Where does logic get its power?
I like defining things so, logic: A method by which humans go from premise to premise that seems to reflect reality if the premises do. What was the "origin" of logic. Why is it that we are simply born with a "rule for deriving rules" and why does it work so well? For example, in mathematics, you CAN'T be wrong if you follow certain axioms because the axioms DEFINE what being wrong is. However you can never go back and "prove" the axioms you just have to accept them apriori. For example, no one knows why if A=B, B=C then A=C. You can't prove this axiom to be true you just have to accept it. Why is it then that humans can get by using arbitrary axioms that they are born with whose validity they cannot prove? And why is it that despite the fact that many axioms fit that description, that only very few work? Again, where does logic get it's reality-reflecting power?
I don't know if evolution is necessarily the answer here either because we don't know if logic is the reflection of reality or if reality is a reflection of logic. In other words, you cannot know whether mathematical axioms reflect reality or whether they're just the only way humans can perceive reality. "Reality" could be like a .zip file and logic our way of interpreting it. If you're playing a video game, the gameplay is not inherent in the source code of the game or in the hardware of the computer, it is an emergent property that comes from the player's and screen's limited processing power and algorithm for translating said source code
Is there any metaphysical basis for logic or are humans just stuck with a certain type of hardware
I don't know if evolution is necessarily the answer here either because we don't know if logic is the reflection of reality or if reality is a reflection of logic. In other words, you cannot know whether mathematical axioms reflect reality or whether they're just the only way humans can perceive reality. "Reality" could be like a .zip file and logic our way of interpreting it. If you're playing a video game, the gameplay is not inherent in the source code of the game or in the hardware of the computer, it is an emergent property that comes from the player's and screen's limited processing power and algorithm for translating said source code
Is there any metaphysical basis for logic or are humans just stuck with a certain type of hardware
Comments (63)
This doesn't seem like quite the right definition of logic. Logic can refer to many things, and the scope or domain of logic has changed over time. Broadly, logic refers to the rules of correct reasoning. More narrowly and more specifically, logic regards explorations of (or rather, theories about) the logical consequence relationship of some formal system under investigation, e.g. classical, Fregean logic. Given some set of assumptions and rules for allowed propositional transformations, what can be derived. That is the modern conceptualization of logic (deductive logic anyway).
Now, you ask a number of questions, which I'll assign numbers for convenience:
Quoting khaled
1) What do you mean by origin? There's the biology of logic, exploring how our logical intuitions about what follows from what developed over the eons. Particular formal systems were created by particular people. Aristotle created Syllogistic logic, Frege created Classical Logic (which is not the same as Aristotle’s), Brouwer and Heyting (more the latter) created Intuitionistic logic, etc.
2) We are not "born with" a rule for deriving rules. Lakan has some stuff on this (it's a well known book, but the name escapes me). We mostly get this stuff, er, pictorally? Might not be the best word. Observation perhaps. We evolutionarily have some dispositions built in but a lot comes from hacking together a set of intuitions based on our experience while young. But these intuitions are often very limited and even fail us often (lots of experimentation done on common logic failures people do).
It's not like we reason according to any particular logic. Hell, people always have contradictions in their beliefs (whether they know it or not). But if we were "born with" classical logic our brain would start making us believe every proposition because of the Explosion principle. It's just an example, but it generalizes. If there is a discernable logic we operate on its very weak and it needs to be like that.
3) We're not exactly born with them, certainly not entirely. And there seems to be a pretty pragmatic explanation here. If the logic we naturally develop begins failing too often we change our logic until we find one that works. Otherwise we die so there's good incentive.
4) & 5)
It's a mistake, I think, to speak of logic having a "reality reflecting" capacity. There are no metaphysical inference rules or axioms, those are formal "objects". Perhaps the best way to characterize this is as follows. If reality didn't have a structure that would be equivalent to trivialism being the case. As there seem to be propositions which are only false, trivialism does not appear to be the case, therefore reality has a structure.
Now, logical systems are structures as well (in the math sense of "structure"), and as with mathematics broadly, it's natural to think there might be [at least one] logic whose structure is "the same" as reality's structure. I suppose we might speak of an isomorphism between the structure of a logic and the structure of a universe. In that circumstance, the success of various logics in practice seems to have a transparent reason: they chart the same algebraic structure. So the relationships which hold between abstract objects covered in logic can be "mapped" to the same relationship holding between real world objects in an equivalent arrangement (it's not identity).
Quoting khaled
It's a difficult question. My best guess is the above isomorphism answer. Otherwise, I'm tempted to say speaking of logic is to categorically be speaking of something very distinct from reality. Penelope Rush has a book on this, aptly titled "The Metaphysics of Logic", though it kinda drops into the Epistemology of logic at various times. I don't think I finished it, but it should give you something. And not to be too unethical, but you can (unsurprisingly) find uploads of the book's PDF online. NAUGHTY NAUGHTY
I had similar conclusions but the main problem I find with them is how they dethrone logic so much. We both seem to have reached the conclusion that logic is: "A rule for making rules that is based off of ragtag collection of intuitions that we are born with strung together which helps us survive". You said that we are not born with logic and that we change it periodically to help us survive which I totally agree with but then that would be putting logic on the same "correctness" level as lunacy. They are both based on primordial intuitions, just that the followers of one survive and the followers of the other perish.
