Infinite casual chains and the beginning of time?
Popular in philosophical discussions about the universe and thusly also factoring into apologetics/counter-apologetics has been talk about whether the universe is finite in time or without beginning. Usually the arguments for time/casual chains without beginning play on the possibility or logical coherency of such ideas as they aren't logically incoherent (see William Lane Craig for objections to this) so it's at most possible such a series lead to our universe as we know it. There have been other varied renditions of these concepts which play on different philosophical convictions or traditions.
Such as:
What are your thoughts on this concept?
Such as:
- In neo-thomism or scholasticism, which has begun to gain traction recently in a modern formulation, such philosophers make a distinction between accidental versus essentially ordered series. The first has it, almost as a trick of our need to find patterns in the world, that a series of events would still occur even if one entity in the series was erased. Essential series require it to be the case that if you removed one previous element or in this case for the universe we can speak of events then the whole series would fall a part right then and there. Here is a video that goes over it.
- Another concept involved in this is the idea of super-tasks or that despite not having a beginning an infinite amount of time could have traversed until we were met with the current moment.
- As I was discussing in another thread, whether you accept time realism or anti-realism also greatly affect the way we formulate or understand the beginning of time. Incorporating the philosophy of time into this discussion including questions of its fundamental nature such as whether we adopt A vs. B theories of time, the relationship to change itself, and its discreteness.
What are your thoughts on this concept?
Comments (267)
Just idle chatter . . . pay no attention to that men behind the curtain. :nerd:
Quoting substantivalism
This more or less coincides with Stanislaw Lem's Ergodic theory of history. Some movements in society are so powerful that changing bits here and there have no appreciable effect. On the other end of the spectrum is the Butterfly effect.
The Page-Wooters mechaism is a fascinating phenomonen. It suggests time is a local phenomenon associated with quantum entanglement. An elapse of time is experienced by observers within a quantum system, but external observers to not observe the elapse of time within the system:
In 1983 theorists Don Page and William Wootters suggested that quantum entanglement might provide a solution to the Wheeler-DeWitt “problem of time”. When quantum objects are entangled, measuring the properties of one changes those of the other. Mathematically, they showed that a clock entangled with the rest of the universe would appear to tick when viewed by an observer within that universe. But if a hypothetical observer existed outside the universe, when they looked in, everything would appear stationary. -source
I'm aware of no metaphysical analysis that would have predicted this, nor that even attempts to account for it. Hence, I suggest metaphysics is futile for understanding it.
Is this exactly the case? I thought it was a bit more complicated than that, but I am not a physicist and could be mistaken. Kenosha Kid? :chin:
It's easy to drift into quantum mysticism with topics like this.
Why?
Quoting Gregory
As does creatio ex nihilo or a beginning for a universe on my end. Both circular repetitive cycles of creation, infinite casual chains, or creatio ex nihilo are equally illogical.
Time as an abstraction you mean. Change is rather fundamental to reality as we know it, especially in quantum mechanics, and time (as in its ordering, simultaneity, asymmetry, the future/present/past existence) could be emergent from such an analysis.
Quoting Relativist
As carrol once said, I believe, "our metaphysics must follow our physics." Recall that we, however, should not postulate mechanisms or theories that may outright contradict our experience. Also, metaphysics may not have discovered it but it damn will analyze the hell out of it. Interpretations of scientifc theories don't come out of experiments but our formed afterwards and preemptively.
There is no mechanized or unmechanized minds in your sense. Only what part of reality is from you and that which isn't.
OK. I take it you are a physicist.
If we’re calling into question “The Big Bang”, indeed “where” did the singularity from which the creation of all matter sprang come “from”? If “where” didn’t exist before The Bang occurred, then neither did “when”. This implies time has a beginning and is therefore finite. Perhaps the term “forever” applies, but that is a time reference. Eternity is not equal to infinity.
Why? Back to our definition of infinity, and I’d appreciate feedback on this. I interpret infinity as “boundlessness”. Expressed in terms of spacetime, no matter how large something gets, it can still get larger; no matter how small, still smaller. No matter how far back in time you go, you can still go back farther; no matter how far forward, still farther.
We know material objects, such as humans, have beginnings and endings. By extension, so do planets and solar systems and galaxies and galactic clusters... ad infinitum. We know “all times exist all the time”. Again, by extension, would that not imply all “places” exist “everyplace”?
Time and space, as we finites experience them, don’t adhere to the same physical “laws” at the quantum level as what we consider immutable in our macro realm. If time, as Albert Einstein suggested, is a “stubborn illusion“, and reality, as Werner Heisenberg suggested, is dependent upon the observer, then the entirety of existence, in all its forms, is interpretive.
Spacetime is a finite system. Infinity, by the “boundlessness” definition, renders space and time meaningless. The only absolute is infinity. And if indeed infinity is a thing, then its definition not only implies, but insists, that everything MUST exist.
Any and all, please weigh in...
Your post is Spninozian. But I object to the ending when you say infinity implies necessity
It's close enough. If you have two entangled electrons for example, one is guaranteed to be spin-up and the other to be spin-down, but it's not defined which is which until you observe them. As soon as someone observes one of them to have one spin, it's guaranteed that the other will be observed to have the opposite spin. Regardless of distance or who observed which first, which itself is not even well-defined because from different reference frames either observation event could be considered "first".
Thinking of it in terms of one observation causing the other to change isn't quite accurate though, because what's actually happening is that by observing one particle, you're now entangled with it, and when you observe the other particle, or someone telling you what they observed the other particle to be, you're guaranteed to see a universe consistent with the other particle having been the other way, because the whole universe that you observe, containing both particles and anyone who's interacted with any of them, has to be entangled with you and the rest of everything you're entangled with, and so consistent with one particle being one way and the other particle being the other way.
(But actually, on any reasonable, non-Copenhagen interpretation, the particles are each really both ways, and you and the rest of the universe that are entangled with them are in a superposition of states corresponding to having observed the particles being one way or the other, but in every state the particles are consistently opposite each other).
I was 8 years old in 1963 when, while watching the premiere of The Outer Limits, the “Galaxy Being” said, “Infinity is god”. That has resonated with me since. Like you, I tend to dispense with the strictly-human (read: religious) definition of God as a single entity, or Trinity. My definition of the universe is, a multi-dimensional holographic projection of consciousness. Whose consciousness? ALL! Erwin Schrodinger said, “There is only one Mind”. That needn’t be “God”, though humans seem to need to believe they were “created” by a so-called higher power. Why cannot we all revel in the idea that consciousness, and not physicality, is the foundation of existence? And, being infinite, said consciousness is not limited in form.
I agree with you that human science is stuck in a rut. If we can’t perceive something with our five physical senses or extensions thereof, we cannot rely on its existence and, at best, it becomes a variable in our equations; at worst, it is ignored. Belief - faith - isn’t necessary if you KNOW “the secret of life, the universe, and everything” (Douglas Adams) resides within all of consciousness, of which we as humans share access. How much access? As much as one seeks. Some use science, others religion. Both are inadequate even when combined, in my opinion.
So, my suggestion to anyone willing to consider, question everything you’ve been taught, be the unique individual you are and revel in that uniqueness, and devise your own perspective rather than subscribe to a collective way of thought. That contributes to the expansion of consciousness rather than echoing the same thoughts as others.
As a clarification, I am not familiar with Baruch Spinoza, but thanks for the reference.
Also, please elaborate: WHY do you object?
I agree partially with your stance. Even many scientists, as you said a couple of times, say we create the world. But I don't believe anything is necessary. If thoughts of necessity are Platonic in nature, I consider that spiritual but not realistic. You know that feeling you get when your with a romantic partner early in the courting, kissing in the dark at a park, and watching the stars? You can feel the contingency of everything. Sinatra captured that feeling in some songs. I think that is reality. Every thing is contingent and there is no reason for the necessary except as a mental escape. There is some book on Amazon, I think it's called Necessary Being... But I don't buy it (pun intended)
Yes, that's what I was getting at. Thanks for your comments. :cool:
Douglas Hofstadter I think argues in his books that we can avoid paradoxes in set theory (and Godel too of course) by realizing we are not mechanized thinkers. Our intellects seem to have something substantial about them that avoids strict mechanism. This might be connected to the mystical part of the mind. (It's all quite complicated) Also, like I said, physicists are never going to find the physical mechanism by which the world started. They are starting with the wrong basics. Time and again they have tried to drive the truck around the turn but it always turns over, as a Thomist once told me. Thomas Aquinas's argument was that an infinity of past events cannot stand on it's own. It needs to rest in a mind. That makes sense, but I don't believe in an infinite universe anways. As I said, I take a more Heideggerian approach to the beginning of the universe. Think with primordial thinking, as he says
There is nothing to say that it's necessarily infinite or finite. These are epistemological questions concerning the nature of our universe.
Quoting Dan Cage
The singularity didn't ever come into existence because if take on a bastardized substantivalist perspective spacetime then there was never a time when matter didn't exist. Also it's not a big bang its a big everything got really close to everywhere else but didn't pop out of existence at any time because for all the time that existed it also existed. Eternity implies that "for all time" it existed which could mean while time existed or given an infinite past. You are making quick use of a substantivalist perspective of time here though, use change instead to justify these perspectives.
I agree science cannot deal with creatio ex nihilo but nor can philosophy/metaphysics as such a concept is to me rather illogical. The problem for you here is assuming there was some time when stuff just didn't change (like before the big bang) then it started to change at t = 0 which isn't what a substantivalist interpretation of general relativity is implying. There are no times before t = 0 and no time when the universe went from timeless to changing which would mean some meta-time existed before the singularity, that's adding on more physics than is present within the theory. By all means go on to do so but you're now dipping into theoretical/experimental physics which requires an inductive verification or falsification.
Do mean extension or temporally? If temporally that's fine but to assume a finite scale to the universe either puts us in the direction of a curved 3-sphere (curvature we have measured means it's close to being rather flat) or is literally finite in extension in all directions but this is rather strange.
Are you partial therefore to process philosophy or a modern rendition of Heraclitus perspective of the world as in constant flux.
I love Heraclitus. Someone can regard a jungle as entity, or a branch of a tree. It's all about one's personal perspective. The world has all the reality it needs to exist on its own while remaining contingent. That's what I meant when I said the world is neither contingent nor necessary in the Thomistic sense. Also, I feel like using curves at the beginning of the universe is no more useful than string theory. One leads to circular regression while the other leads to infinite past universes. I doubt you can demonstrate the mechanism of the origin using only science.
Finally, I wanted to say I smoked some bud a few minutes ago and it immediately accord to me that time goes on forever and should reach an infinity but cant. Therefore logic says the universe will end
I think this is actually the opposite of reality. Analysis of the problems which physics encounters with its representations of time, juxtaposed with the firmly established metaphysical conceptions of causation, is what develops insight into the nature of time. Physicists do not value metaphysical conceptions, metaphysicians do.
I'm open to considering the value of metaphysical analysis in this regard, but it was physics - not metaphysics- that showed time is not absolute, that it is relative to a reference frame (i.e. special relativity). It is physics that showed space and time are coupled, and identified the "problem of time". And it's physicists who are exploring what may be the fundamental basis of time.
What specific insights have metaphysicians provided regarding time?
That physics has identified a "problem of time" demonstrates that the principle they apply, are deficient. The "things" that you say physics has shown about time are the things which lead to the "problem of time", which demonstrates that despite your claim, these "things" are not truths. They are simply useful principles which are limited in their application, demonstrating their deficiencies.
Quoting Relativist
We could begin with the way that we apprehend the substantial difference between past and future. The past consists of events which have actually occurred, and the future consists of events which are possible, as indicated by human behavior. This means that the present as what divides future from past, is ontologically significant.
I agree the "problem of time" implies deficiencies in our concept of time, but my point is that metaphysical analysis would never expose the deficiency.
Quoting Metaphysician Undercover
Yeah, right - no one noticed a distinction between past, present, and future before some metaphysicians pointed it out.
Metaphysics consists of conceptual analysis, and in that regard it can help identify implications of concepts, but the paradigm shifting breakthroughs regarding our understanding of time has been a result of advances in physics - not metaphysics.
Isn't this a metaphysical analysis which is exposing these deficiencies?
Quoting Relativist
Seems you don't know the difference between physics and metaphysics.
Quoting Metaphysician Undercover
Feel free to enlighten me. My impression is that one could say physicists engage in metaphysics when they develop concepts (like the curvature of space and interpretations of quantum mechanics). If you'd like to divide the work of physicists this way, I have no objection, and I think philosophical reflection is important. My main issue is that the relevant paradigm shifts only occur because of new physics, not because of this philosophical reflection. My initial comment in this thread was: "I don't think metaphysical analysis can provide definitive answers about time. On the other hand, physics may develop insight into its nature"
And I haven't seen any reason to think this isn't true. That doesn't mean philosophical reflection can't be of use, but given the weird things we've learned about time through leading-edge physics, it seems unlikely philosophical reflection alone can solve this.
Technically that is just one metaphysical or philosophical interpretation that we could glean from special relativity. Ignoring whether time in that theory exists separate with respect to the change of material objects we still may even have philosophical objections to exactly treating the theory as making time non-absolute. You got your Lorentz ether theory, interpretations of the theory which stress dynamical symmetries being prior to spacetime symmetries, and also questions about what matters when we say something is real in the theory as a question about invariant quantities (such as rest mass). It's unquestionably always the case that proper time is invariant while coordinate time is not because it's an outside analysis done onto other inertial frames of reference. I'm highly skeptical of physical theories which stress such absolute features as fundamental to time but also to physicists who believe they can attain change/time from unchanging/timeless entities.
Physicists can construct new theories that bring about paradigm shifts but they have to do so under the bias of an already preconceived ontology which may or may not be justified. Take general relativity in which it's popular to envision a substantival real existent spacetime which is curved when in reality physicists should be rather dumbfounded as most analysis i've seen into general relativity make the question of whether there is or isn't a real existent spacetime being curved rather unclear. Perhaps physics enjoys throwing numerous metaphysical concepts at the wall until one sticks experimentally.
