. Axioms are axiomatic wrt a particular field -- meaning that they are assumed, but not justified within the context of that field. That does not preclude them being justified by a more fundamental field. As we have just agreed, the original justification of mathematical axioms was not via deduction from more fundamental assumptions, but via abstraction from reality.
That brings us at last to the justification of metaphysical premises, which, similarly, is not by deduction, but via abstraction.
Quoting alcontali
Again, this is nonsense. If we did not care how axioms were justified, there would have been no controversy over the parallel postulate (which there was from the beginning) or about the axiom of choice. It is because we do care about the truth of axioms that so much ink was expended on these issues.
Why do we care? Because mathematics is a science -- as one organized body of knowledge among many. So, we want its conclusions to be true. In fact, truth is a central issue in Goedel's work. The problem he exposed (which completely undercuts your position) is that there are true theorems that cannot be proven from fixed axiom sets. If mathematics did not deal with truth, this could not be the case. If "mathematical truth" were convertible with provability, this could not be the case. So, the axiomatic method does not, and cannot, provide us with an exhaustive inventory of mathematical truths. That means that it cannot be the foundation of mathematical truth as you seem to imply.
Further, if the truth of P is indeterminate, so is the truth of Q if its sole justification is P => Q. On your account, mathematics is no more that a game -- not any different from Dungeons and Dragons, which also has rules that are neither true nor false, but simply to be followed by those playing the game. Funding mathematical research would be a scam in which we are paying people to play arbitrary games, with no hope of advancing our knowledge of reality, however theoretical.
Finally, it mathematics were not true, it would not be applicable to reality. Physicists who included mathematical premises in their reasoning, would be relying on claims of questionable or indeterminate truth, making their own conclusions and hypothetical predictions worthless.
to be continued ...
Concerning the coherence theory of truth, I agree with Bertrand Russell's objections:
Perhaps the best-known objection to a coherence theory of truth is Bertrand Russell's. He maintained that since both a belief and its negation will, individually, cohere with at least one set of beliefs, this means that contradictory beliefs can be shown to be true according to coherence theory, and therefore that the theory cannot work. However, what most coherence theorists are concerned with is not all possible beliefs, but the set of beliefs that people actually hold. The main problem for a coherence theory of truth, then, is how to specify just this particular set, given that the truth of which beliefs are actually held can only be determined by means of coherence.
Therefore, I cannot agree with "Newtonian physics is true with respect to".
Quoting Dfpolis
You would have to visit all possible planets in the universe in order to verify that they are true of real-world geometric relations. You cannot do that. You will only sample some of these. Therefore, you cannot exclude the existence of counterexamples. Hence, these axioms are neither provable nor true about the universe.
Quoting Dfpolis
Entanglement allows for simultaneous being and not being in the real world. Schrödinger's cat is another example. Therefore, nuclear physicists seem to beg to disagree with you.
Quoting Dfpolis
You cannot visit all possible such angles in the real, physical world. Therefore, the theorem is not provable about the real, physical world. It is only provable in the abstract, Platonic world in which the provability of this theorem is the result of the construction logic of that abstract, Platonic world. You can perfectly-well visit all such angles in an abstract, Platonic world. That doesn't cost energy. In the real, physical world, you would need more energy that you could ever practically amass.
Quoting Dfpolis
These mental constructs are abstract, Platonic worlds. They are not real. They are called Platonic because they are very similar to Plato's forms (but not necessarily the same):
[i]Mathematical Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. The term Platonism is used because such a view is seen to parallel Plato's Theory of Forms and a "World of Ideas" (Greek: eidos (?????)) described in Plato's allegory of the cave: the everyday world can only imperfectly approximate an unchanging, ultimate reality.
A major question considered in mathematical Platonism is: Precisely where and how do the mathematical entities exist, and how do we know about them? Is there a world, completely separate from our physical one, that is occupied by the mathematical entities? How can we gain access to this separate world and discover truths about the entities? One proposed answer is the Ultimate Ensemble, a theory that postulates that all structures that exist mathematically also exist physically in their own universe.[/i]
Platonism is the dominant philosophical view in mathematics.
Quoting Dfpolis
Originally, yes.
Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.[1][2][3] Two of the most highly abstract areas of modern mathematics are category theory and model theory.
However, this is no longer the dominant source of inspiration for axiomatization.
For example, the lambda calculus has absolutely no origins in the real, physical world. Nor do the various combinator calculi. None of Stephen Kleene's work, such as his famous closure, have any origin in the real world.
The entire discipline of computability has no connection, and has never had any connection, with the real, physical world. There is absolutely nothing that looks like a shift-reduce parser in the real world.
The mathematical foundations of computer science have never been about mimicking the real, physical world. That would simply be an exercise in futility. A running process on a computer system creates a virtual world of which the nature is studied using Platonic abstractions. Suggesting that these virtual worlds have originally been abstracted away from the real, physical world, is absurd. They do not exist in the real, physical world.
Alan Turing's Halting problem is provable in the abstract, Platonic world of running processes. What is the link with the real, physical world? In what way does the real, physical world contain running processes? Where are the naturally-occurring CPUs and computer systems?
Seriously, mathematics transcends the real, physical world. Physicists are just one group of its users. I do not understand why they think that they would be so privileged in connection with mathematics? Historically, there used to be an empirical link, but that link has been abstracted away a long time ago. There is no 20th century mathematics that still has such link. Mathematicians do not desire such link, because it would hold things back. Such link is very, very retrograde. Ever since the axiomatization of set theory in 1905 by Zermelo and Fränckel, absolutely nobody still wants that link.
Quoting Dfpolis
Well, ... in systems of which the associated language is capable of expressing the axioms of arithmetic.
Gödel was talking about the minimum power of a virtual machine and what we would today call its bytecode instructions. If the bytecode language can express Dedekind-Peano, the language can express (logical) truths that are not provable in the system.
Gödel's incompleteness is a language problem. The language required to express the axioms is more powerful than strictly what the axioms express. It is this fundamental mismatch that causes the problem.