Quoting MindForged
The problem is, there are countless potential ways to formulate such rules and there is no meta-rule about how to do this for which there are no alternatives, at least none that I can see. The main goal for this discussion was to get people to think about such a meta-rule (A method for choosing logical axioms) for which there is no alternative. A "common ground" across all possible systems of logic if you will. Question 4 was supposed to be a trick question because what defines "work" IS the axioms of logic. You can't get an answer to "what works" without knowing something that works and you can't know what works without knowing the answer to "what works". It seems to me that the only way to develop a logical system is to pull yourself up by your bootstraps (beg the question) and I'm looking for someone to convince me otherwise
Really interesting questions. I have the view that it is misleading to try and expain logic, (or more broadly speaking rationality) as logic is what is used to create just such explanations! That might sound a bit facile, but really it's a deep issue, and also, in my view, there is often a lot of circularity or question-begging involved in such attempts.
First and foremost, I am sceptical of neo-Darwinian explanations for logic and mathematical ability. Even though I have no doubt that h. sapiens evolved along the lines discovered by evolutionary biology, I think that describing logic in those terms is an over-reach for the principle of natural selection. It is basically treating logic as a kind of biological adaptation. And indeed some of the ultra-Darwinists, like Richard Dawkins, seem to have no hesitation in considering that logic and the like are in some sense simply like a particularly splendid peacock tail; but that is because in their worldview, Darwinian theory is the basis of every aspect of life and mind. We only exist in order to propogate the genome, and everything is subordinated to that principle.
On that topic, the philosopher Thomas Nagel is of particular interest. In his book, The Last Word, he explores the tendency to 'explain away logic' in an essay called Evolutionary Naturalism and the Fear of Religion (which has been posted online here.) Nagel is particularly interesting because he's a tenured and highly-respected teacher of philosophy, and also a professed atheist, who nevertheless takes a very sceptical view of naturalism's claims to 'explain' reason and logic. He went on to publish a much more robust and controversial book in 2012, called Mind and Cosmos: Why the Materialist Neo-Darwinian Conception of Nature is Almost Certainly False .
Quoting khaled
Isn't that one of the implications of Godel's Theorem?
So, my view is that you can't explain logic - logic is what explains. That doesn't mean logic is omniscient, as I certainly don't believe that it is, but that by its very nature, it is what the rational mind uses to interpret and understand. I think a lot of modern philosophy tends to deprecate that, because the sentiment is reminiscent of the rationalist tradition in philosophy, which is nowadays regarded as superseded. But I'm not so sure.
Logic arises quite naturally out of getting into the habit of imagining nature organised like a machine. So as soon as humans were building huts with doors, or fields with fences and gates, already a mechanical conception of things was taking shape.
A switch is the canonical logical device. It is either off or on, open or shut. And doors and gates are kinds of switches. The world is divided into inside or outside. In the hut or paddock, or outside it. They are machines for the organisation of living. So the origins of logic as a useful way of conceiving of nature go right back to human technological inventions. If we could impose a rigid circuit-like pattern on the unconstrained flows of nature, then we would be laughing.
Logic thus arose as a way to regulate natural flows rather than as a close description of nature. It was a way to impose our artificial mechanical schemes on the world.
Quoting khaled
But we are not born with a brain designed to think mechanically. We are only taught from the earliest age to learn to think that way because we depend so much on artificial ways to regulate an otherwise fairly unruly nature.
It works well in that a logical turn of mind grants humans a good dose of control over material events. But also, machines are brittle things. They break very easily or can give very wrong outcomes. So strict logic - of the kind you are describing - can be just as useless as it is advantageous. Garbage in, garbage out.
Good job we do have properly evolved brains to fall back on when the literalism of logic lets us down.
This is an ancient paradox by pyrenean skeptics.
Quoting Wayfarer
But WHAT does logic explain? The paradox is that in order to answer the question "How am I going to explain" you have to have something that IS explained but in order to explain something you have to know the answer to the question "How am I going to explain". So for example, you can't say "Killing is bad because I saw someone killing someone and that is bad". That's a circular definition. If I asked you "What does bad mean" in order to make the statement "Killing is bad" you have to know what "Bad" is but in order to do that you have to know the answer to the question "What does bad mean". The point is that the axioms for any logical OR illogical system are unprovable in terms of the system
(Ok so I just typed all of this and I realized I'm just describing Godel's theorem but I don't wanna erase it so here goes nothing)
So now the question is how should one choose between these axioms? Based on survival? Why? That's just another axiom. What I'm trying to find in this discussion is an axiom that escapes this, an axiom everyone MUST accept
It's not ragtag, that would suggest the rules are arbitrary. If the rules allow us to survive and understand the world, then the justification for accepting them is straightforward. And intuitions do not themselves make the logic, they are just part of how we get started. As I mentioned, there have been many experiments which show consistent failures of reasoning that people engage in, even those with formal logic training. So our logical intuitions are not on the same level as lunacy, we can check for the usefulness of our assumptions about logic.
Quoting khaled
This doesn't seem true. Consider taking classical logic and removing the Law of Non-contradiction. What happens is the logic trivializes, every proposition becomes provable in the resulting system. That system loses mathematical structure. So there's one "meta-rule" right there: the axioms cannot on pain of absurdity result in the system degenerating like so. There's really to say on this, as I will do below.
This is mistaken, I believe. When I referred to a logic "working", I was speaking extra-logically. As in, the applicability of some logic to figuring things out in the real world and keeping us from making reasoning errors which lead to harm and such. This has no recourse to the axioms of logic determining what "working" means.