It would be good to hear from an actual physicist regarding these comments. We can all speculate. :chin:
What is "proper time"?
[Quote]I'm highly skeptical of physical theories which stress such absolute features as fundamental to time but also to physicists who believe they can attain change/time from unchanging/timeless entities.[/quote]
This paper, The Problem with the Problem of Time, similarly argues that something more is needed - the passage of time is not an illusion. Nevertheless, the Page-Wooters effect seems real. This suggests something is missing from our theories. My question is: who is more likely to find a solution, a philosopher or a physicist? I think the latter.
Regarding the fundamentals of time, I also question whether metaphysicians are equipped to answer it. Physicists are exploring it (see Time: An Emergent Property of Matter).
Unlike metaphysicians, physicists will propose solutions that are consistent with theory, and positioned to develop experiments that can validate their hypotheses.
Special relativity and Page-Wooters clearly show that time is weirder than anyone would have thought. Weirdness like this is not going to be uncovered without new Physics. If Physics can't do it, there's no hope for Metaphysicians.
This is the nature of scientific revolutions. Without science investigation, metaphysicians would be spinning their wheels and getting nowhere.
And without metaphysics we wouldn't know what were uncovering nor where to proceed next.
How do not know this? It's the time measured by a clock that remains in your frame of reference or world line in special relativity.
Quoting Relativist
Philosophical interpretations of special relativity have shown time is weirder than what is expected from everyday experiences. This is an interpretation however that is parasitic upon other philosophical assumptions and the mathematics involved. Literally just look at the numerous different interpretations of quantum mechanics despite their use of the exact same mathematics. I'm not saying don't prod at the world as this would probably be in contradiction to strategies/epistemologies that certain metaphysicians take on (some of which go by the label of naturalized metaphysicians) just that raw sensory data gets you no where without an investigation of what it really means before going forward.
We need to make a distinction between abstractions/quantitative theories of our reality and the interpretations of those theories (from metaphysics) that go into deciding our ontology.
Very good.
Tetens, who lived in the 17 hundreds, said: "The idea of a body set in motion, which neither acts upon any other body nor is acted upon, leads the mind to the idea that the motion of the body will continue unchanged; and even though the latter idea be derived from perceptions, yet its connection with the former ideas is an effect of the power of thought, which according to its nature brings about in us this relation between the two ideas; and the connection between predicate and subject, which is made by this operation of the mind, is far more reason for the conviction that our judgment is true than the mere association of ideas based on perceptions."
I think Teten's point is that we have to have some sort of philosophy to start out doing science. Otherwise we just have sequences of perceptions that could change in order, intensity, and quality at any time. Hume developed this to it's logical conclusion and took the West to the East (Shunyata). Maybe there is something deeper in the mind which actually can understand matter, and which faculty can be analyzed. Yet what some people call "scientific common sense" other people call philosophy. Such disagreements are interesting! Hegel wrote in 1807 (long before Einstein) that the "reality of time has the solid form and shape of space". He came to this by way of philosophy
And what do physicists mean when they say something like "we can just change the math on this one a little". They literally say stuff like this all the time!! If the math merely reflects the quantities measured, it would seem ALL of physics is about experimentation. So where does that leave theoretical physics? I think in philosophy, but I am willing to be corrected
I don't think that's the case, because to do work as a physicist is to follow the precepts of the discipline. Only if a physicist steps outside the discipline, to do metaphysics, could such a paradigm shift occur.
Quoting Relativist
Again, I'll stress the point that the discipline of physics will follow the temporal concept which it has adopted. One doesn't develop any new insight into the nature of time, by adhering to the principles given. It is only by going beyond the given principles (practicing metaphysics) that such insight is developed.
Quoting Relativist
Would you agree, that when Einstein went beyond the accepted principles of physics of his day, he was practicing metaphysics rather than physics? Since he wasn't following the conventional rules of physics, we cannot say he was doing physics. If you agree, then why would you think that it's physics rather than metaphysics which gives us insight into the nature of time?
No, I do not agree that Einstein went beyond the accepted principles of physics of his day. He was addressing some outstanding problems in the physics of the day.
As I said previously, one can classify some of the work of physicists as "metaphysics", but what's the point? Physicists aren't typically trained in the field of metaphysics, they're trained in physics, and this does not seem to have handicapped them. Theoretical physics entails developing new frameworks - which could be labelled metaphysics. For example, when the standard model of particle physics was proposed, one could have called this an exercise in metaphysics (it proposed a suite of particles that constitute the fundamental building blocks of material reality), but it's not the sort of metaphysics a philosopher could do because it depended on knowledge of physics.
You can call it philosophy if you like, but understand it's the sort of philosophy that can only be done by physicists. Personally - I don't see any value in categorizing the work of physicists into the separate categories of physics and metaphysics.
I see Relativist's point now. It's interesting though to think about matter itself and try to distinguish what is philosophical about it and what is scientific about it
Sure, he was addressing existing problems. But he came up with a new principle, which implies necessarily that his thinking went outside the box, represented as "the accepted principles of physics of his day". If it is required that his thinking went outside the principles established within the discipline of "physics", when he came up with his theory, we cannot say that he was doing physics at the time. If he was not engaged in metaphysics, then what was he doing? Why not call it what it is, metaphysics?
Quoting Relativist
The point is to demonstrate that you are wrong in your conclusion. Physicists do go beyond the work of physics, into the field of metaphysics. And, they aren't trained in metaphysics, as you accept. So why not accept as well, that their metaphysics is very often deficient, faulty in comparison with classical metaphysics, because they are not educated in some of the fundamental principles of metaphysics? And your conclusion "this does not seem to have handicapped them" is demonstrably false.
Quoting Relativist
The standard model is extremely deficient. It accepts uncertainty (the uncertainty principle), as inherent within the thing being modeled. What kind of a model is that? We're modeling something, but fundamental aspects of the thing being modeled cannot be modeled using our metaphysical principles, so we'll just incorporate "uncertainty" into the model. The problem here is that the metaphysics of time being employed in the standard model is very deficient in comparison with the classical metaphysics of time, and this produces an extremely deficient model, full of uncertainty.
You seem to think that because the metaphysics is produced by physicists rather than by metaphysicians, it is better metaphysics. However, you agree that physicists are not trained in metaphysics, so it appears like you would be very wrong here. Then, to support your claim you propose a model which has uncertainty as a fundamental principle. How does this in any way support your claim that physicists are better able to produce metaphysical principles than metaphysicians? The pervasiveness of the uncertainty principle in modern physics, and things like dark matter and dark energy in cosmology demonstrate very clearly that modern science is handicapped by its metaphysics.
If you're going to label as "metaphysics" any work physicists do that is outside the box of established physics, feel free - but it doesn't change anything. I'd be more inclined to just call the entire venture "natural philosphy", as was the norm prior to the 19th century. Categorizing the work of physicists as partially science and partially philosophy just seems a forced fit into semantic categories. It's harmless, but doesn't serve to improve the process.
You say it's "demonstrably false" that their ignorance of metaphysics has handicapped physicists. Please provide one or two good examples.
Quoting Metaphysician Undercover
Sounds like you don't understand what I'm talking about. I'm referrring to the Standard Model of Particle Physics, which consists of things like quarks, leptons, bosons. This model was proposed in the 1960s to explain the large number of (supposed) elementary particles that were being generated and identified in particle collisions. The model proposed that those observed particles were actually composed of these more elementary components. It was derived mathematically, but over the decades was verified experimentally.
The uncertainty principle isn't directly related to this, so perhaps you were mistaken. Nevertheless the uncertainty principle of quantum mechanics has also been verified experimentally - so I'm sorry, but it's nonsensical to dismiss its reality based on some metaphysical principles. Physics needs to come first, and the metaphysics needs to be consistent with it. Not the other way around. As I said earlier, physics has proven the natural world is weird at the fundamental level, a fact that would never be exposed by pure philosophical reflection.
OK, then let's call it metaphysics, if you're ok with that. Now, are you willing to recognize that a metaphysician, trained in the principles of metaphysics is most likely a lot more capable of doing this work (metaphysics), than is a physicist, who is trained in the principles of physics, and not in metaphysics?
Quoting Relativist
I did, in my last post, it was your example of the standard model of particle physics. It incorporates uncertainty as a fundamental principle of quantum physics; obviously bad metaphysics.
Quoting Relativist
The uncertainty principle is a feature of all quantum field theory, and therefore the standard model as well. Of course it's been verified experimentally, when you are uncertain of something it's easy to demonstrate this. But that doesn't mean that the uncertainty is not derived from bad metaphysics.
Yes and no. Metaphysicians are better equipped for conceptual analysis, including developing general metaphysical frameworks, but they would be abysmal at the "metaphysics" that is part of the core work of theoretical physicists - the thinking outside the box. As I brought up earlier, no metaphysician would have thought up the Page-Wooter mechanism, had the insight about time that we gained from special relativity, predicted quantum uncertainty, nor proposed the nature of quantum fields as (possibly) fundamental. Metaphysicians can reflect on these advances, and perhaps propose a metaphysical framework (like ontic structural realism), but they won't actually be contributing to the advance of physics - even if you choose to label this "metaphysics".
Quoting Metaphysician Undercover
But you're wrong, so I infer that you have no actual cases in which an ignorance of metaphysics impaired physicists.
Quoting Metaphysician UndercoverBut even if you denied quantum uncertainty, you can't deny the existence of these particles. Furthermore, quantum uncertainty has been verified.
[Quote]Of course it's been verified experimentally, when you are uncertain of something it's easy to demonstrate this. But that doesn't mean that the uncertainty is not derived from bad metaphysics.[/quote]Is this a joke? If not, then it just indicates you don't know what you're taking about.
At the core of of theoretical physics are the concepts of time and space. We have no empirical access to time, we cannot sense it in any way. Nor do we sense space. The only approach we have to the nature of time and space is through conceptual analysis. So it is blatantly contradictory to say that metaphysicians are better equipped for conceptual analysis, but not equipped for the core principles of theoretical physics.
Quoting Relativist
The problem is, that from the perspective of classical metaphysics, the "insight" of special relativity is not an advancement at all, it's a step backward, a rejection of discipline. Special relativity assigns ambiguity to the point in time designated as "now". But precise measurement of time requires precise determinations of the points "now", which mark the beginning an ending of the measured duration. Without such precision we have uncertainty. Hence the uncertainty principle, emerges as the result of the ambiguity which special relativity assigns to the point in time.
Quoting Relativist
Assertion will get you nowhere. Where's your evidence which demonstrates that the uncertainty principle is a product of good spatial and temporal conceptions? That special relativity is useful within some parameters, and not useful in others, is evidence of bad spatial temporal conceptions.
Quoting Relativist
I don't deny quantum uncertainty. I just explained how it is the product of bad metaphysics.
For someone who doesn't believe that 2 + 2 and 4 represent the same thing, and who essentially rejects the very idea of symbolic reasoning, I'm impressed that you've worked your way up to quantum physics. Out of idle curiosity, what exactly is your objection to quantum physics? After all, most physicists don't think about metaphysics at all; they just "shut up and calculate" as the saying goes.
Quantum physics isn't making any metaphysical claims at all. Its only claim is that it predicts lab experiments to a dozen decimal places. By that standard it's the most successful scientific theory in history. It doesn't need metaphysical justification. It's "only" science. Nobody (not me, at least) is claiming that quantum physics is reality. Some people believe that but they're wrong.
It's a model. A hell of a good one. But any metaphysical claims are just that, metaphysics.
So aren't you about to argue against a strawman here?
Maybe a bird would experience force and gravity differently with his body than a homo sapien
If you're interested, just go back and read the posts I made in this thread. They aren't large, and there isn't a lot.
Presentism sees the actual world in similar respects; all that exists is the present state of information, and so the denotation of a temporal "beginning" is arbitrary, as is the distinction between past and future.
To use computational terminology, presentism understands history as being lazily evaluated.
Quoting Gregory
@jgill Your take on the issue of an infinite past is interesting. Reminds me of Zeno's paradox of motion. So, the past could be finite, say it extends 1 unit into the past. However, the catch is cause/motion happens in decreasing, fractional time intervals. Take the following time series: 1, 1/2, 1/4, 1/8 a la Zeno. The universe is at t = 1; the cause of the universe, a, happened at t = 1/2; the cause of a, let's call it b, occured at t = 1/4; the cause of b, call it c, took place at t = 1/8; so on and so forth. This means that an infinite number of causes can be accommodated, so long as each preceding cause of what is itself a cause, say x, occurs at half the time required for x to occur. This effectively solves the problem of an infinite past entailed by a chain of infinite causes because, given the above framework of how preceding causes take only half the time for subsequent causes, it's possible for a finite time interval to contain an infinite number of causes.
:chin:
What an odd thing to say, considering that you asserted physicists have been impaired by their ignorance of metaphysics, and your examples were a fail.
Quoting Metaphysician Undercover
That is a novel view of an "uncertainty principle" That's interesting that you think that time can't be measured precisely. You're wrong, but it's interesting that you believe it.
Quoting Metaphysician Undercover
Fishfry - don't waste your time.
As for special relativity, it's scope was narrowly concerned with the logical consistency of theories such as maxwell's equations that employ temporal indexicals but otherwise lack explicit temporal frames of reference. So I think it's right to point out that special relativity isn't particularly relevant to phenomenological puzzlement and concerns about the nature of time, but at the same time SR cannot be criticised on that ground, for the nature of phenomenological time wasn't the theory's intended purpose and SR leaves the relationship between theoretical space-time and ordinary experience undefined.
I see you haven't addressed my examples, only contradicted yourself, saying metaphysicians are better trained to do metaphysics than physicists, yet physicists are decidedly better at some forms of metaphysics.