In fact, Tarski's undefinability theorem is much better at expressing what Gödel's conundrum entails:
Smullyan (1991, 2001) has argued forcefully that Tarski's undefinability theorem deserves much of the attention garnered by Gödel's incompleteness theorems. That the latter theorems have much to say about all of mathematics and more controversially, about a range of philosophical issues (e.g., Lucas 1961) is less than evident. Tarski's theorem, on the other hand, is not directly about mathematics but about the inherent limitations of any formal language sufficiently expressive to be of real interest. Such languages are necessarily capable of enough self-reference for the diagonal lemma to apply to them. The broader philosophical import of Tarski's theorem is more strikingly evident.
Quoting Dfpolis
It does work for morality. According to Kant's Critique of Practical Reason, the core of a moral system are its categorical imperatives, i.e. its axioms. In fact, Socrates already suggested that: "The understanding of mathematics is necessary for a sound grasp of ethics."
Quoting Dfpolis
That is the empirical view in science, but a constructivist heresy in mathematics:
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists. Even though most mathematicians do not accept the constructivist's thesis that only mathematics done based on constructive methods is sound, constructive methods are increasingly of interest on non-ideological grounds.
If your only tool is a hammer, then the entire world will end up looking like a nail. If you cannot transcend the sandbox of physics, you will misunderstand and mismanage everything you ever do, outside physics. Is it so unthinkable to you that other epistemic methods are different from your own? Doing mathematics in the way you suggest, is simply not mathematics. It would be a failed form of physics.
Quoting Dfpolis
Only pre-20th century mathematics mostly originated via abstraction from reality. However, most of the progress that has been booked after that, does not.
Quoting Dfpolis
Gödel does not talk about correspondence-theory "true". You can even trivially understand that from his canonical example:
S = "S is not provable in theory T"
Is S provable in T? No, because that would be a contradiction. Hence, S is (logically) true. Therefore, we are now sitting on a theorem that is (logically) true but not provable.
The language L associated with T is powerful enough to express S, and therefore, S is a relevant theorem in T.
The undefinability theorem does not prevent truth in one theory from being defined in a stronger theory. For example, the set of (codes for) formulas of first-order Peano arithmetic that are true in N is definable by a formula in second order arithmetic. Similarly, the set of true formulas of the standard model of second order arithmetic (or n-th order arithmetic for any n) can be defined by a formula in first-order ZFC.
In other words, it will be "true" and not provable in T, but it will be provable in any theory of which T is a sub-theory. The real, physical world is not chained into this tower of theories. Hence, it has nothing to do with correspondence-theory "true".
Quoting Dfpolis
Yes, mathematical theorems are not correspondence-theory "true". They are only provable in their abstract, Platonic world.
Quoting Dfpolis
There are no mathematical truths. There are only theorems provable from the construction logic of their abstract, Platonic world, i.e. their axioms.
Quoting Dfpolis
Agreed.
Quoting Dfpolis
There is no hope of advancing our knowledge of reality through mathematics. In relation to theories about the real, physical world, mathematics only supplies a consistency-maintaining bureaucracy of formalisms. Physics uses these formalisms. Hence, mathematics is useful to physics.
Quoting Dfpolis
Mathematics is not applicable to reality. You will have to use another discipline for that purpose. You may indeed encounter mathematics as a tool to maintain consistency in what this other discipline claims, but that does not mean that mathematics would say anything about the real world.
Quoting Dfpolis
Physicists do not include mathematical premises in their reasoning. They only maintain consistency in their theories by using mathematics. That works like a charm.
Hardy already admitted exactly that, in 1940, in "A Mathematician's Apology". It is not a secret:
[i]Hardy preferred his work to be considered pure mathematics, perhaps because of his detestation of war and the military uses to which mathematics had been applied. He made several statements similar to that in his Apology:
I have never done anything "useful".
No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.
Hardy regards as "pure" the kinds of mathematics that are independent of the physical world.[/i]
Or even:
We have concluded that the trivial mathematics is, on the whole, useful, and that the real mathematics, on the whole, is not.
Furthermore, the low-hanging fruit is only moderately useful. It is rather some of the hard, abstract stuff, that initially looks useless, even for centuries, that will eventually turn out to be a real game changer. For example, Euler's centuries-old work on number theory, became a multi-trillion dollar business when Rivest-Shamir-Aldeman (RSA) kicked off the world of public-key cryptography.
Seriously, it is not the quick wins that make humanity progress.
Quoting alcontali
This shows a disqualifying lack of understanding of the scientific method. There is no case in physics, or in any other science, in which observations logically imply a theory. Observations are particulars, while theories make universal claims. The implication you suppose has an undistributed middle and is necessarily invalid,. This has been clearly understood since at least the 1230s, when Robert Grosseteste wrote canons for the scientific method as it exists today.
Quoting alcontali
While I agree that conditionals can express truths independently of the truth of their antecedents, they need not be the "real knowledge," whatever that may me, What most scientists seek to know is how their observation sets can be understood in terms of more fundamental universal principles, aka theories, the P in your proposition.
It may be true, for example, that if there were no observers there would be no observations, but few scientists would consider this to be getting to the meat of the matter, to be "the real knowledge,"
Quoting alcontali
Yes, and no. The portion of mathematics following from propositions abstracted from nature, or testable by observation (e.g. the parallel postulate), is scientific. The portion deriving from unfalsifiable hypotheses (e.g. the axiom of choice) is clearly not scientific, for it violates the accepted canons.
Quoting alcontali
As this is entirely irrelevant to the OP, I shall leave you to it.
Quoting alcontali
You are missing the point. I am not saying that we shouldn't test the axiomatic foundations of physical theories, but that our capacity to investigate those foundations shows that being an axiom does not preclude justification. Your response shows that you agree, but want, for no stated reason, to exclude mathematics from the fields whose axioms can be investigated and potentially justified. That the parallel postulate was suspected from the beginning, and the uncertain status of the axiom of choice shows that your views are hardly universal.
Quoting alcontali
This alone is sufficient to reject your views. We can prove it by (1) noting that apples and pears are both fruit, (2) that they are also both units, and (3) applying ordinary arithmetic via the dictum de omni. Feel free to rebut this.
Quoting alcontali
This is irrational and inconsistent. You claim that mathematics need not be justified by observation. I hope you would agree that it is a mathematical truth that 2 + 2 = 4. By the dictum de omni, this is true if and only if it is true in all instances. Whether the instances are observable or not is irrelevant.