But you ask how justify logic without begging the question, basically. There's two ways I can think of how to do this. You justify a deductive logic by means of abduction, a model of theory choice. Whatever logic, in some specified domain, comes out the best on the criterion of theory choice is the correct one for the domain (we can assign them scores basically). That's not question begging, it's using a different type of reasoning.
Another way would be to pick a very weak logic which contains principles no one disputes but which does not contain principles under disagreement. Whatever that logic ends up being, it would have to, for example, have a conditional which satisfies Modus Ponens. That will be a common ground across logics that are actually used. Either of these means suffice.
Quoting MindForged
It IS entirely ragtag because any rule you choose to use as an axiom is by definition based on no other reasoning. Take the Law of non Contradiction for example. In terms of practical value this law is priceless however it IS an axiom and it IS entirely arbitrary. God could've woken up one day and decided "hey you know what, let's get rid of the law of non contradiction" and created an absurd yet consistent universe. A better example is fuzzy logic. It has no binary truth value but it is still very useful and entirely consistent. You can only say it is not ragtag to the extent that it helps us survive when applied.
Quoting MindForged
Why not? This binds our logical systems to practical value, which brings it back to the definition you started your reply with. Now logic requires neither rigor not any specific axioms, it just needs to be useful when applied to the world. It just so happens that rigor is extremely useful when applied to the world so we use that in almost all logical systems
Quoting MindForged
Again, you are binding logic to practical value which is exactly what the start of your comment tries to refute.
Quoting MindForged
Keyword: "that are actually used"
I'm not looking for a way to justify logic in terms of practical usefulness (because you can justify almost anything that way) or in terms of consensus as a result of practical usefulness. I am looking for a way to justify it that is entirely devoid of practical uses. I think this is impossible but I wanted to see other people try.
In other words my question is "Is 2+2=4 because that's how the world works, or is 2+2=4 because the homo sapiens that survived said so". I think there is plenty of proof for the latter and none for the former and I want to see if others reach the same conclusion. This is why I tell people to find me this axiom that is entirely indisputable without resorting to arguments from practicality
Logic can determine validity because of its relation to fact. Logic is the expression of the relation between the fundamental and the auxiliary; between the intrinsic and the extrinsic; between the absolute and the relative; between fact and perspective.
One of our main deficiencies is in how we define reality or how we determine what is fact. For example, many would argue that an object in their house is fact/real maybe because it has 'objective' existence or because the proof of its existence can be evident to others. However, according to me, it fails to be a fact/reality because it can cease to be that object. My definition of fact/reality is that which is; that whose value is absolute; the indisputable, the undeniable, and in that sense, it describes that which remains even when everything else ceases. For example, we may break down matter into an ever diminishing quantity and yet something is always bound to remain. That, which is fundamental to everything; that, which is absolute in its manifestation, is fact/reality. And even though it seems exceedingly abstract, we can conceive of what we refer as our world and our life as being based upon this fact/reality, which permeates and configures everything we are. Nature/Natural law(s) - or what we call the laws of existence - are the activities expressed by fact/reality and logic is the expression of that relationship between fact/reality and nature.
Mathematics, science, philosophy, metaphysics, etc., are just a few interpretations of the logic which we understand.
The best way to conceive of fact/reality is as a union of principle and potential. If we try to confine it with a form, then it defines its own limitation and ceases to be absolute.
I think the computer is based on the binary code. Both software and hardware are designed to interact through the binary code according to the relationship between physical configurations and the preset algorithms.
What will this mean in the end for me?
What will this phone and these words and all of this confusion on this website displaying the fateful hymn of the human race called Philosophy mean to me when I turn my face against the wind, on the side of a mountain toward a storm, on the side of a cliff observing roaring, crashing waves on a rocky shoreline?
The point is that logic is absolutely meaningless, as is every human invention that prolongs the inevitable point of overcoming this life and not fearing death. After such a point, everything about life is seen across an uncrossable rift. Nothing about language, too, is logical. What is logical about me adressing you right now? Nothing important about existence has ever had its foundation in logic.
I think this might prove, er, challenging. :wink: The point is that "axiom" is another word for "guess" or "assumption". And axioms are the worst sort of assumptions, because declaring an axiom says "this is a guess, but I intend to reason on the basis of this guess. So any conclusions we reach depend on our guess being true. Yes, that's right, the guess that we are unable to prove - we would if we could! - is the foundation for future reasoning.... :chin:
So, is there a guess (an educated guess, perhaps, but still a guess) that everyone MUST accept? I suspect not. Only if it could be proven could you even hope for universal acceptance. [Humans being humans, many of them would choose not to accept it anyway.... :fear: ]
Yes, that's sort of how it is. :up: Axioms are guesses, so we should not use them to justify our arguments here. And there's nothing else, assuming you don't have a provable foundation for whatever it is you're thinking about. If you did, you wouldn't fall back on axioms, right? So yes, I think logic guides us to use usefulness (or something similar) when there's nothing better available. :chin:
Isn't that just a description of hard Objectivity? Objective Reality is that which is, in my mind. But then we end up derailing this thread into the eternal subjective/objective discussion, which probably isn't helpful. Suffice it to say that your definition is superb, but unusable (by humans) and impractical for that reason. It has no value to humans because it describes a reference that is (and must remain) unavailable for comparison. A yardstick that cannot be used to measure things....