Quoting Relativist
Are you familiar with the frequency-time uncertainty exposed by the Fourier transform? Once you familiarized yourself with this uncertainty principle, you'll see that what it says exactly is that time cannot be measured precisely.
Consider that to measure time precisely requires the ability to determine the shortest time possible. However, a time period is measured by means of some determinable frequency. How could we determine the number of cycles/time period (frequency) of the highest frequency, without having a higher frequency by which to compare it to, as a temporal measurement? To determine the frequency requires a measured period of time, and to determine the period of time requires a determined frequency. Hence uncertainty. So what the uncertainty principle says is that a precise moment in time cannot be determined because the frequency required to determine this, cannot be determined; and the frequency required to determine this, cannot be determined because the precise moment in time cannot be determined. Do you see the vicious circle which creates the uncertainty principle? Having a measured period of time is dependent on determining the frequency of something, and determining the frequency of something is dependent on having a measured period of time. Therefore as we move toward a shorter and shorter period of time (precise measurement of time), there is greater and greater uncertainty.
LOL.
Quoting Metaphysician Undercover
Well this isn't so bad. I seem to recall that Heisenberg uncertainty comes ultimately from Fourier analysis or some such. The idea seems to be referenced here.
I'm not sure how this relates to your concerns regarding QM; but I will say that this particular remark of yours is quite a bit more sophisticated than your usual nihilistic denialism of basic symbolic reasoning whenever you attempt to discuss math with me. Odd that someone who denies that 2 + 2 and 4 represent the same thing, is willing to accept the Fourier transform.
I certainly agree with your point that Heisenberg and ultimately the theory of Fourier series imply that we can't measure time with absolute precision; and that measurement precision trades off between time and frequency. But we already knew this so I don't know the point you're making. Heisenberg's uncertainty principle is in any event an epistemological and NOT an ontological fact. It's a limitation on what we can know (with our current theories) and says nothing about what truly is.
Which is the same point I made to you in my previous post. Science isn't making any ontological claims. You're fighting a strawman of your own imagination.
A historical note that I find interesting. What was Cantor doing when he discovered set theory? He was studying the zeros of the trigonometric polynomials that arose from Fourier's study of heat transfer.
That is: If you apply a heat source to one end of an iron bar under laboratory conditions, and carefully observe how the rest of the bar warms up; you will inevitably discover transfinite ordinals and cardinals.
Cantor's work arose directly from physical considerations. This point should be better appreciated by those who dismiss transfinite set theory as merely a mathematical abstraction.
That view assumes counterfactual definiteness; the belief that the possibility of stopping a moving arrow to construct a definite position implies that the moving arrow must have a real and precise but unknown position when it isn't stopped or it's position otherwise measured.
Yet this unquestioned assumption of counterfactual definiteness is the reason why Zeno's paradox appears paradoxical. To my understanding, Zeno's arguments are perfectly sound, which means that i have no choice but to reject counterfactual definiteness in order to resolve the paradox, and is the reason why i believe that Zeno ought to have stumbled across the underlying logic of Heisenberg's principle (when it is interpreted ontologically).
Of course, the rejection of counterfactual definiteness is only one means of making sense of quantum entanglement and which is also the view of the Copenhagen interpretation, which means that Heisenberg uncertainty is interpreted as ontological ambiguity/incompatibility, rather than as epistemic uncertainty.
When I say for example that 1+1=4, I mean it esoterically. When Hawking says time acts as a fifth direction of space, he is talking as a scientist. He says nothing was before this curve in spacetime, meaning I think that the free lunch is contingent. Quantum uncertainty may be the root of physics, the answer to Descartes's vortex of the universe. Any talk of the "necessary" is sitar music thinking, and if our brains control time we have access to the heart of contingency
Touché . . . Good point! :smile:
But if objects are trans-finitely infinite, how can they remain finite as well
I had this in a signals processing/wavelets class a while back. There's a standard proof here.
The Fourier transform of the momentum operator applied to a wavefunction is the position operator applied to that wavefunction. There's a theorem in signal processing called the Gabor limit that applies to dispersions (variance) of signals; the product of the dispersion of a signal in its time domain representation and the dispersion of a signal in its frequency domain representation is at least (1/4pi)^2. Math doesn't care that time is time and frequency is frequency, it might as well be position and momentum. The Gabor limit applied to (position operator applied to wavefunction) turns into the Heisenberg uncertainty principle for position + momentum of wavefunctions.
It's illustrated in the link you provided, if you Fourier transform a Gaussian with variance [math]x[/math], you get a Gaussian with variance [math]1/x[/math]; the product of the two variances is strictly positive. If you scale the original distribution by k, the Fourier transformed distribution will be contracted by 1/k. Contractions in transform space are dilations in original space. When dilations in time result in contractions in frequency, it isn't so surprising that the product of "overall scale"/(variance) of time and frequency has a constant associated with it.
It isn't an epistemological limit.
In statistical modelling, there's a distinction between epistemic and aleatoric randomness. Epistemic randomness is like measurement error, aleatoric randomness is like perturbing a process by white noise. One property of epistemic randomness is that it must be arbitrarily reducible by sampling. Sample as much as you like, the uncertainty of that product is not going to go below the Gabor limit. That makes it aleatoric; IE, this uncertainty is a feature of signals that constrains possible measurements of them, rather than a feature of measurements of signals. There is no "sufficient knowledge" that could remove it (given that the principle is correct as a model).
Do you have a source for this? I'd love to see the connection.
I don't have any references saved but I Googled around and found these. No warranty is expressed or implied as they say. I found these links but did not read them. Some are behind academic paywalls, a practice I will abolish under pain of death when I am made Emperor. There were many more links out there if you Google "Cantor trigonometric series."
https://www.researchgate.net/publication/274008538_About_Cantor_Works_on_Trigonometric_Series
https://www.jstor.org/stable/41133323?seq=1
https://arxiv.org/abs/1503.06845
https://www.maa.org/press/periodicals/convergence/mathematical-treasure-cantors-on-trigonometric-series
The long and short of it is that by the mid 1850's, people were interested in trigonometric series because Fourier had shown that these highly abstract series were vitally important in understanding heat flow. So mathematicians got interested in them.
Now remember this is a little before the time that analysis finally got completely rigorized. And trigonometric series posed challenges to the handwavy calculus of the day. Questions of convergence weren't well understood. The efforts to formalize analysis were in part driven by these kinds of issues.
Fourier showed that a given function could be decomposed into a trigonometric series; by analogy, in the same way a musical note is composed of tones and subtones. A natural question is, given a series, how do you know whether it converges to some function: And given two series, how do you know if they might happen to converge to the same function?
That latter is equivalent to saying that the difference of the two functions converges to zero. We are naturally lead to be curious about the structure of the zeros of a trigonometric series.
My understanding is that the zeroes might be distributed in many different ways. There might be one at every integer, say. Or what if there was a zero at each of 1/2, 1/4, 1/8, etc. But now what if there were those zeros, and you threw in at 1/4, a nearby sequence that converges to it: [math]\frac{1}{4} + \frac{1}{n}[/math]. So the main sequence 1/2, 1/4, 1/8, ... could have little tendrils coming off it. And each tendril could have tendrils. Each tendril would be countable, but there would be a graph of unimaginable complexity to keep track of.
In order to notate and keep track of the tendril graph, one would inevitably discover the transfinite ordinal numbers. The transfinite ordinals arise more or less directly (by way of abstract math) from purely physical considerations.
As I say, this last bit is my own personal understanding of how trigonometric series must have led Cantor to the ordinals. I could be wrong. It's a belief looking for the written evidence, which is probably behind a paywall somewhere. (Note -- The Wiki page on trig series that I linked seems to confirm my theory in a general way).
Now at this point, Cantor, who was very religious, decided that after all the infinities he'd just discovered, the ultimate infinite must be God. So he dropped his work in real analysis and gave himself over to set theory. Today set theory has become the standard conceptual framework for mathematics; but Cantor's theology is long forgotten. I wonder if he'd be more happy or more sad at those two outcomes.
That's a very interesting post. I don't know if it's specifically aimed at something I wrote. It doesn't sound like it offhand. If you say that 1 + 1 = 4, what do you mean? Esoteric as in woo? Crystal healing and Rosicrucians? Better narrow this down for me else I don't know what you mean at all. I used to know of many esoteric practices.
What does Hawking have to do with this? I wonder if you mis-tagged me perhaps? None of this convo sounds familiar. Free lunch is contingent? What am I supposed to make of that? I apologize if I was at one point having the other side of this conversation and no longer remember. Descartes's vortex theory is a discredited and discarded theory of gravity that lost to Newton's. It has absolutely nothing to do with quantum uncertainty.
Quantum uncertainty may be the root of physics. Ok. What's that mean? Sitar music thinking? What is that? Like dropping acid listening to the Beatles? I am really lost here.
"... if our brains control time we have access to the heart of contingency"
Ok. I can't argue with you there! Is the heart of contingency near the root of physics?
Definitely style points, this was a great post. I don't understand it though.
The point here would be that transfinite numbers are an abstraction but not an isolated one. They're an abstraction that arose naturally from the study of heat; just as the infinity of natural numbers is an abstraction that arises from everyday counting.
You clearly do not understand, if you think that I accept the Fourier transform. I accept it as an example of an unresolved problem. And when that unresolved problem is united with the bad metaphysics of special relativity, the result is the uncertainty principle of quantum mechanics.
Relativist seemed to be arguing that a metaphysician is better trained to do metaphysics than a physicist, yet there is some metaphysics, such as the metaphysics of time, which a physicist is better trained to do. However, the uncertainty principle is clear evidence that physicists should leave the metaphysics of time in the hands of metaphysicians.
Quoting fishfry
Thanks for offering your take on this. I think this is exactly where the unresolved problem lies. It appears like the size of a chosen base unit might be completely arbitrarily decided upon. Yet the possible divisions are not arbitrary because divisibility is dependent on the size of the proposed base unit. Take 440 HZ as the baseline, for example. From this baseline, one octave (as a unit) upward brings us to 880HZ, and one octave downward brings us to 220HZ. So the higher octave consists of 440 HZ, and has different divisibility properties from the lower octave which consists of 220 HZ. This results in a complexity of problems in music.
Well I had a thread a few days ago that got closed because I claimed math maps out the impossible and that the opposite flip side is true of every mathematical statement. So perhaps the negative numbers are positive and vice versa, e.g. I was trying to start a conversation but people got upset. I don't deny math's usefulness and it's beauty, but math might not be the last statement about math itself.
Quoting fishfry
Well I tagged you because other people weren't responding to posts I was making here. I started out ny explaining what I meant about the math thing so you don't think I'm a nut. The OP here, however, was talking about Aquinas, who said that the world was contingent and needed a necessary God. Physicist are now saying nothingness was before the big bang, making the world contingent without the need for "the necessary". Sean Carroll explicitly says this. He says the world is a brute fact of quantum fluctuation, using Russell's old phrase btw
Quoting fishfry
I think any mechanical theory can be resurrected in the search for a "theory of everything". I said quantum physics is answer to Descartes, but perhaps Descartes is the answer to QM. Newton replaced Cartesianism with a lot of forces. God was the ultimate one that Descartes had wanted one force to control everything and thought God could be found only in the mind. Perhaps that "one force" is pure leverage, as he thought. It's a thought that needs to be worked out for sure, but the Stanford Encyclopedia says there is growing interest into Cartesian physics again
Quoting fishfry
Probably. There are studies that literally argue our brains control time. There are lots of Youtube videos that run with this and say we are in almost complete control of our "free lunch", given us by the universe. There might be some truth in these videos that the universe gives itself to us freely. And then there are Napoleon Hill types (the forerunner of The Secret), that say our thoughts are in complete control of everything. These ideas may have a kernel of truth still
Quoting fishfry
Well I think my point was that objects are finite on one side, but flip the coin and it's infinite was well. There no end to the descent into an object. Imagine taking a spaceship (one that forever shrinks) into a banana. Only infinity is in there. This seems to be a contradiction of logic. I have had enough trouble trying to explain the problem to people, let alone getting a satisfactory explanation. Think about it: objects are finite and infinite in the same respect
Thanks for your response man :)
And the man who directly tried to refute his whole philosophy:
https://plato.stanford.edu/entries/leibniz-physics/
A+ for original thinking, Greg! :cool:
Tonight I've been reading about Nagarjuna on the Internet Encyclopedia of Philosophy. I feel like most of us on this forum are Westerners. Modern physics is getting into more Eastern ideas even since Borh, and our philosophical culture is resistant, and maybe it should be. I read the Tao of Physics book and felt it was purely a philosophical work. Modern physicists speak of pure nothing, while even the Eastern idea of sunyata-nihsvabhava doesn't mean “non-existence”. The word for that is actually Abhava. But when the world's existence was granted, Indian thinkers still thought the answer was the interconnection of all within one motion, within which is allowed infinite regress (Anavastha in Indian thought) and circularity (karanasya asiddhi). Some Vedic philosophers did believe in what they called svabhava, which can be compared to the modalities of Liebniz, so there is division within Eastern thought as well
What I wanted to say though was that we are culturally Westerners (most of us) and unless we want to be like Pyrrho, we want a satisfying explanation of how this world came about. Pyrrho said he doubted and doubted that he doubted. Stephen Hawking had a paper trying to argue that this type of paradox (i guess introduced into math by Godel?) could be in matter (in the universe) itself as well. That's a little too loopy for me.
It's been a good day
The Indian words for physical Pratityasamutpada are anitya, anepikrita, nihsvabhava, or shunyata. The last is the most used word. Just because I don't like infinite regress (A cause B, because B cause C which cause A because A causes C), that alone doesn't mean it's not true. But I like ideas about the world to be clear: "A literally cause B". However, Zeno seems to have prove Heraclitus true instead of Parmenides. If the world is pure fluidity, what kind of mathematics would even apply anymore to the world? I thought that might be an interesting question for those schooled in mathematics
My only answer is philosophical (and maybe even esoteric), because I don't know enough non-Euclidean geometry to deal with that question. I imagine the universe started from gravity and quantum uncertainty, as I suggested already, but I don't read up on modern physics so I can't really take an authoritative stance.