Further, I do not accept your restriction of science to fields that employ the hypothetico-deductive method. You cannot define you way to a conclusion about reality. If 2 + 2 = 4, it does so always and everywhere, not merely in some domain you arbitrarily choose to define.
Quoting alcontali
Mathematicians construct no worlds. They merely work out the implications of axioms that may or may not be justified by our experience of the real world. If the axioms are justified, those implications will be applicable to the world from which the axioms are derived. If the axioms are unfalsifiable hypotheses, those applying them are merely playing complex mental games. They are entitled to play their favorite games, but they can hardly expect society to support their play.
Logic is a science which provides rules for mediated thought about reality. God does not have mediated thought, but knows all reality immediately in his act of sustaining it being. Therefore God does not need or use logic.
So, I simply deny both horns of your supposed disjunction. God is unqualified being. The beings of experience depend on God. Humans develop logic to think about being in a rational way. So, the order of precedence here is God -> created being (including humans) -> logic (created by humans).
No, not just my thoughts, but those of a community of scholars who have been investigating the issue for 2500 years. But, even if they were mine alone, noting that does not rebut my analysis. To do that you have to deal with what I said in a substantive way,
Quoting Fooloso4
I said what the opposite is in the line you quoted: not red -- not this or that kind of not red, but anything not red, aka the privation of red.
I haven't heard back from you on this, so I am going to assume I have misunderstood your claim. I think where I am getting tripped up is when I read the phrase "all possible acts", I think a set of all possible actions such as "lifting a hand", "taking a step" or "creating a physical being ex nihilo". So when you say that an infinite being can engage in all possible acts, it seems obvious to me that this is wrong because an infinite being can only execute a small subset of the set of all possible acts (some of which can only be executed by finite beings).
However, you seem to be thinking of the "set of all possible acts" in a different way. In your previous response you seem to be indexing possibility to the being in question. So instead of talking about the set of all possible acts in total, you're talking about the sum of all possible acts for a being of type X. So to say that a particular infinite being can engage in all possible acts means that it can engage in that subset of possible acts that any infinite being could execute. Whereas a particular finite being could never engage in the set of all possible acts that any finite being could execute (e.g. a man with no hand could not raise his hand, etc.).
Just trying to understand you. Is that anywhere close?
Yes, but the idea of a particular brick requires that that brick modify your nervous system to create a representation you can be aware of. So, by acting in you, the extramental brick penetrates you (your neural representation is identically the brick modifying your neural state). It is this shared being that makes knowledge possible.
Your awareness of the brick's activity is your idea of the brick. Aristotle points out that the one act of awareness actualizes two distinct potentials: You capacity to know and the capacity of the brick to be known (its intelligibility). So, again knowledge is based on subject-object unity -- this time joint actualization.
Not quite. Infinite being can effect any possible act either directly, or by indirection. While God can't eat a ham sandwich Himself (as that would entail finiteness), God can create a being who can. So, God can effect any possible act, while a finite being cannot. In other words, there is no barrier to effecting the act, there is only a problem if one over-constrains the act so as to make it instantiate a contradiction.
Quoting Theorem
I hope that I have resolved this to your satisfaction above. God can do anything that does not instantiate a contradiction, because it is not possible to instantiate a contradiction. Finite beings have intrinsic limits to their power to act, so that there are possible acts not within their power.
I have been visited by God all of my life & God demonstrated to me the science he uses to control the universe while staying outside of time & space.
What we think of as the material universe & world is only actually an energy. And that energy is moving at a particular wavelength/speed which is the Primary Dimension of the universe.
We mortals measure the 3 dimensions of objects including the universe & that presents us with measurements in time & space, that we are always striving to find newer ways to work with & overcome; in order to improve our lives.
But the basic (primary) unseen dimension of the universe is its wavelength & that dimension dictates the measurements of what all the other dimensions will be within the universe.
So when God manipulates the wavelength of the universe & of himself he completely steps out of the dimensions & their measurements that we are all locked & bound tightly in.
And so we see a universe that is vast & unconquerable 'while God sees a holographic type 'insignificant illusion that can be put aside completely & manipulated in any way at all.
God has demonstrated this to me over & over & let me hold metallic magnetic type elements that alter the wavelength of any atoms coming near them.
God builds very real solid gates from these simple elements & when we walk through the gates our atoms have their wavelength instantly changed & we enter a parallel world with all new dimensions & measurements, that are totally different than the earth's dimensions. It is completely real & stunning to experience.
I've watched millions of beautiful people join forums over the years to describe the wonders God has shown them, & without fail every person was instantly mocked into silence by the ignorant people who infest every forum. And not one webmaster or vile mod god has ever stopped the people from being mocked into silence.
Every webmaster & mod ignorantly works to facilitate & uphold the mockery of anyone who has a wonderful tale to tell about their meetings or experiences with God etc. In this way the web has always destroyed most all new knowledge the world of man has about God.
It does that by luring & destroying every new individual, as they arrive on demon infested sites to tell their wonderful story. It allows them to be insulted & bullied into silence.
So the good people of the world, & all the others, are without much new information about God because the web has destroyed/silenced all the people who tried to give that new information. Instead you are stuck with the old scriptures which cannot be removed so easily & yet have very little scientific type information about God.
Anyway I just found this forum a minute ago & haven't read any of your comments yet. But I read a bit of the opening post & it mentions how God can do everything mortals cannot do, & I just wanted to explain that God can do all those things because God has an extra dimension (direction/measurement) to work with, & that dimension is the speed of the wavelength that the earth & universe is made from.
By stepping aside from that wavelength God steps outside of space & time & can shrink all of space to zero & be anywhere in the universe at once; & stop time completely & casually walk around us, (at what to us would be the speed of light), & manipulate everything that happens in the world of man down to a T.
And we would experience it as miracles & impossible coincidences etc when it is actually just a science God is using to step outside of time so that he can manipulate everything that happens inside of time.
God has demonstrated vast amounts of his powers to me & I know they are true. God shows me the future thousands of times & it always comes true even when I think it is not possible for such things to happen.
So I know God is real & from real life experience with God I know that he simply uses science to control time & space & everything that is locked inside them. It is all so very simple to God & it could be simple to our own scientists too when they figure out how to manipulate the wavelength of the energy that the earth & universe are made from
When you have rebutted my argument, you may claim this. Without pointing out a false premise or a logical misstep, this remains your unsupported belief.