You would have indirect access, which is what we humans have to 'Objective Reality' anyway. This is why subject/object stuff gets so difficult. Our access (to Objective Reality) is indirect, and so OR is unknown to us. So we can't use it as a reference by which to judge other things. It would be ever so handy if we could.... :wink:
My understanding is that logic is ultimately based on the principle of identity: A=A. It seems impossible to mount a successful argument against identity because an argument against identity would automatically refute itself (it would deny that the argument is what it is). Not to mention that denying identity just seems plain bonkers. So, logical truths seem to be necessary truths.
Now, there are some logicians who entertain so-called "paraconsistent" logics where the principle of identity is violated. However, note that even in doing so they still rely on the principle of identity, otherwise they would not be able to make any arguments at all. In their paraconsistent logics, the principle of identity is violated only in arbitrarily selected cases, so that the rest of their logical system remains consistent and thus capable of producing arguments.
I have heard that paraconsistent logic can be useful for example in database analysis where it can come to meaningful conclusions even when parts of a database contain inconsistent information (that is, information that violates the principle of identity). By isolating these inconsistencies, paraconsistent logic can prevent them from contaminating and thus making useless the rest of the database. Paraconsistent logic in general does not say that the inconsistent information is true (although some paraconsistent logicians, called dialetheists, do make this outlandish claim).
Apparently, the principle of identity also holds in the physical world we live in, which is not surprising.
I just don't want to ground logic purely in practical survival value because then there is no stopping someone from saying "I'm going to violate the principle of identity and if it kills me, so be it". In fact that man would be just as logical as Aristotle himself. And everyone would be just as logical as a complete lunatic ultimately. I have come to accept that relativism myself but I want to see people try to refute it. Who knows maybe I'm wrong. The main point is that axioms cannot defend themselves at all and that all of our logic, morality and lives is built on them so ultimately, there is nothing stopping the murderer from killing or the lunatic from insisting that 2+2= 67. The problem now becomes self-referencing and you have to call to doubt the statement "axioms cannot defend themselves at all" because even THAT is an axiom and that's what I'm trying to do with this post. Find me an axiom that is undoubtable
Quoting Pattern-chaser
I am looking for something you must be accepting SINCE you're human. Something that can never be refuted. Something like "I'm conscious" that is actually useful. Although I see some people doubting even their own consciousness. I want something completely self evident and irrefutable.
Quoting litewave
True, but it would also refute every other argument with it. It's like an intellectual suicide bomber. You can refute the principle of identity, refute your own refutation and still be perfectly consistent in a state of eternal "I don't know". That's what the phyrrhonean skeptics did and I believe their position is the most valid and unassailable in philosophy.
Don't we all! :up: But there is no such thing in the real world, I don't think. Objectivism, and the certainty that comes with it, is an intellectual game, nothing more (to us humans). There is nothing for us such as you describe. Sorry. :fear:
It's not even an eternal "I don't know" (because that would also mean "I do know"). It's nothing. An inconsistent statement refers to nothing (its parts may refer to something but the statement as a whole refers to nothing).
You are oversimplifying the means with which we interact with reality. First, we know our perception is based predominantly on our interpretation of past experiences, which is why, we employ less restricted techniques towards discovery of the unknown. This is where conception comes in. The idea that our planet is a sphere/spherical was conceived millenia before the telescope was invented. The idea of the atom is also an approximation of what energy would be like in those circumstances. We are yet to observe actual atoms. Reason does not just employ logic to give context to past experiences, it also tries to project possibilities, and the success so far is because of the underlying fundamental unity of fact/reality which we all presume and are yet to be proved wrong.
It is unfair to suggest that humans don't have the capacity to know everything when we have a limitless potential to unfold. We are like children, we are constantly growing and learning. The coherency to the idea of a greater intelligence/system of activity which exists even in fields like metaphysics shows the degree to which we can conceive of fact/reality. Even though astrology is not dependable in the sense of constellations and the impact of celestial bodies on our behaviours, can you imagine how much information those primitive civilisations conceived of and the degree of proximity to the principles which they are based on. It is quite baffling that they would conceive of constellations (collection of celestial bodies), only for us, with the use of equipments for actual observation, to discover solar systems and galaxies. How ingenious is it for them to conceive of psychology based on a relationship of the external world and our instinctive behaviours. They may have put too much significance in the abstract but, considering how sound the idea of attitude and response to external stimuli is, all they needed was the right perspective and modern science would still be ancient metaphysics.
The limitation of perception to the bounds of experience is a significant one because it compels us to focus our efforts towards our immediate circumstances before we think to venture further. What good is there in knowing everything when we do not have comprehensive control of our persons, impulses, thoughts (biological, psychological, social, etc). Charity begins at home is based on a universal principle: you cannot see in others what you do not see in oneself. We cannot carry out conception without the development of perception, and the greater our perceptive abilities the further we can conceive.
"Imagination is more important than knowledge. For knowledge is limited, whereas imagination embraces the entire world, stimulating progress, giving birth to evolution." - Attributed to Albert Einstein.
However, without requisite knowledge our imaginings would yield little of significance.
As to the computer analogy, I think it is flawed just as the brain-in-a-vat hypothesis because they imply a separation between fact/reality and our perception of it. What we perceive is an expression of fact/reality not something disconnected or veiled from it. Someone said, "a logician could infer the niagara or the pacific ocean from a drop of water," the same applies to observing a computer screen or from the perception of an expression of fact/reality. If it hadn't happened, we would not be having these kind of discussions.