This guy thinks an infinite regress which does not reside in a divine mind is impossible:
https://www.youtube.com/watch?v=ZJDYPZYMt0Q
I just say simply that potentiality (infinite vagueness) turns into actuality (finite objects). I think Heidegger already answered that Youtuber in the 20's. The thread on Heidegger going on right now is great for anyone out there wanted to know more about this
Great stuff!
Quoting fdrake
Ok. I will take another look at that.
Quoting fdrake
Uh oh I'm in trouble. This is the opposite of what I thought was true.
So first, I did not follow all the technical details you presented yet. My general understanding is that first, there are two things going on. One, the mathematical formalisms of convergent series, Fourier series, etc.; and two, whatever it is that nature itself is doing. Mathematical model versus reality.
My understanding is that, for example, the Planck length is the length at which our current theories of physics break down and may no longer be applied. So that we can't sensibly speak of what might be happening below that scale. We can't say that reality is continuous or discrete; only that our current theories only allow us to measure to a discrete limit.
So the Planck scales (space and time) are epistemological and not necessarily ontological. That is my understanding. Why are you saying that uncertainty is true of nature, not just a limitation of what we can know?
Quoting fdrake
More good stuff. I found an article that said that the outcome of a coin toss is aleatoricaly random before it's flipped; but once it's flipped, it's epistemically random. Someone who can see the coin has a different rational belief in the probability than one who hasn't.
This is a good distinction to make.
But I am still confused about your conclusion. You're saying that a situation is ontological if there's no knowledge I could have that would settle the matter. Whereas I seem to mean something different. There's what we can know, and there's what really is. Two different things.
Can you help me understand why you think uncertainty is ontological? What does it mean that reality itself is uncertain? Isn't it just our measurements that are?
I have not been talking about Zeno's paradoxes of motion at all. I don't understand why you're mentioning it.
Quoting sime
Oh I see the connection you're making. Perhaps Zeno was getting at the fact that the universe CAN'T be continuous, hence the Planck length. Something like that. Is that what you mean?
Quoting sime
I don't know what counterfactual definiteness is.
I'll stipulate that uncertainty is part of nature in the Copenhagen interpretation. That's a good point to keep in mind, thanks. But interpretations are metaphysics and not physics. Nobody knows what's "really" going on. For all we know it's all been determined at the moment of the Big Bang; or, everything that can happen does happen in some branch of the multiverse. In those interpretations, there is no ontological randomness or uncertainty. Fair enough?
Oh I see. I don't generally read every post, just the ones that tag me, unless it's a topic I'm especially interested in. So I may have missed your other posts. I am not a moderator and have no influence on what posts get closed, or why.
Quoting Gregory
I myself am very openminded and pluralistic about math. In fact mathematical pluralism is a philosophical idea that's coming into vogue through the idea of the set-theoretic multiverse. That there's not one right set of rules for math; but rather, there's a whole universe of different axiom systems, related in some overarching superstructure of some sort. It's all pretty far out there. But I'm perfectly ok with alternative math thinking.
That said, however, negative numbers can NOT be positive. The positive numbers can be defined as a particular set of real numbers that satisfy a formal property. If you called them the negative numbers you could do that, but they'd still be the positive numbers. The negative numbers are logically different.
By contrast, in the complex numbers you can't define positive and negative numbers. You literally can't distinguish between [math]i[/math] and [math]- i[/math] using any logical formula.
So yes, we are free to imagine; but our imaginings must still meet certain standards of logic and mathematical interest.
Quoting Gregory
LOL. I'm the rhetorical foil of last resort? I'm not sure how to take that ... :-)
But do bear in mind that I have not seen any of your prior comments on this topic so feel free to loop me in from the beginning and don't assume I have any idea what we're talking about.
Quoting Gregory
"They closed my last thread and nobody else will talk to me so I'll try my ideas out on you," may not be how to accomplish that. [Just joking, hoping you have a sense of humor].
Quoting Gregory
I am ignorant of classical philosophy and can not comment on Aquinas or any of his contemporaries.
Quoting Gregory
I love Sean Carroll. I've watched a lot of his videos. I love his vocal delivery, I find it very soothing. His mathematical and physical clarity of exposition are wonderful. He is a lot like Feynman in that he's a great physicist and a great teacher.
Now, when Sean Carroll is doing physics, he's doing physics. And when he's doing metaphysics, he's doing metaphysics. I'm aware he advocates the multiverse interpretation. But that's a metaphysical stance.
So when I say I love Sean Carroll, I would add that when he's doing physics I believe him; and when he is advocating for his favorite interpretation of QM, that's just his opinion.
The entire business of interpretations is nonsense. Newton didn't have an interpretation or an explanation of why gravity worked. He only knew that his theory predicted the results of observations and experiments. The same can be said, and that's ALL that can be said, for quantum mechanics.
Quoting Gregory
That's very interesting. The difference between Descartes's approach and Newton's was that Descartes gave a mechanism for gravity; and Newton only described how it behaved. I frame no hypotheses, a very famous instance of Newton's tremendous insight into the very nature of science. Sean Carroll and all other celebrity physicists by day and metaphysicians by night, should study it.
If Descartes's vortices are coming back that would be great news. Have you a specific link please?
Quoting Gregory
I like to read widely too, but I try to be selective in what I believe. Perhaps you might tune your filter a bit. Newton himself was a mystic; but when he wrote about science, he stayed with science. He was a mystic when he was doing alchemy or looking for coded messages in the Bible. In his science papers he's very straight up hard core math and science. You might find it helpful to make that distinction for yourself.
Quoting Gregory
Sorry don't know which coin that is. You know Gabriel's horn? It's a cone that has infinite surface area but finite volume. It's a famous calculus puzzler.
Quoting Gregory
No I don't follow that example. Why would "only infinity" be in there? Say a guy has a blood clot in his brain and you want to fix it before it bursts and kills him. So you take a team of neurosurgeons, put them in a submarine type of contraption, shrink them down to tiny size, inject them into the body into a blood vessel, and have them navigate to the brain to repair the clot.
This was the plot of the 1966 science fiction movie Fanstastic Voyage. I mention it only because it's an example where you shrink a spaceship to the size of a banana, to the size of a tiny spec of dust, even, and all the people and equipment inside it would just shrink proportionally. Of course this may be physically nonsense; but it's at least conceptually feasible if only in a science fiction sense. We can imagine it. In particular, there's no infinity in there. Just tiny little people. And why not?
Quoting Gregory
You're very welcome. I hope you got your money's worth. And thank you! There are some on here who won't speak to me at all.
I am surprised you've heard of it. Yet you don't agree that 2 + 2 and 4 refer to the same thing. In my prior conversations with you, you've convinced me that you utterly reject symbolic mathematical formalisms. And without those, there certainly aren't any convergent infinite trigonometric series. Those are very abstract gadgets. There's a mismatch in your level of discourse.
A couple of months ago you refused to except the notion of the finite field extension [math]\mathbb Q[\sqrt 2][/math], the field of rational numbers adjoined with a symbolic square root of 2. That is a much simpler construction that Fourier series. It's illogical for you to complain about the one and then casually invoke the other to make some point.
Quoting Metaphysician Undercover
But special relativity and physics in general need not be about metaphysics. "Shut up and compute," which they say about QM but which might just as well apply to relativity, special and general. Do theories explain the world, or just describe it's approximate behavior in our laboratory experiments?
We keep coming back to the same point. Nobody is making metaphysical claims except you. I agree that SOME scientists think their theories are True with a capital T, but I don't. You're fighting against someone's opinion that isn't mine.
Quoting Metaphysician Undercover
I can't comment on these inside baseball conversations with other posters. I rarely even read my own posts, let alone anyone else's.
Quoting Metaphysician Undercover
Ok, fine. I stipulate that. Science isn't metaphysics, science is not ontology. What of it? I've been conceding you this point for days. You won't even acknowledge that I've said that, you just keep coming back with arguments as if I haven't said it.
Quoting Metaphysician Undercover
I was describing how Cantor stumbled upon the transfinite ordinals while studying the zeros of trigonometric polynomials. Not sure how this applies.
Quoting Metaphysician Undercover
Sounds a little handwavy to me.
I ask you directly: Do you understand that I make no ontological or metaphysical claims for science? I make only the claim of accurate predictions to the limits of the experiments that we can do and the observations we can make.
You know, like when Eddington came back from photographing the 1919 eclipse and proved that the observations were consistent with Einstein's special theory of relativity and not Newton's theory of gravity. That's science. If you want to claim that this doesn't mean it's "true" in some metaphysical or absolute sense, I totally agree with you. So what's your point?
Quoting fishfry
I think I break the terms up differently from you.
To my understanding, you treat all that a mathematical model of something says as epistemic. Because a mathematical model is knowledge of a thing, what it predicts about that thing is knowledge of a thing. I agree with that. And I'm inclined to take another step; if a mathematical model of something is good, I'll accept what it concludes as if it were the thing. I treat good mathematical models as representational knowledge; and they represent the thing. Part of representation to me is being able to stand in for the thing when considering it.
So when the theory says; "it doesn't matter how much you sample about (blah), the variance of (blah) has a lower bound", I tend to treat it as being about (blah), rather than about our knowledge of (blah).
With statistics and averages, I'm less inclined to do this. A lot of randomness in statistical models is epistemic, and thus it can in principle be reduced by sampling. I'm happy treating that as as a fact about how the model's estimates relates to the sample, not a fact about the model the sample is being used to estimate things from. EG; samples of heights of people in Wales having a variance that can be arbitrarily reduced (in principle) by more sampling (epistemic) vs sampling from a signal in time space and that sampling strategy inducing a lower bound on the error in the frequency space regardless of the specifics of the sampling strategy (aleatoric).
But with aleatoric randomness, I'll treat it as a fact about the model. It doesn't matter what samples you do to estimate stuff from the model, the thing is gonna be random. I don't have a "physical intuition" or a "physical meaning" associated with these uncertainty principles when predicated of signals; as if I knew what they implied about reality. Some people seem to do this, interpreting an uncertainty principle about the modelled thing (blah) as meaning (blah) really is a distribution. Maybe it is, it seems useful to think that, but all I wanted to do here by calling it "aleatorically random" was to say that the uncertainty associated with an uncertainty principle is a model property rather than a sample property; it's about the (representation of) the thing, rather than about samples about the (representation of) the thing. In other words, its application is invariant of sampling, so it's about the model.
If you wanna call it "epistemic" because it's some content of the model, and don't want to let the model "stand in" for the thing like I'm inclined to, that's fine with me.
There's no mismatch in my discourse, you simply refuse to try and understand what I'm saying. I believe that two plus two equals four. I do not believe that "two plus two" and "four" refer to the same thing. Since you think that they refer to the same thing, you and I give "2+2=4" different meaning. We simply interpret this phrase differently. It is an ontological difference. So I reject some conclusions of mathematical formalism as unsound, based in unsound premises. This does not exclude me from taking a look at some of these unsound conclusions. Comparing unsound conclusions with what is really the case helps in the effort to produce better premises.
Quoting fishfry
The premises, axioms, theories, are metaphysical claims. whether you recognize this or not. I know we disagree on this, and you think that such premises might be based in something called "pure mathematics". but I explained to you in the other thread why this is an unsound principle itself. There is no such thing as "pure mathematics" in an absolute sense. Mathematics is ultimately guided by utility, and even those who might seem to be engaged in pure math are doing what they are doing (choosing whichever problems they choose to be working on instead of working on other problems) for a reason, so utility cannot be removed from mathematics.
Quoting fishfry
Do you recognize that scientists, in their scientific endeavours, regularly employ metaphysical principles?
Quoting fishfry
In saying that "2+2" and "4" refer to the very same thing, you make a metaphysical (ontological) claim.
Kant said the same thing :) Synthetic vs analytic
Quoting Metaphysician Undercover
They most certainly do
Quoting Metaphysician Undercover
No, that's a psychological claim
No way! I just tagged you because you were "openminded and pluralistic about math" in the past with me
Quoting fishfry
I only read it in the Stanford Encyclopedia of Philosophy on Descartes Physics. It said people are having renewed interest in it. I watched a video once that showed how his definitions of forces and reactions couldn't work on a billiard table. The guy said he had another video on Descartes "flawed" optics, but I couldn't find it and even the first video isn't around anymore. Sad
Any claim, which anyone makes, says something about one's mind, so they can all be said to be psychological claims. So that's really irrelevant. But to say that "4" refers to a thing, and that "2+2" refers to the very same thing, rather than that "4" and "2+2" have meaning (in which case one might see that the meaning of each differs), is to make an ontological claim.
This is true only if "utility" includes fascination with exploring a subject, finding what's behind the next intellectual door, where an investigation might lead, etc. That's been my motivation for many years.
Yes, utility includes that, because there's always a reason why one explores one subject rather than another. I study for the very same reason, to find what's behind the next intellectual door, but I don't deny that there's always a reason why I head in one direction rather than another.
Yes thank you. People often don't like math because it's taught in a dogmatic way. But mathematicians themselves are very openminded, at least after a few decades when the new ideas start to sink in!
Quoting Gregory
I'm not actually familiar with any of the details. I perused the SEP article but didn't see where it said people have renewed interest. May have missed it.
Lol, true. It actually says in the first paragraph of the Stanford article "It is this unique amalgam of both old and new concepts of the physical world that may account for the current revival of scholarly interest in Descartes’ physics."
Oh from https://plato.stanford.edu/entries/descartes-physics/, different article than I was looking at.
So there is scholarly interest meaning historians of science? Or actual scientists? I'd be surprised if the latter.