Quoting Fooloso4
Then you should not claim the authority of Aristotle.
Quoting Fooloso4
This mischaracterizes the argument. First, Aquinas points out that "being" is not predicated univocally of God and empirical beings. Instead, God is called a being because God is the source of empirical being. This is an analogy of attribution. The example is that food is healthy, not because it is in good health, but because it is a cause of health those who consume it. So, the source of empirical being cane be called a being, not that use of "being" is not the same as the "being" in empirical being.
Second, it is not being in the abstract that explains being in the abstract, but a particular, infinite being that explains other finite beings.
Third, in my proof infinite being does not stand as unexplained, but as self-explaining and precisely because it is infinite being, so that what it is entails that it is.
Quoting Fooloso4
I made it clear in the OP that I was not talking about discursive explanations, but about dynamical ones. Still the fact that God's essence is His existence is the discursive reason He is self-explaining in the dynamical sense.
Quoting Fooloso4
Then you will have no trouble pointing to a false premise or an invalid logical step.
Quoting Fooloso4
It is still better to avoid confusion by a judicious choice of terms.
Quoting Fooloso4
I did not posit, I offered a proof. A proper critique would point to specific errors in what I offered.
Quoting Fooloso4
Then what, specifically, are my errors?
I have spent a lot of time responding, but very little of what I have responded to is critical of my actual argument. The fact that many are confused about Aquinas's arguments is not a criticism of what i said.
As for your post on Aristotle, I will not respond to it, as it would take too much time.
If a proof is sound, there is no shame in restating it. Do you have a substantive criticism, or is your only objection that my argument is not in vogue?
Ah, I see. That helps clarify things for me.
It strikes me that the only possible act that God engages in directly is the act of creation ex nihilo. If this is true, then it would imply that God's existence and the existence of some logically possible universe are mutually dependent. In other words, if God exists only when he is exercising some capacity, and if the only capacity he has is for creation ex nihilo, then God exists iff some logically possible universe of his own creation exists.
Are there any other direct actions God can take besides creation ex nihilo? If so, what are some examples?
So if logic is simply something created by humans to think about reality, then God would not in any way be constrained by logical possibility, right?
Do you imagine that when you close your eyes the world disappears? I have done just what you say must be done, only with your eyes shut you do not see it.
Quoting Dfpolis
Here is where we differ. I do not claim the authority of Aristotle. My position is that Aristotle is a zetetic skeptic - he inquires based on the knowledge that he does not know. You are a Christian who accepts what you have been told.
Quoting Dfpolis
The argument is tortuous bending itself into unnatural positions in the hopes of escaping what is plainly evident. Aquinas' supreme being is a being, it is, it exists. As you say: God is "a particular, infinite being".
Quoting Dfpolis
This is an equivocation. Either you can explain the existence of God, that is provide a discursive explanation or you cannot. You have not. If you follow Aquinas you cannot. If you cannot explain the existence of God, you have not proven the existence of God. Positing an infinite being is not a proof of the existence of that being. Claiming that being is infinite and self-explaining is not proof that there is an infinite being that is self-explaining. Every being that is is what it is.
Quoting Dfpolis
More equivocation. A proof is a demonstration. If it is an argument then it is by definition discursive. You claim that there is an:
Quoting Dfpolis
and build your discursive explanation based on that assertion.
Quoting Dfpolis
We know that finite things exist but do you prove that an infinite being does?
Quoting Dfpolis
In defense of this you claim:
Quoting Dfpolis
The finitude of our being is part of what it means for us to be.
Our existence is dependent. It is "explained" by the existence of our human and non-human ancestors, the earth, the sun, molecules, atoms, the fundamental forces. You might argue that each of these is limited, and that may be, but they are also capable of acting in such a way as to give rise to us.
That there is something rather than nothing may be both the starting point and limit of human understanding, but of course this does not satisfy the desire for a God who creates ex nihilo, a desire that conflates itself with the desire to know, a desire that confuses the dependence of individual beings for a dependence of all being save the being on which all is dependent, a being you declare is not dependent.
Added: There is a Jewish tradition that takes the dot in the first word of Genesis ??????????? (read right to left) as symbolic of our inability to go back before when God began to create. We start, as he did, with a world that is chaotic, without form and with nothing distinct from anything else until God began to separate.
God has shown me many things & one day I saw God sitting on a high place creating universes. Each one is like the cell of a honeycomb that fits into all the others & yet is self contained. I asked God how he was creating the universes & he described that he uses the light that people call "God" to will them into existence, & they are all replicas of the other. God would create a universe & then we would go into it & explore it for a while, & then God would repeat the process.
Our own science thinks that in one sense everything is created from light. Yogis are said to be able to hold a crystal glass filled with water in their hands & the light of their own aura cumulates in the water & creates a mini universe in there.
The Vedas state that God lives in water & His aura creates the universes naturally inside the water.
The Bible states that God created the light first of all & then created a space inside water to put the universe in. And water remained above the universe when creation was finished.
So it is a bubble of light energy under water. And I have personally watched God creating universes from light & he explained how he does it & then took me into those universes.
No I don't expect you to understand or believe. hohoho
I simply want to dispel another notion that this thread states as fact. The notion that God cannot do the simple things that people can do etc. That is totally false. God can do absolutely everything we can do & infinite more things. I have held God's hand & walked with God many times. We eat & drink together & enjoy the sights & journeys we go on.
You need to comprehend a simple part of life first. You are a soul in a body & the soul is like an orb of intelligent electric energy that has no physical senses & yet it can experience what the mortal senses are experiencing when it is inside a body. As a spiritual soul you can do nothing on earth but when you are in a body you can do anything & experience everything through that body. That is what God does also. He utilises various bodies to manifest in & experiences & does everything through those bodies. So God is just the same as you or I & can do anything we can do & more. We fall unconscious for a moment when we die & yet God leaves his body in full consciousness & enters a different body. So God can do everything we can do & more. I often see God carrying a body suit around in preparation to use it to manifest in the earth realm.
There is a far deeper aspect to God & the soul that I haven't mentioned. The Spirit of God & our own souls come from bodies that are vastly superior to earth bodies. God has taken me to see it all & I have met countless people that God also showed these things to. Our souls & God's soul enter bodies & live lives in the material world & the other levels of the heavens & do & experience all things in all those worlds; & yet all of our souls are from vastly superior bodies which are waiting back at our source.