Quoting BrianW
It's a conceptual yard-stick e.g., ethics/morality, whose value is symbolic and only manifests in practical reality according to our understanding and consequent application of it.
By what is meant by "facts", there can be no such thing as mutually-contradictory or inconsistent facts.
Just by what our words mean, no proposition can be true and false.
The consistency-requirement is inherent in facts and by what we mean when we speak.
Quoting khaled
But that's true of the whole structure of what describably is. Logical relation among propositions. ....abstract implications. It's a basic structural property of the whole system of what describably is, that there's no proof (and usually no reason to believe) that the antecedents of the abstract implications are true.
For example, when I describe my metaphysics, describing the describable world (including our physical world) as consisting of abstract implications, I emphasize that there's no reason to believe that any of the antecedents of any of those abstract implications are true.
A true mathematical theorem is an abstract implication whose antecedent consists (at least in part) of a set of mathematical axioms.
There's no proof of the truth of that antecedent (the axioms, and whatever else is in the antecedent).
(But, as you know, different axiom-systems choose their axioms differently, so that what is an axiom in one system is a theorem in a different system, and vice-versa.)
That's not just how it is in mathematics. It's true in general, in the describable realm, where there's no reason to believe that any of the antecedents of any of the abstract implications are true.
What there describably is:
Worlds of "If".
Instead of one world of "Is", infinitely-many worlds of "If".
Michael Ossipoff
An analogy is only that. I think you read more into it than an analogy can usefully support. As for brain-in-a-vat, the most important point in considering it is that we can't know - ever - if it's correct. And this is because the relationship between "fact/reality and our perception of it" is unknown and unknowable to humans. "Fact/reality" = Objective Reality. Our perception shows us (interactive) images of a world - a consistent, testable and comprehensible world - whose relationship to Objective Reality cannot be known. So I don't think we can meaningfully or usefully assert anything about whether these two are separated or not. We don't know. Sadly. Hey-ho! That's life! :smile:
Why then are some theories about reality better than others? For example, why is theory of relativity better at making predictions than Newtonian physics?
Because "some theories about reality" are "better than others"? Don't forget reality is the reference; we just try to curve-fit our data and our theories to it. Some just fit better than others, so they're 'better' (i.e. more useful) than others.
Quoting litewave
Because its predictions are more accurate in a wider range of circumstances? :chin:
Sorry, this doesn't answer your question. You asked "why?", but I don't think there's an answer to that. If there is, I don't know it, and can't imagine what it might be. Sorry. :up:
So, you said it yourself - some of our theories apparently fit reality better than others. So the relationship between theories and reality is one of "fitting", or correspondence.
First, I should repeat that we are like children, constantly growing and learning. Therefore, we may not understand everything about the relationship between fact/reality and our perception of it but it is possible to understand some of it. And from the tidbits we understand, it is possible, as some have tried, to infer of the whole, which is one of the applications of logic.
Nature or the laws of nature is that relationship between fact/reality and its many manifestations. Logic, on the other hand, is the expression (or mode of activity) of those laws of nature.
We interact consciously with the many manifestations of fact/reality which we recognise and we attempt to translate the logic expressed into the mental language we possess. It's not that we're incapable, it's just that the job is still in progress (and considering the extensive nature of fact/reality, it may be a perpetual engagement).
When we refer to fact/reality, we always mean the concept not the actual. It's like when astronomers show an image of a galaxy, it's just a model/representation (a decent approximation) but not the actual galaxy. It's the same with our reference to fact/reality - we can conceive of it to a considerable extent even before we experience it. For me, that's one of the utilities that logic presents to us.
We can put it even more simply than that. We create the theories, then test how well they predict the future behaviour of (some aspect of) reality*. The best theories are the ones that best predict.
* - I'm trying not to derail into an objectivity/subjectivity debate, but our relationship with Objective Reality seems to have crept in, and we don't know what that is, or might be. The 'reality' we see in the mental images in our minds may or may not correspond to Objective Reality. We don't and can't know. When I refer to "reality", I refer to these mental images. N.B. I do not assert anything about the source or cause of those images; I define the Apparent World in terms of those images. I define "reality" (i.e. the Apparent World) from within the mind of the human doing the perceiving, because it's what we know. Objectively, all else is pointless speculation.
That is not true, I gave you a perfectly clear reasoning that didn't use the rule. If the Axiom results in trivialism, it cannot be admitted on pain of absurdity and meaninglessness. Avoiding triviality is not arbitrary.
Quoting khaled
Using that axiom is not arbitrary. If you take any logic which validates the Argument from Explosion, asserting a contradiction results in triviality: everything becomes true whenever a contradiction is introduced to an Explosive logic. So again, we have a perfectly non question begging reason to adopt Non-contradiction. And no. If a universe "lacks" Non-contradiction (whatever that means) then the universe is necessarily inconsistent. Inconsistent means contradictory, so your claim is just false.
Quoting khaled
The metatheory of fuzzy logic is classical logic. People don't really use fuzzy logic anyway. It might be useful for some applications but as I said, to actually construct the formalism for fuzzy logic you have to apply classical logic in the metatheory.
Quoting khaled
It's not mere practical value, a trivial logic has *no* value because it has completely dissolved the barrier between truth and falsity. A logic which is trivial leaves no mathematical structure because it has no limitations, it is excessively powerful and thus cannot be applied to anything because it literally tells us that every sentence is true. That is a meta requirement which does not beg the question and which is not arbitrary.