Quoting Gregory
I responded to this yesterday but this afternoon I happened to come across this article by philosopher of science Massimo Pigliucci. He's debunking and ripping to shreds some bit of pseudoscientific woo from a guy named Klee Irwin, whose videos I've seen and who definitely strikes me as a crank. Pigliucci begins:
[quote]
Physicists seem to be on a roll these days. Unfortunately, I’m not talking about a string of new discoveries about the fundamental nature of reality, but of a panoply of speculative notions ranging from the plausible but empirically untestable (and therefore non-scientific), such as Sean Carroll’s marketing of the many-worlds interpretation of quantum mechanics, to sheer nonsense on stilts, like the idea that is the subject of this essay.[quote]
Thought that was interesting in the context of our conversation.
https://medium.com/science-and-philosophy/the-universe-simulates-itself-into-existence-and-other-nonsense-from-modern-physics-32e958b690b
On the contrary. I've made a concerted effort to engage with your ideas. I just can't discern any.
Quoting Metaphysician Undercover
Well then you have no idea what a number is, what a representation is, and you're just flat out wrong both philosophically and mathematically.
Quoting Metaphysician Undercover
I could see that ... except that in all the times we've talked, I've never been able to understand what meanings you assign to the symbol "2 + 2" and "4". You have not succeeded in making yourself clear.
That you attribute this to my own lack of effort in trying to understand you reflects on your own lack of self-awareness regarding the incoherence of your position, whatever it is.
Quoting Metaphysician Undercover
You haven't made a coherent case that I could even agree or disagree with. You've made no case at all.
Quoting Metaphysician Undercover
I say again: If you don't know that 2 + 2 and 4 refer to the same abstract entity, then you are in no position to have an opinion on Fourier series, which are far more sophisticated mathematical objects.
Quoting Metaphysician Undercover
You feel the same way about chess? Yet another of my arguments that you never bother to engage with.
Quoting Metaphysician Undercover
Some do. Some just "shut up and compute," which is a well-known saying in QM. And Newton said, "I frame no hypotheses," and explicitly rejected metaphysical considerations in his theory of gravity.
Quoting Metaphysician Undercover
No, I'm making a claim of Peano arithmetic, a purely syntactic system. I presented you a carefully crafted proof that 2 + 2 and 4 are the same thing. You pointedly ignored my argument and wouldn't even engage with my having presented it. You didn't just say, "Oh yeah well I have it on good authority that Giuseppe Peano cheated at cribbage." You just ignored what I wrote entirely and you continue to ignore it to this day.
You only showed your own ignorance and terror of symbolic reasoning. Yet you persist in caring about it. You had a bad experience with a math teacher along the way and it's scarred you for life.
"Descartes explicitly deems motion to be a 'mode' of extension". author
"Foremost among the achievements of Descartes’ physics are the three laws of nature (which, essentially, are laws of bodily motion). Newton’s own laws of motion would be modeled on this Cartesian breakthrough" author
Descartes "incorrectly regards (uniform, non-accelerating) motion and rest as different bodily states, whereas modern theory dictates that they are the same state." author
"Descartes insists that the quantity conserved in collisions equals the combined sum of the products of size and speed of each impacting body." author
"a body which is at rest puts up more resistance to high speed than to low speed; and this increases in proportion to the differences in the speeds." Descartes
"change is always the least that may occur." Descartes. Therefore the author says "a body’s determination is apparently linked to its magnitude of speed."
"In his Optics, published in 1637, Descartes’ derivation of his law of refraction seemingly endorses this interpretation of determinations. If a ball is propelled downwards from left to right at a 45 degree angle, and then pierces a thin linen sheet, it will continue to move to the right after piercing the sheet but now at an angle nearly parallel with the horizon. Descartes reasons that this modification of direction (from the 45 degree angle to a smaller angle) is the net result of a reduction in the ball’s downward determination through collision with the sheet, 'while the one [determination] which was making the ball tend to the right must always remain the same as it was, because the sheet offers no opposition at all to the determination in this direction'"
"In order to better grasp the specific role of Cartesian force, it would be useful to closely examine his theory of centrifugal effects... Besides straight-line motion, Descartes’ second law also mentions the 'center-fleeing' (centrifugal) tendencies of circularly moving material bodies: 'all movement is, of itself, along straight lines; and consequently, bodies which are moving in a circle always tends to move away from the center of the circle which they are describing' (Pr II 39). At first glance, the second law might seem to correspond to the modern scientific dissection of centrifugal force: specifically, the centrifugal effects experienced by a body moving in a circular path, such as a stone in a sling, are a normal consequence of the body’s tendency to depart the circle along a straight tangential path. Yet, as stated in his second law, Descartes contends (wrongly) that the body tends to follow a STRAIGHT line away from the center of its circular trajectory. That is, the force exerted by the rotating stone, as manifest in the outward 'pull' on the impeding sling, is a result of a striving towards straight line inertial motion directed radially outward from the center of the circle, rather than a striving towards straight line motion aimed along the circle’s TANGENT." (my emphasis, so you can see where modern theory disagrees with Descartes)
The article also says: "If, for example, God removed the matter within a vessel (such that nothing remained), then the sides of the vessel would immediately become contiguous (but not through motion)". It is not through motion because Descartes had what he called the “first preparation for motion”. This is the center of his vortex theory of the universe, which for him acts as a unified mechanical whole. He didn't believe time existed outside us, so there are simply the turnings of the wheels, going back to the first motions. He didn't believe you can prove there is a God from nature. Nature simply works like a clock, and as for clocks (which he loved), they don't delineate anything that is outside our own brains
This is exactly my point, such axioms are based in ontological principles, they are not "pure mathematics. You can insist that there is no ontology to them all that you want, refusing to consider the evidence, in denial, that's a matter of your own free choice.
Quoting fishfry
Actually I demonstrated your faulty interpretation of the premise of extensionality. That two symbols refer to something of "equal" value is not sufficient for the conclusion that they refer to "the same" thing. Being the same implies being equal, but being equal does not imply being the same. You commit a fallacy of conversion.
You are the one in denial, insisting that mathematical axioms are exempt from judgements of true and false, being "pure mathematics", and absolutely abstract, refusing to accept the truth in this matter.
PA is a formal symbolic system no different in principle than the game of chess.
Do you think chess has ontological significance? Yes or no? If no, then why do you think PA does?
Note that as usual I ask you direct, probing questions and you'll respond by changing the subject. I dare you to prove me wrong.
Quoting Metaphysician Undercover
Perhaps we're done for now. I tire of this game.
Quoting Metaphysician Undercover
There is no middle 'e' in judgment. Jus' sayin' but nevermind . Axioms are formal statements, strings of symbols that are well-formed according to specific syntactic rules.
You can have different axiom systems such as Euclidean and non-Euclidean geometry, or Abelian and nonabelian group theory, that are mutually inconsistent yet both interesting and valid; and both applicable in their respective domains.
Therefore there can be no "truth" in axioms; only logical consistency and interestingness. You don't want to understand that, knock yourself out.
I'm taking a break from our chats but perhaps we'll meet again down the road.
Hi, this remark has been on my mind. It's totally counter to everything I think I know, so I wanted to make sure I understand you. This is in reference to whether we can say that Heisenbergian uncertainty is epistemological or ontological, with my strongly taking the position of the former.
I did ask you about this the other day when I replied to your post ... if I did. I remember replying but who knows. In any case, can you explain this more please? I've told a lot of people online that it's epistemological, so if I'm wrong I want to find out.
Depends on the contexts of usage. My friend and I are equal (in the eyes of the law), but we are not the same (in the eyes of the law).
This is distressing. I'm beginning to agree with MU . . . :worry:
Did you see my reply here? Link.
I remember a physics prof in university spending maybe 15 minutes scolding me when I said something like "the uncertainty principle says we can't know...", they responded "The uncertainty principle has nothing to do with how much we know about particles, it's not about our knowledge of the particles, it's about the particles" - not that exactly since it was a lot of years ago now, but that was definitely the gist. They were pretty mad at the suggestion it was epistemic, and their research was quantum theory, so I trust 'em.
Edit: I have another story like that which is pretty funny. We had an analysis lecturer that was extremely eccentric, and one of the masters theses they were willing to supervise was on space filling curves. They handily included a "picture of a space filling curve in a subset of the plane", which was just a completely black square. I asked another prof if the eccentric prof actually wrote out code to draw the space filling curve, since it was the kind of thing he'd do if he could. The other prof got pretty angry and said "Computers can't do that, it's noncomputable, the construction relies upon the axiom of choice!".
It's not that bad! There are lots of equivalence relations!
That's not true, we went through this in the other thread. The application of the rules of mathematics always has a different purpose from the application of the rules of chess. If we want to apply mathematics toward understanding the universe, we need truth (in the sense of correspondence) in the axioms. Playing chess has a purpose of competing with another person for supremacy, within extremely limited conditions. If the rules of the game are designed to fulfill the purpose of the game, the people who have composed the rules must have kept that purpose in mind when creating the game. If not, there would be incoherence within the rules of the game, having been designed for different purposes.
If utility is removed from mathematical axioms, and they are composed simply for aesthetic beauty, then there will be random difference between one set of axioms and another, and real application would not be practical. This is not what we have in mathematics. Therefore we can conclude that mathematical axioms are not composed for aesthetic beauty.
If the purpose of mathematical axioms is simply utility, in an unconditional sense, then different mathematical systems will be inconsistent with others, depending on the purpose (the game) they are designed for. This means incoherency within the mathematical rules as a whole. This is what do we have in mathematics, as you yourself admit.
To produce consistency within the rules of mathematics as a whole, there needs to be one principle of utility, one purpose for which all the axioms are designed. Since mathematics is most widely applied in sciences we can look at the purpose of the axioms within science to get an idea of what that fundamental purpose might be. There are two distinct purposes which appear to me, one is the understanding of the universe, as mentioned above, and the other is for the prediction of events.
These two purposes are distinct. The former involves the bivalent logic of truth and falsity, while the latter involves probability. There is a fundamental incompatibility between these two, expressed in the law of excluded middle. When the axioms of one meet with the axioms of the other, paradox appears, as demonstrated by Zeno. This is because the logic of being (what is and is not) is inconsistent with the logic of becoming (what will be). The arduous task of the ontologist (metaphysician) is to determine the principles by which the two might be related to each other, to establish compatibility between them.
Quoting fishfry
I'm changing the subject because your analogy has been demonstrated as completely insufficient and not irrelevant. Playing chess has a completely different purpose from applying mathematics.
Quoting fishfry
An axiom is a proposition which may or may not be accepted. That is the nature of an axiom. There are various reason why one might accept or reject a proposition. To say that an axiom must follow "specific syntactic rules" is one of these reasons, but clearly there are others.
Quoting fishfry
Obviously you have considered the acceptance and rejection of axioms from a very narrow perspective, without observance of the many real factors involved in this process.
Quoting jgill
The attempt to unnecessarily restrict usage is fraught with problems. We are creatures of habit, and if habitual interpretation is different from the one imposed by a logical rule, the habit will often impose itself into interpretation of the logical conclusion in the form of equivocation.
So for example, we can define "equal" as "same", such that within this logical circle all uses of "equal" mean nothing other than "same", and all uses of "same" mean nothing other than "equal", but there would be absolutely no point to this. We could just use one of those words without losing anything. The only reason to use both, is if they have different intension. But that difference in intension requires that we determine the relationship between the two before we proceed with any logic procedure.
If in common usage, "equal" is the broader category, such that not all cases of being "equal" mean "the same", and all cases of being "the same" mean being "equal", then we ought to adhere to this in our logical definitions and proceedings to avoid possible confusion and equivocation. So there is a fundamental principle which we habitually recognize, and this is that two distinct things might be equal, but only one thing is the same as itself (law of identity). This distinguishes the uniqueness of a "thing" from any other similar or equal thing. But we commonly use "same" to refer to two distinct things which are of the same class, type, or category, and this is a completely different meaning of "same". If we equate "equal" with "same", we appeal to this other meaning of "same", which allows that two distinct things are the same. But then we are in violation of the law of identity.
Quoting fdrake
If agreeing with me was really that bad, I'd be afraid to leave my house.
How can they represent the same Platonic ideal when "+" represents an ideal in itself, which is part of "2+2", but not part of "4"?
Irrelevant. 4-ness is the ideal in discussion. :roll:
They are exactly the same set. If you have some mathematical framework in which 2 + 2 and 4 do not represent the exact same abstract mathematical object, I would appreciate your filling in the details. Even though your area of specialization was far removed from undergrad set theory, I'm sure you must have had some glancing acquaintance with that material at some time in the past.
Quoting Metaphysician Undercover
Ah! My friend @MU I believe I have achieved a glimmer of understanding your position. Let me see if I can say this back to you.
* First, there's what Plato said. Nevermind that he may or may not have been right about the ultimate nature of things. He's got a lot of mindshare over the millennia. But still, he's just a person who wrote down some thoughts in a context very different from ours. So you are saying that according to Plato things are such and so; but that's not necessarily the case.
* If we accept Plato for sake of discussion; then there's an ideal or a class or a category of thought called "plus" and another one called "2". And when you combine 2 + 2 to get 4, you are stating a mathematical equality but not a metaphysical one; because the left side of the equation 2 + 2 = 4 denotes the combination of two ideals and the thing on the right is only one ideal.
Well maybe. I think that point's a stretch. Plato could be wrong. But more to the point, 4 already includes within itself the possibility of being partitioned into 2 + 2. or 1 + 1 + 2, or 1 + 1 + 1 + 1. This is in fact the mathematical subject of partitions. It's what Ramanujan was working on inThe Man Who Knew Infinity. IMO doing a good job of explaining the partition function to a general Hollywood audience is one of the greatest math feats in cinematic history.
Point being that if 4 is an "ideal" or whatever you call it by itself, it ALREADY CONTAINS the possibility of all its positive integer partitions.
Truly, 2 + 2 and 4 are the same Platonic object. I don't find your argument convincing for this reason:
Sure, 2 + 2 expresses the fact that 2 and + can be combined to make 4. But 4 already expresses the fact that 4 can be represented as 2 + 2. Partitions are a natural and built-in aspect of a number.