So I know from decades of vast experience that God is not limited in any way that this thread is trying to put forth. I understand your logic but it is based on incomplete knowledge & understandings & that has led you astray. You'll need to meet God in person to know more about God.
The theory (Q) is justified by its experimental test reports (P). Therefore, P => Q.
The universal claim is not justified by visiting all cases in the universe. It is justified by visiting a mere sample. That is also why Q is not provable, as a counterexample cannot be excluded. That is the essence of the scientific method.
Quoting Dfpolis
Mathematics has its own canons. Science is one epistemic method and mathematics is another. Seriously, if your only tool is a hammer, then the entire world will soon start looking like a nail.
Quoting Dfpolis
That would only lead to infinite regress. Therefore, this approach is rejected in mathematics. As Aristotle said: "If nothing is assumed, then nothing can be concluded."
Quoting Dfpolis
Maybe you should read the basic instructions of Oregon State University for freshmen novice students:
[i]What "proof" means in everyday speech:
In casual conversations, most people use the word "proof" when they mean that there is indisputable evidence that supports an idea.
Scientists should be wary of using the term "proof". Science does not "prove" things. Science can and does provide evidence in favor of, or against, a particular idea. In science, proofs are possible only in the highly abstract world of mathematics.
What should scientists say instead of "proof"?
Scientists should use the term "evidence" instead of the word "proof". When we test our hypotheses, we obtain evidence that supports or rejects the hypotheses. We do not "prove" our hypotheses.
While this may seem like a subtle difference, the words we use can subconsciously color our thinking. "Proof" suggests that a matter is completely settled, that we have had the last word on something.
...
In this class, therefore, I will ask you all to be mindful of using the term evidence rather than proof.[/i]
You seem to have missed the very basic training that was supposed to teach you not to use the term "proof" outside axiomatic derivation in mathematics.
It looks very much like the Oregon State University would disqualify you, and bar you from calling yourself a scientist.
In fact, that is a generalized problem with scientism. The worse the scientific training, the more the person becomes prone to the problem:
Scientism is an ideology that promotes science as the only objective means by which society should determine normative and epistemological values. The term scientism is generally used critically, pointing to the cosmetic application of science in unwarranted situations not amenable to application of the scientific method or similar scientific standards.
As I have argued already, mathematics obviously has its own normative and epistemological values.
Quoting Dfpolis
The statement "2+2=4" is trivially provable from Dedekind-Peano's axiomatization of number theory. Still, the fact that the statement is provable in the abstract, Platonic world of number theory does not necessarily make it correspondence-theory "true" in the real, physical world.
In fact, that is not even possible, because the numbers "2" and "4" are an abstract language objects that do not appear in the real, physical world. You can also call them "two" and "four", or "deux" and "quatre". These things are not real-world objects. They are language expressions. Since when do language expressions have physical attributes? How can something be part of the real, physical world without any physical attribute at all?
Quoting Dfpolis
The implications, i.e. theorems, are exclusively justified from necessarily following from the axioms. It has nothing to do with the real world. The axioms themselves are never justified. Otherwise, they would not be axioms, because their justifications would then instead be the axioms. That way of thinking obviously just leads to infinite regress. Hence, justification of axioms is a fruitless activity.
Quoting Dfpolis
Justifying axioms is exactly what does not make sense for mere procedural reasons. If you must justify the axioms, why would exempt you from also justifying their justifications? That approach leads to infinite regress, and is therefore not viable.
Quoting Dfpolis
The Stack Exchange question How does one justify funding for mathematics research? undoubtedly gives a reasonably good overview of why there is quite a bit of funding for reality-divorced, pure mathematical research.
One large and growing source of funding over the 20th century have been the military and intelligence departments. For example, you cannot do strong cryptography at any reasonable level without developing elaborate seemingly unrelated theorems in pure number theory.
In the link, you can see what kind of government departments and agencies subcontract research in mathematics. These grants are obviously not for plucking low-hanging fruit, such as slavishly mirroring reality.
Another funding source has been companies like IBM, who may rather be interested in fundamental computer science but often ends up dabbling in, and publishing pure mathematics. For example, Elsevier, a large academic publisher also has grants for research in mathematics.
Seriously, there is quite a bit of funding for reality-divorced research in pure mathematics.
I do not intend to provide detailed replies to each of your posts, which have become repetitive. Instead, I will simply read them to see if you've answered any of my points.
'll begin by summarizing my position. I agree that mathematics does not seek to justify its axioms. This point was made by Aristotle 2500 years ago. That does not mean that most of its axioms are not justified. They are just not justified by mathematics.
We may divide the axioms into three classes.
1. Most axioms are abstracted from our experience of nature as countable and measurable. You have agreed that this is so historically and have offered no reason why is not true today. To be concrete, children learn to count by counting particular kinds of things, but soon learn that the act of counting does not depend on the kind of thing we are counting, only that it be countable. Thus, they abstract concepts such as unit and successor from the experience of counting real-world objects. This is the empirical basis of arithmetic and its axioms.
Since we are dealing with axioms abstracted from, not hypothesized about, reality, there is no need for empirical testing for them to be known experientially. Further, since the axioms are instantiated in reality, which cannot instantiate contradictions, we know that such axioms are self-consistent without having to deduce their self-consistency.
As we can trace our concepts to experiences of nature, and since there is no evidence concepts exist outside the minds of rational animals, there is no reason to posit a Platonic world. Doing so is unparsimonious and irrational.
2. Some axioms are hypothetical.
a. Some hypothetical axioms can be tested, e.g. the parallel postulate. You have not objected to my claim that the parallel postulate can be tested by measuring the interior angles of triangles.
b. The remaining hypothetical axioms can't be tested, e.g. the axiom of choice. These are unfalsifiable and unscientific, We agreed that unfalsifiable hypotheses are unscientific. I have pointed out that as, unscientific, pursuing their consequences is merely a game, no different in principle than any other game with well-defined rules, such as Dungeons and Dragons.