Quoting khaled
I'm not binding logic to anything, I'm pointing out a common motivation for why we bother constructing such formal systems in the first place. And I certainly didn't refute that in my first post. As my first post says,
Quoting MindForged
Practicality plays a role, but it's not the only role.
Quoting khaled
I already told you two ways to do this:
Quoting MindForged
That's how you justify logical systems without begging the question or being entirely arbitrary.
Quoting MindForged
Why not? Why should we avoid triviality?
Quoting MindForged
Inconsistent wasn't the right word here sorry. I meant feasible
Quoting MindForged
People do use fuzzy logic in many many applications such as "facial pattern recognition, air conditioners, washing machines, vacuum cleaners, antiskid braking systems, transmission systems, control of subway systems and unmanned helicopters, knowledge-based systems for multiobjective optimization of power systems, "
Source: first site that pops up when you look up fuzzy logic uses.
Not only that, but the fact that fuzzy logic shares some axioms with classical logic does not in any way indicate that those axioms are to be shared by all systems of logic. That is a genetic fallacy.
Quoting MindForged
Yes and the common motivation you pointed out was: So the system doesn't blow up. But as for why the system SHOULDN'T blow up you've given no answer. You've simply asserted "the system should not reach the point of triviality" but you've never said why and the only reason I can think of is practical uses.
Quoting MindForged
Oh really? What else plays a role?
Quoting MindForged
The fact that no one disputes them is no proof of their validity.
Quoting MindForged
What are the criterions of theory choice? Because as far as I know that's a matter of opinion and practical utility. One might choose to use the most elegant theory, the most accurate theory, the easiest theory to use, etc. https://en.m.wikipedia.org/wiki/Theory_choice
The criterion of theory choice are, guess what, purely practical
If it's consistent, what's the problem? Logic is intact.
Because triviality is incoherent. It dissolves all conceptual barriers, prevents any kind of analysis or understanding, leaves the resulting mathematics without any structure at all. It is true absurdity.Quoting khaled
Incorrect. With the exception of knowledge based systems (e.g. SQL), all those examples use the Boolean logic which is just a physical implementation of classical propositional logic. Don't bother with Google search results that don't go into any specificity, those things you mentioned are based on classical computers, they utilize classical logic.
Quoting khaled
I did not say that. First off, I wasn't talking about the axioms of fuzzy logic, I was talking about the metatheory: the language/logic within which you construct the logical system in question. For fuzzy logic, it requires assuming classical logic. Other logics (e.g. Intuitionistic logic and paraconsistent logic) can avoid this classical assumption in their metatheory, but fuzzy logic cannot.
Quoting khaled
I did answer why, repeatedly. It becomes completely incomprehensible *in principle* and loses any possible use towards anything, whether practical or theoretical. That's why triviality is, in logic, also referred to as absurdity. It has no structure to it, it's just the arbitrary entailment of every sentence.
Quoting khaled
Theoretical virtues: simplicity, fruitfulness, adequacy to the data, lack of ad hoc elements, unifying power, etc.
Quoting khaled
You asked for their justification. Validity is a separate notion that requires already making assumptions by which validities can be derived. If no one can agree on any assumptions (which never actually happens) then the conversation is over, there's no common ground to work from. Assumptions are necessary.
Quoting khaled
I listed them earlier in this post. And they're not just practical utility, you yourself just mentioned how they make theories more elegant, which is not necessarily a practical thing. And it's certainly not a matter of opinion. A theory which has equal explanatory power to another theory but which makes an extra ad hoc assumption is a worse theory because it contains an assumption that is not needed to explain the data. It would not be mere opinion to point out that flaw, it's just the truth.
Quoting MindForged
That is a practical consideration. As I've said before all of your explanations as to why we should avoid triviality are practical explanations. If triviality one day proves to be a more useful form of logic we will switch to that.
Quoting MindForged
All of these are practical virtues. They are virtues because they are useful. I don't mean practical as in used in physics, I mean practical as in both theoretically and physically applicable
Quoting MindForged
Yes and the problem I'm having is that there is no reason for anyone to agree on assumptions that is not itself an assumption
How does it have anything to do with practicality? If you apply a trivial logic to purely theoretical problems (pure mathematics, for instance), it's just as useless (due to its incoherency) as it would be in practical matters because it forces you to derive every sentence as a theorem so you end not getting a answer that can be understood in principle. It cannot be more useful because it asserts that everything is true. There is no possible circumstance or theoretical issue where that assumption is a more useful, because no possible state of affairs or problem which can be answered or understood by recourse to pointing at every sentence.
Quoting khaled
No they are not, they are literally theoretical virtues, properties of theories. People, due to practical necessity, make arbitrary assumptions all the time. In science, or whatever other field, that's a black mark on a theory. You are just labelling random things "practical" with no explanation. These virtues apply to theories in pure mathematics as well, and by definition pure math has no known application to physical reality or practical use (otherwise it becomes part of applied mathematics).
Quoting khaled
Except for avoiding triviality, except for practical use (or even practically necessity), except for understanding the structure of the actual world, except for developing good theories as opposed to bad ones, etc.
When you’re asking why such thing as the law of identity holds, you can’t avoid a circular argument, because in order to explain why anything is the case, the mind needs to be able to grasp such things as the law of identity.