Am I at least representing your position correctly?
I'm speaking of the two symbols. 2+2 and 4 are not the same symbols. And I don't appreciate your snide remark. Of course they represent the same mathematical object. I'm not that far gone! They are "equal" in the sense they represent the math object, but are not the same symbols. :angry:
Thank you. I missed that. I'll reply separately.
Quoting fdrake
My own sense is that the very last people in the world who have a clue about philosophical issues are the physicists. I've personally seen big time, well-known celebrity physicists, make elementary errors talking about infinity, or whether what they study is real. Most physicists, or at least many, actually think their theories are True in some absolute sense. Or more commonly, they don't even think about it at all. They just "shut up and calculate," which is very wise advice.
When it comes to metaphysics. physicists are the last people I'd listen to; and celebrity physicists the least of all :-)
Quoting fdrake
I'm not sure what was funny about that except that it's perfectly computable and doesn't require choice at all. Did I understand that and/or get the math right? And on a practical level we could input the resolution of the printer or display device, and calculate exactly how many iterations of the curve would show up as solid black. And it would of course be a finite number, so definitely computable and not needing any mathematical foundations beyond counting to a large but finite number. That's way less than the Peano axioms. An ultrafinitist, someone who doesn't believe in the infinitude of sufficiently large sets, would be able to compute the space filling curve to the point that it appeared black on the display. I'd be willing to guess you don't need that many iterations. Your eye couldn't make out the lines, it would all black pretty soon.
You've forgotten about summation. It might be the case that "4" represents 4-ness, but "2+2" represents a particular instance of the general rule of summation, not 4-ness.
Quoting fishfry
I think you almost understand, but not quite. The symbol "4" represents a particular unity, if we adhere to Platonic idealism. Four is an object, a number. It may be the case that this number could be constructed through the summation process of 1+1+1+1, but this process is not the same thing as the object itself. Processes are not objects, they are activities which objects are engaged in. A cause is not the same as the effect. So it is ontologically incorrect to say that this process which creates the object "4" is the same thing as the object "4".
Evidence of this fact is that the object "4" may be created in an infinity of other ways, "6-2" for example. So, all these logical possibilities which are inherent within "4", cannot be the same as "4" because each one is itself a different process. The fact that a different process can be utilized to make an object indicates that the process is not the same thing as the object.
Eh, if it was someone else I wouldn't've trusted it. The guy lectured in quantum physics and philosophy of quantum physics. I'm sure that it can be doubted.
Quoting fishfry
I think they operate quite rightly, provisionally treating the theory as if it is the thing is part of how it works I think. If the discussion we'd have is "what properties of a model can be treated as standing in for a property or behaviour of the thing", that'd be quite different from "are all models merely epistemic" - the first would actually be about the uncertainty principle, the second is a much broader realism vs anti-realism of scientific content debate. If you and I have to go through the latter to get to the former, that's fine with me, both are interesting.
You know, no one I've told the story too ever thought about it like that. The thing that I found funny about it was that the other prof didn't doubt that the eccentric prof would go in MS paint and make a black square to represent a space filling curve to some approximation, he criticised the ability to represent it exactly constructibly. You know a-priori that a sufficiently computed space filling curve in the unit square is indistinguishable from filling in the unit square in MS paint.
You are looking behind the symbols to the mathematics they represent. They are certainly equal in this regard. But if you look superficially at the compound symbol "2+2" and the singular symbol "4" as ink squiggles on paper, they clearly are not the same. But, of course, that's not your perspective. I am simply giving an instance when two things are equal in one sense, but not the same in another sense. You and fishfry can argue ad infinitum it seems. :roll:
Then there is the sequence of continuously differentiable functions that converge uniformly on [0,1] to that line segment, but whose arc lengths go to infinity:
[math]{{z}_{n}}(t)=t+i\frac{1}{2\sqrt{n}}Sin\left( n\pi t \right),\text{ }t:0\to 1[/math]
No matter what the magnification, once chosen, n sufficiently large produces a straight line one unit long on the computer screen.
Maybe putting it to a vote could be interesting — in The Lounge, though.
Typing 2+2 and 4-2 into a pocket calculator could be an accompanying exercise.
There is no question that 2+2=4. Not even a fool would deny that. The question is whether "2+2" represents the same object as "4".
Quoting jgill
I think it's true that fishfry and I will never agree, but the disagreement between you and I appears to be as to what constitutes a "mathematical object", or "Platonic ideal". Mathematicians may have defined "object" in such a way that "2+2" represents the very same object as "4", but I disagree with this definition, as it does not properly represent what a Platonic ideal really is. So I believe that the definition was manufactured for the purpose of doing what the mathematicians wanted to do with it, rather than with the purpose of representing what a Platonic ideal really is. That is not an acceptable way of doing logic, to manufacture premises which will support the desired conclusion. It is a case of petitio principii
The problem is, as Aristotle demonstrated, that there is an inherent and fundamental incompatibility between a process (becoming), and an object (being). The object is intelligible, and the process is fundamentally unintelligible. So a symbol like "+", or any type of operator, or function, does not represent an object, and represents something which is fundamentally unintelligible. And if we allow this element of unintelligibility into the object, to say for instance that "2+2" represents an object, then the object itself becomes fundamentally unintelligible. This might be the Kantian perspective, to represent the noumena (intelligible object), as fundamentally unintelligible, but it is not the Platonic perspective, and you can see how it is inherently contradictory to say that the intelligible object is fundamentally unintelligible.
In other words, if the Platonic ideal is supposed to be an eternal Form, meaning a truth which escapes from the corruption of time, it cannot be represented as containing within itself a temporal process. So these representations of Platonic mathematical objects, which allow processes (functions) to inhere within the object, are not proper representations. They are not proper because any such process, which inheres within an eternal object, must have infinite temporal extension, being a never ending, never changing infinite process, such as Aristotle's perfect circular motion. But this metaphysical idea has been demonstrated as a false one. Ideal perfection cannot be granted to a process.
,
Abstract quantities (is the phrase)
You and I don't really disagree, MU. I enjoy reading your posts, learning of philosophical perspectives I never considered the years I was a practicing mathematician. And I enjoy reading posts by fdrake and fishfry when they pertain to elements of mathematical thought of which I have only superficial knowledge.
If I had known colleagues who were concerned about Platonic ideals, irrational numbers, or transfinite set theory I might have more to offer, but those issues were at best peripheral to our interests. As one of approximately 36,133 descendants of Weierstrass I have been happy using the notions he and Cauchy championed. :cool:
A number such as what is indicated by the numeral "4", is an abstract quantity. In the case of "2+2" , there are two distinct abstract quantities signified with "2" and "2", along with an operation signified with "+". Therefore it is incorrect to say that "4" represents the very same abstract quantity as "2+2", because clearly there are two distinct abstract quantities signified by "2+2", related to each other by the signified operation "+", not one quantity.
Quoting jgill
We all have our own interests. Since one of mine is philosophy, and mathematics really is not, I approach this issue from the perspective of being concerned about Platonic ideals rather than the associated mathematics. Many others in the forum will say to me, forget about what Platonic ideals are, or whether "Platonic ideals" is a valid concept, take the axioms for granted, and discuss the mathematics. But if the substance of the axioms is Platonic ideals, I want to understand the validation.
I have that happen to me a lot.
Are you identifying an object such as the number 4 with the process that "creates" it? I think that's a pretty big stretch. I can't imagine Aristotle wouldn't have been that wrong, so I'm guessing your interpretation is.
In other words you seem to be associating 4 with the "process that created it," so that a 4 stamped whole on God's forge is different than one made by jamming 2 and 2 together.
This notion makes no sense to me. The number 4 is the number 4, and it's inherent in its nature that it can be represented many different ways. Are you claiming Aristotle said that a thing is actually "thing plus method of making it?" And what makes him right and everyone else wrong?
No I'm not making such an identity. But I'm saying that if you assert that "2+2" is the same object as "4" you are claiming such an identity. The process of adding two with two will make four, but it is not four. I am saying that the process which makes four is not the same as the number four itself. A cause is not the same thing as its effect. You are insisting that the two are the same.
Quoting fishfry
I really can't believe that you do not see the difference between what "2+2" represents and what "4" represents. The former indicates two quantities of two, with an operation of addition also indicated. The latter indicates one quantity of four. To interpret "2+2" as representing the number four is very clearly a misinterpretation.
The proof is that we can represent the relationship between two distinct 2s in many different ways, such as "I have 2 dogs, and 2 cats", "2,2", "2+2", "2X2", etc. In all such instances of representing two distinct quantities of two, they must be interpreted as two distinct quantities, to avoid misinterpretation. If you do not follow this simple rule of interpretation you completely disregard the application problem of adding apples and oranges. If two groups of two are automatically four there is no way to avoid the category mistake described as adding apples and oranges. In other words, you do not allow any provision for the reason why they were represented as distinct in the first place. Therefore, in insisting that "2+2" represents the same thing as "4", you are denying any valid reason for representing the two 2s as distinct in the first place, and nullifying that representation, of two distinct 2s, as an invalid representation.
It seems to me that 2+2 says more than just 4. It says how you can get 4 from starting with 2.
This is the same error @jgill pointed out that I made the other day. I do not assert that 2 + 2 and 4 are identical. They're obviously different symbol strings. They do refer to the same abstract object, as does 3.999..., 6 - 2, and the smallest positive integer [math]n[/math] such that there are two non-isomorphic groups of order [math]n[/math]. All those descriptions refer to the same abstract object; same as in identical.
The "means" or "process" of getting to the abstract object is irrelevant. In fact given the abstract object represented by 4, all the other representations are already inherent in it. You deny that. That is the crux of our disagreement I believe.
Quoting Metaphysician Undercover
The abstract number represented by '4', which I represent as 4 (but do not confuse the referent with the symbol), is not an effect. It stands alone, and in its very existence incorporates all of its representations and the processes that they bring to mind. But the processes are not the thing. There are multiple processes that may lead to the same abstract thing, as this example shows. But I don't think of this as a process leading to 4. I think of 4, as the primary object, that already incorporates all of the processes that could lead to it. 2 + 2, 3.9999..., etc.
Quoting Metaphysician Undercover
That's because I'm not hallucinating "causes" or "processes" where there are none. The causes and processes are secondary to the essential existence of the abstract number 4. You have your ontology backwards.
Quoting Metaphysician Undercover
You're stubborn, I'll give you that.
Quoting Metaphysician Undercover
Oh, proof. Why would I waste my time looking at, or even acknowledging that you've provided a proof? You don't offer me the same courtesy.
But again you're just repeating your confusion. The number 4 incorporates within it 2 + 2 cats or 3.999... or whatever. They all point to the same thing. They're not "ways of getting to" the thing. I can't imagine why you have such a strange idea.
Sheboygan, Wisconsin is the same identical city whether you get there from Milwaukee or Green Bay. 4 is the same number whether you "get there from" 2 + 2 or 3.999... Why you think these two cases are different I can't imagine. Unless you think that [math]\text{Sheboygan}_{\text{Milwaukee}} \neq \text{Sheboygan}_{\text{Green Bay}}[/math]. Is that what you think?
Ah. Harkens back to the last words of the state as they executed the heliocentrist. Before they were disproved and later overthrown of course. How reminiscent.
For sake of conversation, I don't think they actually executed any heliocentrists. If you're thinking of Giordano Bruno, Wikipedia points out that ...
"Starting in 1593, Bruno was tried for heresy by the Roman Inquisition on charges of denial of several core Catholic doctrines, including eternal damnation, the Trinity, the divinity of Christ, the virginity of Mary, and transubstantiation. Bruno's pantheism was not taken lightly by the church, as was his teaching of the transmigration of the soul/reincarnation. The Inquisition found him guilty, and he was burned at the stake in Rome's Campo de' Fiori in 1600."
Neil deGrasse Tyson somewhat misrepresented the Bruno case on his tv show. Bruno's fatal heresy was religious and not necessarily scientific.
Nor was Galileo executed. He was confined to house arrest. Even this story is more nuanced than commonly known. The Pope was not a science denier but was in fact an enlightened, scientific man; and Galileo was the Pope's good buddy. Galileo went out of his way to cause his old friend trouble and that's a large part of what happened to him.
And nor, as long as I'm here, does the earth revolve around the sun in any absolute way. If you stood outside the galaxy and plotted the paths of the earth and sun, they'd spiral around each other as the spirals moved through the universe. Only by drawing a coordinate system with the sun in a fixed position can we write down the "orbit" of the earth. And if we wanted to, we could assume a fixed earth and write down the orbit of the sun. A fable like "The earth revolves around the sun" involves simplifying assumptions that are not metaphysically true; unless by truth you mean historically contingent scientific convenience and consensus.
I'm thinking of taking up geocentrism. It might be the last sane stance left in a crazy world.
We're just going around in the same circle. By what principle do you say that this string of symbols "2+2" refers to one object? How would you distinguish which symbols refer to an object, on their own, and which objects require a string of symbols to represent them? Is it your rule that the left side of an equation refers to one object, and the right side of an equation refers to the same object?
Quoting fishfry
It's not irrelevant because "2+2'" clearly refers to an operation, or ":process". There is an operation symbol "+", within the phrase. This is the fact you are ignoring, and are in complete denial of. How can you deny this fact? It's right there in black and white, "+". You look at "2+2" and read it as symbolizing the abstract object "4", refusing to interpret what the symbols actually represent. If this is not a very clear and obvious example of misinterpretation, then how else can you explain your ignorance of what is written? Do you actually recognize what is written but have some reason to deny it?
Quoting fishfry
Do you not see that this is a false way of looking at an effect? If there exists an object, and there is a multiplicity of processes which may have led to the existence of that object, only one of those processes is the correct process which caused the object. It is false to say that the object "incorporates all of the processes that could lead to it". This misconception leads to many ontological problems, because it allows that infinite possibilities, and infinite chains of processes inhere within an object, rendering an object as inherently unintelligible. To employ a system of mathematics which makes the existence of objects unintelligible, by incorporating infinity into the object's existence is self-defeating, if one's goal is to understand the existence of objects.