Against this you claim that " Axioms can best be considered to be arbitrarily chosen." Best on what basis? What is optimizedt? If the axioms are formalizable in arithmetic, we have no way of knowing that they are even self-consistent. On my account we do. Surely it is better to know we are dealing with a self-consistent system than to waste a lifetime on what may turn out to be utter nonsense. So, how is your notion "best"?
As any knowledge abstracted from nature can be applied to nature, there is no problem with physicists using true mathematics to deduce conclusions about nature. Physics do this routinely. On you account this would be a grave error, for it would be mixing premises of indeterminate truth with premises that are true empirically. Yet, mathematical physics is one of the most successful sciences. Your theory can't explain this success. On it, what mathematical physicists do is completely unjustifiable.
The difference between physics and mathematics is not that one is about nature and the other not, but that they are about different aspects of nature. Math is about nature as quantifiable (countable and measurable), while physics is about nature as changeable, and mathematical physics is about the quantitative aspects of nature as changeable.
You object that we can prove nothing of the real world, but have provided no rational for this. You have not explained why I can't prove there are two pieces of fruit in a bowl, or that two objects and two more objects are four objects. Even if there were the mythic "Platonic World," that wouldn't mean abstract concepts can't be instantiated. In fact, the only way we learn concepts is by abstracting them from their instances. So, no more dogma. Let's have a proof if you have one.
You object that set theory is not about nature as countable, but it is. It's just not about it in the same way as number theory. This is because sets are collections of objects, and, in the context of set theory, "object," "unit," and "element" are convertible terms. That is why sets have cardinality.
The reason for Russell's paradox is not some formal problem that requires a theory of types (though a theory of types avoids the problem). The reason for it is that there is nothing in reality from which we can abstract the concept of the set of all sets that do not include themselves, just as there is nothing in reality from which we can abstract the parallel postulate or the axiom of choice. In other words, there is no (actual or potential) well-defined collection of objects (note the real-world reference) that is the set of all sets that do not include themselves.
I know that you will object that the "objects" in the definition of "set" need not be physical, but I did not claim that they were. They can be intentional beings, i.e. concepts in the minds of real persons.
Quoting alcontali
Belief need not be rational. People know they can't afford something because they know their financial situation, but buy it anyway because they want it. They allow their desire to convince them that they can afford it. There are thousands of examples of desire-based beliefs overriding known facts. Knowledge cannot be a species of belief because we can know one thing and believe the contrary. Plato did not want to acknowledge this, but it's true.
Quoting alcontali
But, confining ourselves to the formal approach you champion, we can't know that any system formalizable in arithmetic is self-consistent. So, almost any system may be trivial on you account. You need to do better. All you're doing is ruling out obvious nonsense, leaving open the possibility that all mathematics may be obscure nonsense,
Quoting alcontali
We agree, You're doing something more fundamental than a science when you examine the foundations of a science -- metamathematics or metaphysics, for example.
Quoting alcontali
Poor Pierre-Simon Laplace! Poor Carl Friedrich Gauß! Poor Jules Henri Poincaré! Poor Emmy Noether. Poor John von Neumann! If they'd only had your insight, they might not have wasted their time doing both. As with your statement about how Euclid influenced Socrates, you seem to like beliefs that ignore history.
Quoting alcontali
I said nothing about the coherence theory, which I reject.
Quoting alcontali
Non-sequitur -- as it is based on attacking a position that is not mine.
Quoting alcontali
You have no idea of what "entanglement" means, do you?
I am tired of this. Do some reflecting on what I said.
No, we're not going to get stuck. I'm not saying that your concept of a brick is whole brick. It is a projection of the brick. (Think of a projection of power.) The fact that the brick is acting on and in you by modifying your neural state does not mean that the whole brick is in you. Only a subset of what it can do is in you. Still, it is acting in you.
We think of physical objects as having well-defined boundaries, but that way of thinking does not exhaust their reality, They are surrounded by a radiance of action: they have a gravitational field, scatter light, and so on. This radiance of action is as much a part of their being as their core. If we took it away, they would no longer be the same. They would be something different. It is this radiance of action that penetrates us in modifying our neural state.
Good Op with some good reasoning.
The golden template of being having our lessor being coming from a greater Being is not what we observe hereabouts, for we note the ever more complex obtaining from the simpler and the simple, but there would seem to have to be something even behind the simplest—something eternal.
The template is also not impressive since it has to be discarded after only one usage, to avoid an infinite regress; however, this can be accomplished the way you have it, which is that the Being—albeit an assumption to have it be a person-like system of mind—is 'infinite'/'unlimited.
To have 'infinite'/'unlimited' to be substantial as a completed, finished state is troublesome, given that the 'infinite' cannot be capped as extant. There are dangers in using a word like 'infinite' as a stand-alone something or an amount/extent reachable, for its definition tends to some series or extent going on and on.
We also don't see that all was made instantly through an utmost power, but that the accumulations were long and slow, we barely making it through the great extinctions.
Perhaps I can add some support to what we might share as there having to be something eternal.
It would seem that the ultimate basis/existence needs be eternal, given that its supposed opposite, Nothing, cannot be. For those who might post about 'from Nothing', whatever appears from 'it' requires some capability/possibility/potential/random and so that would be the eternal something and so a total 'Nothing' was not had as claimed, bringing us back to an eternal. Perhaps the eternal is 'possibility', this needing only the same 'possibility' behind it.
It's still seems a bit troublesome for there to be an eternal something without its ever having been made, but with 'Nothing' out of the picture we have a mandatory eternal basis with no option, no choice; the eternal has to be; it must be. There is no selection or election.
What would the eternal be like? Well, how could it be anything specific/particular when there is no point before or outside it for it to be specified/designed? How does the eternal as something not at all particular be anything if it is so nebulous? Unknown, as rather formless and timeless, but, falling into assumption, might it have to be anything and everything?
Is the everything, then, all at once or little by little? We don't know the mode of time, whether it's of eternalism or presentism, so, we must profess our ignorance there, and other places, too.
What parallel do we have for something that is never anything particular? Well, the state of the universe never stops changing (precluding stillness), everything always transforming, even a trillion times a second, even if some semblances appear unchanging to our slow viewpoint. It can only be the eternal that is ever transforming (yet does so in a way that doesn't basically change it).
All in all, a 'maybe' is still a 'maybe', even if probabilistically unlikely, and so I'll give 'God' a generous 'maybe'.