I think what you’re grappling with, in very high-level terms, are the ‘transcendental arguments’, which are that ‘X is a necessary condition for the possibility of Y—where then, given that Y is the case, it logically follows that X must be the case too.’ ‘X’ here is ‘the ability to recognise logical propositions’, and ‘Y’ refers to the existence of logical propositions. So, in this case, in order to know that there are logical propositions, you must be capable of knowing what what a logical proposition is. And understanding why we know such things, is a much more complicated issue, I think, than is assumed when you analyse the problem in terms of adaptive necessity.
Quoting khaled
How does ontology come into it? It’s a question of semantics. Because A! Is a different symbol to A, then there’s no reason to assume it means the same, unless you designate the exclamation mark as meaningless.
I just explained why. A trivial theory loses ALL meaning, it's literally meaningless and without structure. It can't be used for practical or theoretical purposes. That's been my repeated explanation, it's not a practical justification.
Quoting khaled
If the theory isn't consistent and Explosion is valid, then the theory becomes meaningless and thereby cannot be used for anything practical or theoretical. And you don't have to have an understanding of the natural world. But then no one will want to communicate with you in any capacity so it's a pointless conjecture. All you're really doing is asking "But what if I wasn't interested in that?" A question which is of no interest to anyone but yourself. I've already justified having a non-trivial theory above, you just keep misrepresenting or ignoring what I say.
Quoting khaled
If your point is that there's no necessity in having any particular goals then you're shifting the goal posts and are in fact doing exactly what I just said: You're complaining that there's no purely logical reason to have some goal or other. That's a matter of what interests you, but good luck finding people who have no interest in having a non-trivial understanding of the world or who completely dissavow all meaning of everything whatsoever (otherwise known as trivialism). It has nothing to do with self-justification, that's a fool's errand. It doesn't exist.
Quoting khaled
Um, they are ontologically distinct. "A!=A" provably leads to a contradiction, and thus (in Explosive logics) it entails triviality (total meaninglessness). We can sensibly speak of objects which lack identity (see Non-reflexive logic), but it has nothing to do with negation. If you have non-self-identical objects they are ontologically very different than self-identical objects, surely this difference is obvious? One has the property of self-sameness and the other kind of object lacks that property, they are qualitatively different. The reason Identity wins out is that even if we take into account the possible existence of objects that lack ontological individuation, any object we actually deal with practically and in mathematics do have identity, so it just makes sense to preference that. Quantum objects lacking identity just won't be relevant to almost anything else ever. And besides, QM is rather new so prior no one really could conceptualize how an object could even lack an identity. So yes, that was a good reason to hold to it if one seems to find it impossible for it to be otherwise.
They could be wrong, sure, but unless you can give good reason why they are (or why they could be) wrong then you might as well just make fart noises. Simply objecting to something is not a reason to consider that thing is incorrect.
I never did lol. Its more like evolution of ideas rather than biology. So for example evolution from "the earth is flat" to "it ain't"
Quoting MindForged
Yay you agree. I was simply pointing out that which axioms you choose to adopt cannot be determined without the use of other axioms so you ultimately end up with an arbitrary logic. The only reason the law of identity holds as you've said is because
A) not having it would result in an incoherent and absurd system of logic and
B) a system of logic has to be coherent and consistent
My point is you cannot get A from B nor B from A and so one should just admit that they're both arbitrary because they are. You justify A using B then claim that everyone has B. While that is true, I'm trying to find a way to get B that does not rely on consensus, pragmatism or arbitrariness (thus the title of the discussion: where does logic get its power. So far you've clearly shown that everyone has B but I'm asking WHY everyone has B and you cannot use an answer that refers to C if C is also as arbitrary as A and B)
I think we disagree on the meaning of arbitrary. I use it to mean "has no proof"
Also what's that whole paragraph about QM? What does QM have to do with anything
Fuzzy logic simply introduces grey to an otherwise black-and-white scenario. It is implemented using "classical" (Boolean) logic, because that's what it was created for. In its most recent incarnation, fuzzy logic allowed programmers to code for decision-making that is not limited to two truth values, but exists on a spectrum where TRUE and FALSE are merely the extremes, not the only possible truth-values.
In circumstances where truth-values exist on a spectrum, people do use fuzzy logic.
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In my previous reply, I told why I don’t think logic has that problem. It just comes down to a consistency-requirement. Need it be proved that there aren’t mutually contradictory or inconsistent facts, or propositions that are true and false?
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That consistency requirement is built-into your experience-story, because any definite yes/no matter is, tautologically, one way or the other, and that doesn’t need proof.
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What I was saying that the describable world, including our own physical world, consists of systems of abstract implications, and that our own physical world consists of a complex system of inter-referring abstract implications about hypothetical propositions about hypothetical things (with the many consistent configurations of mutually-consistent hypothetical truth values for those hypothetical propositions).
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…and that there’s no reason to believe that any of the antecedents of any of the implications are true. I suggest that they’re false.
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In my other reply, I made a false analogy between that and the mathematics axioms. As you’d surely agree, no one would say that the axioms of the number-systems are in doubt, even though they’re stated as unprovable axioms.
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You mentioned an axiom that, if A = B, then B = A. I don’t think that has to be regarded as an unsupported axiom. Instead, just say that, for some un-ordered set containing two elements, both elements are the same as eachother. That’s all that need be said. This asymmetrical wording “A = B” as opposed to “B = A” is just a writing-convention (because we write in a line) that makes it look like two different or separate statements, when they’re both just ways of saying: “The elements of that un-ordered set of two elements are the same thing.” The illusory problem results from the fact that we write along a line, always writing one thing before another thing.