Quoting fishfry
I can agree with you on this point, the causes and processes are secondary. But are you ready to agree that since there is a "+" in "2+2",this phrase refers to a process?
Quoting fishfry
Again, you are ignoring the significance of "+". Please read the phrase, and interpret it according to what the symbols actually say, not according to some preconceived notion of what you want the symbols to say.
Quoting fishfry
Right, now if you were in Green Bay, and followed the directions of how to get from Milwaukee to Sheboygan, you would not get there from Green Bay. Likewise, if you were at 6, and followed the directions of how to get to 4 from 2, i.e. "+2", you would not get to 4 from 6, following those directions.
This is your problem, you are reading "2+2" as 4, instead of reading it as directions of how to get to 4. .
Yes. My rule and everyone else's. That's what the equal sign means.
The equal sign means that the two sides are equal, just as "equal" indicates. Here's what Wikipedia says:
"The equals sign or equality sign, =, is a mathematical symbol used to indicate equality. It was invented in 1557 by Robert Recorde. In an equation, the equals sign is placed between two expressions that have the same value, or for which one studies the conditions under which they have the same value."
Clearly you are wrong to say that it's everyone's rule, that the equal sign means that the right and left sides refer to the same object. This rule is an expression of your idiosyncrasy.
I already went through your converse error, but I'll explain it to you again, as you don't seem to get it for some reason. I believe the formal fallacy is called affirming the consequent. If two symbols refer to the same thing, then there is necessarily equality between what the symbols refer to. But this does not mean that two equal things are the same thing. Do you understand this so far? Many things are equal, like two human beings, two dogs, or two cats, in the sense that the two distinct things can be given the same value. A human being might be equal to a dog if the evaluation criteria is being an animal. And do you see that the equal sign means that the right and left side are equal, as the Wikipedia articles says? How can you conclude, without the fallacy of affirming the consequent, that two equal things are necessarily the same thing?
Profound stuff.
After months of arguing this point, fishfry still seems to think that the equals sign means the same. Next, fishfry will offer me a proof of this. As you can see, we've been through it before.
How could he possibly offer a proof? It's a definition!
But yes, we have been through this before. You remain unconvinced, but that is about you, not about "=".
Fishfry claimed to have given me a proof of this, in the other thread, and continues to refer to this proof.
Do you accept this definition, that to be equal is to be the same? Are you and I the same, just because we're equal? Oh yeah, I remember now, you have no respect for the law of identity either, and you equivocate with "the same" in your interpretation of Wittgenstein's so-called private language argument. You think that if two distinct instances of sensation are similar, they can be said to be "the same" in the way that a chair remains the same chair if no one switches it out when you're not looking.
Do you understand the reason why Aristotle formulated and stated the law of identity in the way that he did? He did this to have a tool to be applied against such logical sophistry. When "the same" is used in a way which is not consistent with the law of identity, then we are not talking about objects. Objects are identifiable according to the law of identity. So this culture of mathematicians who use "same" in this way, and then proceed to talk about the mathematical "objects" represented, are engaged in this form of sophistry which we might call deception.
If we take jorndoe's suggestion, and say that numerals represent abstract quantities, we see very clearly that "4" represents one abstract quantity, and "2+2" represents two distinct abstract quantities with a mathematical operation of addition represented. If we replace "abstract quantity" with "object", there is no rule which dictates that "2+2" could represent one object. So this culture, which assumes that "2+2" represents an object, which is the same object that is represented by "4", just because two plus two is equal to four, is a culture of sophistry and deception.
Quoting Metaphysician Undercover
Quoting Metaphysician Undercover
"2+2=4" ? 2+2=4
?
Good point, MU. :nerd:
The question then, is who is doing the equivocating? Meta apparently denies that 2+2 is the same as 4. It's not at all clear, as @fdrake, that he means something different to '"2+2" is not the same as "4"'.
SO, to be clear,
2+2 is the same as 4, and
"2+2" is not the same as "4"
It seems likely that @Metaphysician Undercover does not use quotes in the way the rest of us do.
Quoting Metaphysician Undercover
So if you follow the directions and complete the process, then 2+2 = 4?
it's quite obvious, that in no way is 2+2 the same as 4. That's the point. It's very clear that 2+2 is equal to 4, meaning that the two have the same value within some value system, but at the same time it is also very clear that these two equal things are not the same thing. That is the way that "equal" is normally used, to refer to two distinct things of the same value. We never say that because two things are equal, they are therefore the same thing.
If you are defining "equal" to mean "the same as", as fishfry does, this is an unacceptable definition for a logical system because it is not consistent with the law of identity
Quoting Luke
Of course, 2+2=4, and this is an acceptable statement. As I said already, not even a fool would deny that. What is at question is whether "2+2" and "4" both refer to the same thing. In other words, is there a difference between being equal and being the same.
Well, thing is... most folk will disagree.
So again, you have a specialist use that is at odds with common use.
Just sayin'.
The law of identity, and logic generally, has moved on a bit since Aristotle. I've been unable to follow your argument that such is not consistent with the law of identity... SO, for example, it would generally be accepted that Hesperus = Phosphorus. Would you accept that?
There can be a difference; it depends how the terms "equal" and "the same" are being used. But the terms "equal" and "the same" can also be used synonymously. Is this the basis of your dispute?
Really, you think that two equal people, because they are equal, are the same person. I think you are very wrong to think that most people would disagree with me. I think that there is a very small, and distinct culture of people who claim that equal things are necessarily the same thing. You might happen to be a part of this culture, and you like to believe that most folk are like you, to make it feel like your culture is more important than it really is.
Quoting Luke
My argument is that this use, to use "equal" and "the same" synonymously, is in violation of the law of identity, and therefore unsuitable for any system of logic.
Yeah, you are better off skipping the question and answering something else. Nice dodge.
Just so we are clear, Quoting Banno
Did you read my quote from Wikipedia?
Quoting Metaphysician Undercover
Since Wikipedia agrees with me. it seems highly unlikely that most folk would disagree with me. Notice how "same" is qualified with "value". The right and the left side of the equation have "the same value". Anyone who knows how to read English knows that this does not mean that they are the same.
I already went through this. If two symbols refer to the same thing, they are equal. But it is a fallacy of affirming the consequent to say that if two things are equal they are therefore the same.
What does the use of these terms have to do with the law of identity?
You seem to be saying that "equal" is a suitable term in relation to the law of identity, but "the same" is not. That is, you are attempting to prescribe the use of these terms to be non-synonymous. But why can't these terms be used synonymously in relation to the law of identity?
The law of identity is a fundamental law of logic, established to prevent deceptive use of terms. such as equivocation. We are discussing the use of terms within a logical system, therefore the law of identity is applicable.
Quoting Luke
Yes, "equal" and "the same" could be used synonymously. But if we adhere to "the same" as defined by the law of identity, and consider "equal" as it is used in mathematics, they are not synonyms. That's the point, this definition provides a false representation. That definition is a false premise. The equals sign is not used to indicate that the right and left side of the equation refer to the same thing, it is used as described in my quote from Wikipedia, to indicate that the right and left side have the same value. Therefore, to define "equal" as indicating "the same", for the sake of a logical argument concerning the nature of mathematical systems, or "mathematical objects", is to start with a false premise. Such arguments which take this definition as a premise are unsound because this is not the way "equal" is used in mathematics.
It appears to me like some people participating in this thread have seen "equal" defined in this faulty way, so according to that definition they conclude that "equal" is actually used in this way in mathematics. Do you see the equivocal sophistry here? Because it is defined in this way, they are misled into the conclusion that it is used in this way. They clearly have not taken any time to investigate, observe, and notice the reality of how "equal" is actually used in mathematics. If they had, they would see that mathematicians use "=" to indicate that two things have the same mathematical (quantitative) value, not to indicate that the things designated by the two sides of the equation are the same thing. So when these people produce a logical argument about the nature of mathematics, or "mathematical objects" and start with this definition as a premise, their arguments are completely unsound, being based in that false premise, which is not representative of mathematics.
I explained to fishfry already, that if the two sides of an equation actually referred to the very same thing, equations would be totally useless in application. To resolve problems, equations are used to compare distinct situations, knowns are compared with unknowns, producing information about the unknown situation through comparison with the known. If both were exactly the same, such a comparison would be unnecessary because we would know that the supposed unknown is really exactly the same as the known, and therefore really known as the same. The equation would give us no new information.
You're arguing that both sides of an equation have equal (the same) value, but that they are different expressions of that value? Sounds reasonable.
What are you talking about? How can you be so daft in your interpretation, when I've explicitly stated over and over again what I am arguing. Your misinterpretation appears to be completely intentional, an intentional straw man.
I am arguing that what is represented by the right side of the equation has "the same value" as what is represented by the left side of the equation. But we cannot conclude that what is represented by the right side of the equation is "the same" as what is represented by the left side of the equation, if we adhere to the law of identity in defining what "the same" means. Do you understand the difference between "having the same value", and "being the same"?
I think you understand what I am saying, so don't bother replying with another straw man, fake interpretation. But if you have a relevant objection then I'd be glad to see it..
So of course, there must be a first manuscript, by the hand of Euclid himself, else none of the other manuscripts could have any objective reality whatsoever.
Two diamonds have the same value, but are not the same. They are equal in value. They appear equal when viewed without high magnification. Just babbling, pay no mind. :roll:
Thanks jgill, the others just don't seem to get it. We could say the same thing about all forms of measurement. Two different things are two kilograms, or two meters long, so they would be equal in respect to the particular system of evaluation. Likewise, "2+2" and "4" are equal in respect to quantitative value, but this does not mean that the same thing is signified by each of these two, only that they are equal in that particular system of evaluation.
Sense of irony is not strong with this one, I see.
Yes that's very cool. I do happen to know that Robert Recorde invented the equal sign. I keep hoping someone will ask me someday.
Quoting Metaphysician Undercover
You're wrong mathematically and we are not getting anywhere. I tried to beg off the conv a while back but seem to be having difficulty executing on my intention. We're not making progress. I have nothing new to say.
Quoting Metaphysician Undercover
I understand your belief that two things that are mathematically equal are not the same thing. You're wrong. If X = Y then X and Y necessarily refer to the same abstract object. There is no question about it.
Quoting Metaphysician Undercover
Yes, and this is called the fallacy of equivocation. Using the same word, equality, with two distinct meanings within the same argument. In human affairs, equality has a different meaning. When Thomas Jefferson wrote that "All men are created equal," he of course did NOT mean that they were mathematically equal, as 2 + 2 and 4 are equal; but rather equal under God and nature as human beings.
Mathematically, no two human beings are equal. They could be equivalent modulo various properties. If they both live in California or if they are of the same race or work in the same profession or so forth, we could call them equivalent. Or if we want to assert the desirability of the state of affairs in which they each have the same chances and possibilities in life, that would be another form of human equality.
But it's not mathematical equality. I'd like to say it's beneath you to stoop to such a low rhetorical trick. But I guess it's not beneath you after all. Frankly it's beneath ME to have to explain this in words, it should be obvious that mathematical equality and Jeffersonian equality are not the same thing.
Quoting Metaphysician Undercover
Because that's what mathematical equality is. That's how mathematicians define equality. Ultimately you have the same set on both sides of an equation. Once again you erroneously take your ignorance of mathematics as profundity in philosophy.
If two expressions do NOT refer to the same abstract object, then they are NOT equal.
That is a mathematical fact. Though of course it is not a fact in the Jeffersonian sense of equality. Two distinct people could be equal under the law. Equivocation. Same word different meaning depending on context.
Quoting Metaphysician Undercover
WHAT? That is completely nonresponsive to the point, which is that Sheboygan is still Sheboygan regardless of how you got there.
Nevermind. If you respond I'm going to try not to. Just for my own sanity. Interacting with you is fun in a tongue-in-my-sore-tooth kind of way, but I need a little break please.
Yes, that’s why I said that both sides of the equation are different expressions of the same value. What part do you disagree with?
Why does Wikipedia agree with me if I am wrong? I can assure you that I didn't write the page.
Quoting fishfry
Why does Wikipedia disagree with you and say that under specific conditions the two things referred to have the same value, not that they are the same thing?
Quoting fishfry
Yes, two men are mathematically equal. One man is mathematically equal to another man. Each being "one" man, indicates that they are mathematically equal. Furthermore, each person, having the right to vote is mathematically equal to every other person, so they count the votes to see who wins the election. It is clearly the case that human beings are mathematically equal in a democracy, each having one vote. There is no other form of equality. "equal under God and nature as human beings" is just a fancy way of saying that under the condition of being human, we are all mathematically equal.
Quoting fishfry
If you really think that two men are not mathematically equal to another two men, or five dogs are not mathematically equal to another five dogs, or an object of five kilograms is not mathematically equal to another object of five kilograms, or a five kilometer stretch of highway is not mathematically equal to another five kilometer stretch of highway, such that there is some other meaning to "mathematically equal", then tell me what that other meaning of "mathematically equal" is.
Quoting fishfry
Oh, now I see your problem. You think that because some set theory defines "mathematical equality" in this way, then this is what equality means in mathematics. As I explained to Banno, and to you already, this is a faulty definition, the one employed by the axiom of extensionality. It does not truthfully represent how "equal" is used in mathematics. It was devised for some other purpose, not for the purpose of representing how "equal" is used in mathematics. So, some set theorist defined "equal" in this completely faulty way, totally unrepresentative of how "equal" is actually used in mathematics, and you employ this definition as a premise in your argument against me. Your premise is a false premise, as evidenced by the Wikipedia quote. Your argument is unsound, being based in the false premise that mathematicians use "equal" in that way. They do not.