Those who would preach either "God is, for sure!" or "God isn't, for sure!" are in line for being called 'misleading', and worse, 'dishonest'. Neither way can be honestly taught as truth.
That we can't know which is which, 'God' or not, appears to be the only truth to be gotten out of all this, but to some believers this would indicate that they cannot be blamed.
It all gets worse, due to fixed will, and that the supposed 'God' of the main religions can't be approved of, but those are other, secondary, stories, yet they hint that the possible making up of dogmas can run into grave contradictions.
Mathematical physics is still physics. It is not axiomatic. It will ultimately still be experimentally tested. The amount of mathematics used by physics does not change its fundamental nature. It certainly does not turn physics into mathematics. It just makes sure that it is incredibly consistent. It is its consistency that explains its success.
Quoting Dfpolis
That is exactly the difference.
Quoting Dfpolis
Mathematics is not number theory. Most mathematical theorems are not about numbers or quantities.
Quoting Dfpolis
You can represent a set by its membership functions and disregard what elements it contains. From there on, the paradox becomes a problem with these membership functions. The function will not manage to return a result, simply because it never stops running. That is how the problem appears when it is modeled in software. The way automated systems behave, is unrelated to physical-world problems that they would mirror, because they often don't, and in this case, they certainly don't.
Quoting Dfpolis
Only category theory is termed general abstract nonsense.
In mathematics, abstract nonsense, general abstract nonsense, generalized abstract nonsense, and general nonsense are terms used by mathematicians to describe abstract methods related to category theory and homological algebra. More generally, “abstract nonsense” may refer to a proof that relies on category-theoretic methods, or even to the study of category theory itself.
Not all mathematics is abstract nonsense, but the very best stuff certainly is.
Creatio ex nihillo was in the past. One an ongoing basis God engages in creatio continuo -- mainting conteinfent beings in existence.
Quoting Theorem
God primarily maintains His own being. Thus, Aristotle called Him, "Self-Thinking Thought." This is an immanent activity -- directed to self-perfection as opposed to a transient activity, which is directed to others. So, God's immanent activity is contingent on nothing else.
The necessity of God upon the universe is not ontological, but epistemological. Knowing the universe is sufficient to lead us to know that God exists by necessity.
I eat sandwiches for God, and so do all the other sandwich eaters. We can only eat because we exist, and we only exist because we are divine activities.
Quoting tim wood
As I discussed in my thread on the analogy of necessity, there are different kinds necessity and possibility depending on the contextualizing basis. What is physically possible can change over time, as the initial conditions do. It could also be different in other universes with different laws. What is ontologically possible is not like that. Ontological possibility is only limited by the ontological principle of contradiction. If a fully specified A is, then it cannot not-be That never changes.
Quoting tim wood
That is why we need to be very careful with out definitions.
Quoting tim wood
False. God can do anything. The problem is that contractions cannot be things
Quoting tim wood
I'm an omnivore..
Logic is as it is because, to be salve veritate (truth preserving), it has to reflect the nature of being. Being is not a constraint, because being only excludes non-being -- which is to say being excludes nothing. What excludes nothing is not a constraint.
Quoting Fooloso4
This is false. I explained, discursively, why God's essence (what He is) entails that He is.
Quoting Fooloso4
This is false.
There is no point in spending more time responding to you when you do not understand and respond to what I actually write. Two false claims are enough.
Perhaps you missed my post; from my view it is at the end of the previous page.
You are missing the point. Deductions are only sound if the premises are true and the logic valid. According to you, no mathematical proposition is true. So any argument a scientist makes using a mathematical premise is necessarily unsound.
Quoting alcontali
If you are only going to repeat you faith claims, and not try to justify them there is no point in posting on a philosophy forum.
Quoting alcontali
I did not say it was number theory. This is not the first time you have twisted my claim, saying I was talking about number theory when I did not mention it. This is not honorable. I named other areas of math, and explained how set theory was based on nature as quantifiable.
Quoting alcontali
Again, doing so leads to a contradiction precisely because proceeding in this way makes assumptions that are not based on abstraction.
Since you did not respond the main argument of my last post, there is no point in continuing. I am simply wasting my time.
Yes, I did miss it. It did not appear in my email notifications. Thank you for your thoughtful reply.
Let me say that, while I am Cristian, I don't think that we can have proof that God acts in a Christian way - that we have no proof of a "Christian God," or a Jewish or Moselim God for that matter. Belief in such a God is a matter of faith. It may be justified internally by some more or less intimate relation. Knowing that relation (an I-Thou) points to a Thou, making faith a genuine, but incommunicable, kind of knowledge. It may be justified externally, not by empirical knowledge, but by the worthiness of the commitment it calls for.
Still, I think the logic of arguments such as those of Aristotle, ibn Sina and Aquinas (and the one I posted here) is sound. Just because what logic tells us is limited, and perhaps even inadequate to a well=lived life, does not mean that it is false. So, I think we must agree to disagree. I think that we can prove that there exists a timeless Power maintaining the universe in being.
What determines the nature of being--God, or.something else?
i think the question involves a category error. Being is in indeterminate, not determinate. As what essences limit and so determine, existence is not itself determinate. It is the indeterminate power to act.
Being is some way(s) rather than other ways, no?
I'm not sure what you mean. Surely anything that can act in any way must be, and nothing can be unless it can act in some way -- for it it could not, it would be indistinguishable from no-thing.
Well, for example, you said that "Logic is as it is because, to be salve veritate (truth preserving), it has to reflect the nature of being." So you think that there's some way that the nature of being is--the nature of being has such and such set of characteristics, and not this and such set of characteristics, that are reflected by logic, right?
Quoting Dfpolis
The page in Britannica is good starting point to answer your objections:
Axiomatic method, in logic, a procedure by which an entire system (e.g., a science) is generated in accordance with specified rules by logical deduction from certain basic propositions (axioms or postulates), which in turn are constructed from a few terms taken as primitive. These terms and axioms may either be arbitrarily defined and constructed or else be conceived according to a model in which some intuitive warrant for their truth is felt to exist.
In my opinion, the premises in mathematics should be thought of as arbitrarily defined. Axioms are indeed not correspondence-theory "true":
In epistemology, the correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds with) that world.