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Likewise the additive commutative axiom: Just speak of combining the two numbers. The apparent need to write one number before the other is just a consequence of our writing in a line. That matter of the order in which the two numbers re written is an unnecessary artificial concern. So the commutative axiom for addition is obvious too. The algebraic symbolic language for addition is intended to model the cardinality of the union of two sets whose cardinalities are known.
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Of course with some other element-sets and operations, such as some groups and their operations, commutativity doesn’t apply, because it’s a different kind of an operation, an asymmetrical one in which the two elements it’s applies to don’t have identical roles or treatment.
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Anyway, the matter of the number-system axioms and the more general matter of the antecedents of the abstract implications that I spoke of aren’t the same. But, as I said, a true mathematical theorem is an abstract implication whose antecedent consists, at least in part, of some mathematical axioms.
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My main point in my other post was just that, because of the not-necessarily-true (probably false, I’d say) antecedents of all those abstract implications that I claim are the basis of our physical world, then having to just accept axioms in mathematics, and have only implications based on an unproven “if “, doesn’t sound so bad, when one considers that that’s just the way things are throughout the describable world. So mathematical theorems’ conclusions (or consequents) are a matter “if “ like everything else in the describable world.
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Michael Ossipoff
Quoting Michael Ossipoff
Yes. Or else you'd never know it was true. All you'd have is an intuition that just happens to work very very well and I'm trying to ask where that intuition came from
Quoting Michael Ossipoff
I know. It wasn't intended to "sound bad" I'm not trying to slander science and math. I'm just wondering where all of these basic axioms came from (axioms such as "there aren’t mutually contradictory or inconsistent facts, or propositions that are true and false"). They clearly are not provable but they work so damn well it's a miracle.
Here's something that I said:
A tautology just tells another way of saying the same thing. Such a statement is its own proof, and needs no other proof.
Michael Ossipoff
That's not what I said, I said one's goals cannot be reached by pure logic. The axioms one adopts can be done so rationally (non-arbitrarily), as I gave two means by which to do so.
Quoting khaled
Then as I said you're just pointing out an is-ought distinction. The ought has nothing to do with the logic itself, it regards the normativity of logic. And unless you completely disavow all normativity your argument really seems besides the point. Even just considering the logical formalism itself, a trivial logic is without use or understanding in any circumstance. Everyone rightly assumes you care about what the words you say mean when you use logic because otherwise your communication would be ineffective.
Quoting khaled
A & B are the norm precisely because there would be no point in having one without the other. If you don't care about being coherent at all there'd be no reason to construct a coherent logic, and vice-versa. I've given non-arbitrary, non-pragmatic, non-consensus answers. Recourse to models of theory choice (abduction) is not arbitrary nor any of the others characteristics you mentioned.
I would still put both of your answers under pragmatic.
Let's define pragmatic here just to make sure we're on the same page: Accepted for a reason that is not logical proof
Quoting MindForged
How can you reach axioms to adopt without starting with certain axioms. Logic requires premises. You can't reach a conclusion without premises. I am pointing out that there is a near infinite number of premises you can start with. Both methods you have highlited adopt certain premises themselves.
For the first, using a model of theory choice, you'd have to choose WHICH model to use. That cannot be determined by the models themselves. There are multiple theoretical virtues such as elegance, accuracy, complexity, number of assumptions, etc. You only pushed the problem one step back so now instead of deciding what premises to base my logic upon I know have to decide which criteria to use to decide which premises to base my logic upon. You ultimately still need an arbitrary pivot.
The second is literally the definition of consensus based logic.
Quoting Pattern-chaser
Quoting BrianW
So when I ask you "Am I a brain in a vat?", hoping to take advantage of your apparent access to Objective Reality, you're going to ... refer to your concept of what OR is, and let me know what you think the Objective answer to my question might be? No, I'm sorry, it doesn't work like that. The only piece of Objective knowledge you own - the only piece you ever can or will own - is that Objective Reality exists. You can say nothing more about OR than that. Your "conceptual yardstick" is an attempt to justify some sort of access to OR, when you have none. None. :up:
Objective knowledge is not subject to doubt or challenge; it has only one possible truth value. Please do not pretend to Objectivity, hoping to lend to your outpourings the infallible authority of Objectivity. Your outpourings have no more authority than mine or anyone else's. Sorry. There is no Objectivity for a human; none at all. [Apart from OR actually existing.]
Well evolution presupposes they exist. Evolution has a general linear A to B timeline. So natural selection is saying, this is the way the universe is and now you have matching mental apparartus. I don't think logic is a peacock tail. Now I do think a lot of mental properties might be peacock tails but it would derail this thread if we went into it.
If logic was purely the result of biology then it would be some form of idealism where concious minds are literally remaking the world as they come into being. I don't think that is correct. I think the common sense intuition is probably right even though it goes against relativity. The brain does piece things together into a coherent reality but I think it's matching an existing reality with logical rules already in existence.
Yes. Fuzzy logic was, as I understand it, a means of programming a more flexible arrangement than two-valued logic, using what is available, which is binary logic. It's a way of allowing a computer to reflect real-world conditions that don't really match the computer's inherent abilities. It's a practical compromise.