The possibility that these premises would be conceived according to a model in which some intuitive warrant for their truth is felt to exist harks back to the core philosophy of mathematics, which is Platonism.
In Plato's Theory of Forms, ideas in this sense, often capitalized and translated as "Ideas" or "Forms", are the non-physical essences of all things, of which objects and matter in the physical world are merely imitations.
Just like in Plato's Allegory of the Cave, there may indeed be some further unspecified link between both the real, physical worlds and the abstract, Platonic world of mathematics.
I am not necessarily opposed to this view, but I think that it is, for all practical purposes, unusable.
This unspecified link is certainly not correspondence-theory "true". Therefore, for all practical purposes, it is safer to consider mathematical axioms to be arbitrarily defined, rather than somehow esoterically linked to the real, physical world.
So, yes, I maintain my position that axioms are not correspondence-theory "true".
The dominant philosophy in mathematics is Platonism, and most mathematicians subscribe to it:
A major question considered in mathematical Platonism is: Precisely where and how do the mathematical entities exist, and how do we know about them? Is there a world, completely separate from our physical one, that is occupied by the mathematical entities? How can we gain access to this separate world and discover truths about the entities? One proposed answer is the Ultimate Ensemble, a theory that postulates that all structures that exist mathematically also exist physically in their own universe.
The reason why you criticize this view is because you are not a mathematician while you insist that mathematicians should think about mathematics like you do, i.e. as some kind of theory that is isomorphic with the real, physical world. Your views are completely rejected in mainstream mathematics. It is not me who would be "repeating faith claims", but it is you who are deeply mired in your false, pagan beliefs and other heresies.
No. In all seriousness, if I had the energy I had in high school, then I might be tempted to learn about these things. As it stands now, most of my time is spent trying to figure out if everyone around me is lying to me or whether I am really delusional.
Still, these are not constraints, because they exclude no-thing.
Defining a method is not an argument justifying the application of the method. Clearly, many mathematicians are concerned the justifying their axioms. I am also concerned about this issue. You seem not to be. So, we do not share a common interest.
You continue to make unargued claims. You are attacking Platonism, which I do not hold. You are attacking my claims, not by offering a substantive critique, but by the ad hominem that I am unqualified to comment, despite having studied advanced math and its history. So there is no point in our continuing to dialogue on this topic.
So re those three statements, are they the case because God willed it so, or are they prior to God so that God has no choice in them, either?
Neither.
Nothing is prior to God, because if something were, God would be dependent on it, and so not self-explaining, Further, statements are the expression of discursive (time-sequenced) thinking, and as God is unchanging, God does not engage in discursive thinking.
The statements are the result of finite, discursive minds expressing a partial understanding of being. As all being is willed by God, His will makes the statements possible in two ways: (1) by creating intelligible being to be understood and (2) by creating discursive minds to understand it.
In sum, God wills being, and the statements are the result of humans grasping part of the intelligibility of being.
If being is willed by God, then "neither" isn't the answer. The answer would be God willed it so. But then God could have willed being so that it's other than it is, right?
Quoting Terrapin Station
If God willed "something" other than being, God would will no-thing. That is the whole point of the ontological principle of excluded middle. Being is not the kind of thing that admits of intrinsic change.
"Being" is not a definable term, as it is intrinsically indeterminate. The only way to "change" it would be to make it what it is not, viz. either not-being or something determinate -- so replacing being simpliciter with a determinate kind of being.
If you justify the axioms, then the justifications will become the new axioms. Your strategy simply leads to infinite regress. That is why the axiomatic method does not allow this. As Aristotle wrote: If nothing is assumed, nothing can be concluded.
Quoting Dfpolis
I subscribe to mathematical Platonism. However, for practical reasons, I do not make use of the possible link between the real, physical world and the abstract, Platonic world of mathematics. I rather leave this link unspecified. In fact, so does everybody else.
Quoting Dfpolis
Well, in that case, don't.
Only if the justification is axiomatic. It is not. See my new thread on the foundations of math.
Quoting alcontali
Citation? We need not assume what we know by experience.
Quoting alcontali
Which is why this irrational belief continues to find adherents in mathematics.
I have found a reference here:
Aristotle also popularized the use of axioms (self-evident principles requiring no proof), claiming that nothing can be deduced if nothing is assumed.
Unfortunately, it does not say in which one of Aristotle's books he writes this. I suspect that it must be 'Metaphysics', but I am not sure about that.
Well, if Aristotle said this -- I guess he did, and there are other links who say that he did -- he will most likely have done that somewhere in 'Metaphysics', probably, book gamma; but it could also be in 'Posterior Analytics'. So, if someone feels like scanning the text ...
Quoting Dfpolis
Can you give an example of where Aristotle does that?
What makes this the case, God or something else?
The nature of being and God IS being.
2) There's no absolute proof that there is any entity separate from and outside of existence that acts upon it. It may be difficult for us to envision that existence itself has a life of its own. It may not fit our rules of logic. That doesn't mean it isn't possible. Also, there's problems with the argument that there has to be something or someone outside of and separate from existence that acts upon it because then it begs the question of who acted upon the original actor. The premise itself is contradictory. It says that a thing can only be acted upon by an external source and then goes on to say there's something that doesn't follow those rules. It's either one way or the other.
3) Saying that people whose intuition implies there's a God are more correct than those who have different intuitions is stepping outside of logic. It's unverifiable. You are going to have millions of people who say their intuition is correct at the same time conflicting with your intuition. All that really does is produce people who are so sure of themselves that they are willing to inflict pain on people with different perspectives. That is not productive at all. People that are more humble and aren't seduced by intuitions are generally more considerate of others and others values.
So that's the same thing as saying "the nature of God" no?
Yes, as long as you do not take "nature" to entail limiting determinations.
Okay but there is a limit in that being is some ways and not others. We've already gone over and agreed that it's some ways and not others. The ways it's not are the limits.
But, what being is not, is nothing.
For example, the fact that nothing can be and not be in one and the same way at one and the same time, contra if it were the case that something could be and not be in one and the same way at one and the same time.
I understand the contrast, but not its point.
And I think there is very little we can prove if you mean "prove" in a scientific sort of way? I'm pretty sure we can't prove what you said above, though.
Perhaps belief in God can enjoy a similar kind of status without upsetting too many people on either side of the debate.