Quoting Luke
The different expressions represent different things with the same value. "2+2" says something different, it represents something different from what "4" represents, though we say that the two distinct things represented have the same value within the arithmetical system.' I don't really know what you would mean by "different expressions of the same value". That sounds like you are assigning value to the expressions themselves, rather than to the things represented by the expressions.
But it was not a representation of what I am arguing anyway, that's why I criticized it as a straw man. I am arguing that the different expressions are not different ways of representing the same thing, as in Banno's example of "Hesperus = Phosphorus". That is what fishfry is arguing, that you have the same thing represented on both sides of the equation. Even if we try to reduce "2+2", and "4" to being simple representations of "value", as you seem to want to do, we'd have to qualify what type of value. So we might say that they both represent "the same quantitative value", or "mathematical value". But we still cannot say that they have "the same value" in an absolute sense because there are all sorts of different value systems. That's why the Wikipedia quote refers to "the conditions under which they have the same value". "Value" is relative to a particular system of evaluation. So when it is said that "they have the same value", it is implied that they have the same value within a particular system of evaluation, the mathematical system.
I am hardly responsible for anything on Wikipedia, let alone your own interpretations of same. I didn't spend any time looking at that Wiki page. I know the math. Critiquing Wiki on this issue is not of interest to me at the moment. Some Wiki pages are better than others. Especially when it comes to the lead sentence or paragraph of a technical subject, many simplifications are made and many subtleties ignored. They're trying to give naive readers a sense of an idea. Summary and overview. Not to be taken literally and used as some kind of trump card in an online discussion. Jeez man you are reaching.
I'm really interested in diving into this but haven't had time to think about it much or read your other post to me on the subject. Instead of deferring my response to your posts indefinitely in the false hope of eventually saying something clever, for now I'll just retreat into what I think my position is.
The Planck scale is the scale at which our current physical theories can not be applied. We don't know what's going on at distances and times smaller than the Planck length and time, respectively. That's why I say it's epistemic.
I am not sure I follow the argument from Fourier series to saying that "therefore the Planck scale is ontic."
I don't think I'm conflating the problem of models in general with the idea of the Planck scale. Except that you can't apply a model outside of its domain of applicability, which is the same as with the Planck scale. Good question. With models in general, they don't so explicitly tell us what we can't know. If we have a model, people can disagree about whether it applies to a given situation. But with the Planck scale, everyone agrees on where the theory applies and where it doesn't. I'm afraid I don't have any better thoughts on this topic at the moment. But it is important to me because I have a strong belief that the Planck limits tell us what we can know, not what is. I wish I understood your argument better.
Do you understand what you mean by it (in your first sentence of the quote above)? Why do you think I mean anything different? You’re arguing against yourself here.
Quoting Metaphysician Undercover
I thought we were all talking about “the mathematical system”?
Sorry Luke, I have no Idea what you're talking about here. I did not use "it", and you're not making clear what "it" refers to. I said something different from what you said, so I think it's highly unlikely that we both meant the same thing. Since we did not say the same thing, it makes no sense to use "it" to refer to what both of us said.
Quoting Luke
Just making sure that you understood this. You're statements appeared somewhat misleading, as if you were talking about "value" in an absolute sense, implying that numbers express the value of something in an absolute sense, rather than a specific type of value.
If you can't even follow the discussion, then never mind.
:D
Since 4=2+2, 2+2 and 4 are interchangeable.
Doesn't matter if you write y=3x+2+2 or y=3x+4, though the latter is a bit shorter.
Which, by the way, google plots like so:
Hopefully it's not too much for you; from memory, it's something like late elementary school / early high-school material.
Prompted by our conversation I went and looked at what Wikipedia says. It 100% absolutely agrees with what I said. You're being quite disingenuous to claim otherwise.
From Equality (mathematics):
"In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. [my emphasis] The equality between A and B is written A = B, and pronounced A equals B. The symbol "=" is called an "equals sign". Two objects that are not equal are said to be distinct. [my emphasis]"
That's exactly what I'm telling you. Baffled that you claim that Wiki says otherwise when plainly it says exactly what I'm saying
I don't see how that's relevant. Since you and I are both human beings, we're interchangeable when someone says bring me a human being. It really means very little.
Sorry, I don't normally use Wikipedia and I only looked at the page on "equals sign".
Nevertheless, what is at issue is whether a so-called "mathematical object" is an object identifiable according to the law of identity. It is not, because two equal, but different things, such as the addition operation of 2+2, and the number 4 are said to be the same object. Therefore, despite what the Wikipedia quote indicates, and many mathematicians might claim, these two different things, the operation represented by "2+2", and the number represented by "4", cannot be "the same" if we adhere to the law of identity, which denies that two distinct things are the same object... The mathematical axioms which state that these two distinct things are the same thing are nothing more than deception. I know you'll continue in your denial, but so be it.
Confusing quantity and predication (as well)? Try differentiating, see what happens.
Quantity is a predication. There is no such thing as quantity, without it being a quantity of something. I think that's half the problem here, some people seem to think that quantity is a thing in itself, rather than a predication, as all measurements are. That way, instead of looking at what "2+2" really represents, they just assume that it represents "a quantity".
But the equal sign is not the topic of discussion. The concept of mathematical equality is. No wonder you name-checked Robert Recorde. You looked up the wrong thing.
Quoting Metaphysician Undercover
Completely ignoring the point I just made. Anyway I just wanted to note that you looked at the wrong Wiki article and when pointed at the right one, which 100% supports my point of view, you change the subject.
2 + 2 and 4 point to or refer to or represent the exact same object. It's not possible to do math without that understanding.
It was when I first produced that quote. We were interpreting "2+2=4", a phrase which the equals sign is a part of.
Quoting fishfry
That is bull shit. Clearly I do not have that understanding, which you claim is necessary, in fact I insist it's a misunderstanding. Yet I can get four from two plus two. Therefore I can do math without that misunderstanding, which you say is required to do math. I don't deny that two plus two equals four.
I only assert the obvious, that "2+2", which represents an operation of addition, does not represent the same thing as "4", which does not represent an operation of addition. If you, and your mathematician friends, want to keep living your deluded lives of believing that they do represent the same thing, then so be it.
Tell it to Wiki, which yesterday you claimed was the ultimate authority on these matters and which, once you realized it agrees with me, you no longer have any interest in.
Quoting Metaphysician Undercover
So be it.
... or of anything/whatever, hence the utility of a calculator.
Say, a set of my left ear, that soccer match, the Moon, and the experience of vanilla taste I had the other day when eating icecream, comes to 4 in quantity; kind of trivial to count.
Quoting Metaphysician Undercover
You're now confusing quantity, predication, measurement, ...
Say, a set of you and I comes to a quantity of 2, [math]|\{you, I\}| = 2[/math]; kind of trivial to count.
Say, where [math]\phi[/math] = is human (predicate), it so happens that [math]\phi(you) \wedge \phi(I)[/math], I assume.
You're making a wicked mess of things. :confused:
If ““2+2”...does not represent the same thing as “4””, then in what sense are they equal?
So you're agreeing with me, a quantity is necessarily a number of things, therefore a property of those things, hence a predication. You named that group of things as a thing itself, "a set", and you predicate "quantity" as a property of that named thing, the set..
Quoting jorndoe
I can't agree with your conclusion. To me, your use of strange symbols is what is making a "wicked mess". We can look at what is meant by "quantity", "predication", and "measurement" without leaving the English language. Quantity and measurement are both types of predication. You seem to agree with me, so why complain that I'm confused and making a mess of things? In your examples you predicate "quantity" as the property of a set. Do you not consider this to be predication?
Quoting Luke
In a mathematical sense, obviously. As I explained to fishfry, it's really the only sense of "equal" that there is. "Equal" is a mathematical term. To say that two things are equal is to render them in a form which allows us to proceed with mathematical operations such as counting them. We cannot count apples and oranges unless we say that an apple is equal to an orange. It is only by assigning equality to distinct things that we are able to count them One apple is equal to an orange, and then we count them, 1,2. So apprehending different things as having an equal value allows us to count them, 1,2,3,4....
Notice that it is necessary and fundamental to the operation of counting, that equal things are distinct things. If equal things were the same thing, we would count the same thing over and over again, and the count would clearly be invalid. Therefore, we can conclude that it is a fundamental and necessary axiom of arithmetic, that equal things are not the same thing. Otherwise all arithmetic would be invalid, like counting the same thing over and over again to claim a quantity of things, is an invalid count.
And why does "2 apples + 2 apples" "not represent the same thing" as "4 apples"?
Quoting Metaphysician Undercover
Confuzzlement has roughly gotten worse with each comment. :confused: Start over?
(A1) If something is random, it is either epistemically random or aleatorically random.
(A2) The position and momentum states of quantum particles are random.
(A3) The position and momentum states of quantum particles are either epistemically random or aleatorically random. (1,2, modus ponens)
(A4) If something is epistemically random, the uncertainty associated with that randomness can be arbitrarily reduced by sufficient sampling.
(A5) The uncertainty associated with the product of position and momentum (time and frequency) cannot be arbitrarily reduced by sufficient sampling. (If you localise in time, you disperse in frequency and vice versa)
(A6) The position and momentum states of quantum particles are not epistemically random (4,5, modus tollens).
(A7) The position and momentum states of quantum particles are aleatorically random. (1, 6, disjunctive syllogism).
Aleatoric randomness is randomness that plays a causal role in a model - it is part of the modelled dynamics, epistemic randomness is randomness that does not. I don't think this gives an interpretation of how randomness works causally here, just establishes that it is a property of the entity modelled (the wavefunction's position and momentum observables). Whether it's appropriate to say that quantum shit really does behave like this because the model says so I think is a different question (realism vs anti-realism of scientific theories).
This is only assuming that all of the relevant data is being sampled. Assuming Bohm's interpretation, for example, you can never sample the value of the hidden variable, no matter how good your sample is. In the Everett interpretation, your sample does not include all branches of the wavefunction. Both interpretations are metaphysically deterministic, but both predict epistemically random measurement outcomes.
On the other hand, if you were sampling digits of pi, for example, then unless you already knew what you were sampling, you would never see that it is non-random from your sample, even if you were getting every digit with perfect accuracy. And if you knew what you were sampling, then the question would not arise.
Quite obviously,"2 apples + 2 apples" signifies two distinct groups of two apples, and the "+" represents an operation of putting the two groups of two apples together into one group. There is no such two distinct groups of two, nor the operation of addition signified by "4 apples". Therefore it is very clear that the phrase "2 apples + 2 apples" represents something very different from "4 apples".
Do you understand the difference between saying "4 objects", and specifying a specific configuration of four objects? A specified configuration is not the same thing as the more general "4 objects". This is the type of difference I am talking about here. In both cases, "2 apples + 2 apples", and "4 apples", we are saying something about four apples, but "2 apples + 2 apples" says something more specific than the more general "4 apples". So we cannot say that the two phrases represent the same thing.
Quoting jorndoe
Go ahead. You're the one quizzing me. It appears we have great difficulty understanding each other.
Quoting fdrake
I don't think I agree with this (A4). If the appearance of randomness is caused by inadequate principles by which the samples are modeled, then no degree of sampling will reduce the appearance of randomness.
So you agree that the group resulting from this operation of addition is “4 apples”? That is, you agree that “2 apples + 2 apples” = “4 apples”?
Quoting Metaphysician Undercover
It is obviously signified by the equation “2 apples + 2 apples = 4 apples”. Both sides of the equation are equal in value or quantity. They “represent the same thing” in terms of value or quantity, which is the point of the mathematical equation. I’m not sure what point you are trying to make instead.
Yes, I think I've stated about four times now, on this thread alone, that I agree that two plus two equals four.
Quoting Luke
I've been very clear in the point I'm making, so I don't understand why you're not clear about it. The point is that "2+2", and "4", do not represent the same thing, as "same" is defined by the law of identity, contrary to what has been claimed on this and other threads.
To say that "they represent the same thing in terms of value or quantity", is to qualify "same thing". It is to say that they have some quality which is the same, this quality being named as "quantity". Therefore it is does not say that they represent "the same thing" as determined by the law of identity. I can say "red roof" and "red car", and claim that these two expressions represent the same thing in terms of colour, just like you say "2+2", and "4" represent the same thing in terms of quantity. This does not mean that they represent the same thing in any strict definition of "same thing".
Jorndoe claimed that I confuse quantity with predication, but obviously quantity is a form of predication, and it is jorndoe who is confused, not I.
Yees. I am assuming the things accurately described as random are random. Do any of the interpretations you referenced remove the distribution from the theory?
Quoting SophistiCat
I don't quite understand the relevance of this. Can you elaborate? Are you saying that the real world might have a hidden number that removes all the randomness associated with quantum variables?
Well, I have a mostly pop-sci "knowledge" of QM, my college physics being too rusty to be of much use, but as far as I know the "pilot wave" of Bohmian mechanics would make measurements deterministic - except, of course, being hidden, it is not part of the measurement. And MWI says that the full wavefunction evolution is deterministic (as the Schrodinger equation shows), but we can only measure one of its eigenvalues at a time, since our subjective state in which the measurement outcome is recorded doesn't encompass the full quantum state. If you perform successive measurements on identically prepared systems, the branching wavefunction will leave a trail of random results in each individual branch, even though across all of the branches every set of measurement outcomes will be the same.
Quoting fdrake
I am saying that if it did, we wouldn't know it just from this one sampling. We might guess that it looks suspiciously like the digits of pi, for example (if we were lucky to sample from the already calculated range), but such numerology is perilous. For example, in the past there were a number of attempts to "derive" the empirically measured fine structure constant of particle physics from the ratios of integers and important transcendent numbers like e and pi. Nothing came out of it, as more accurate measurements successively falsified all such hypotheses. (Perhaps we shouldn't retrospectively dismiss these exercises as unscientific numerology, but instead look at them as failed heuristics that once in a blue moon do lead to discoveries.) But the moral is that we usually require more context to establish a causal mechanism behind a phenomenon than a single sampling, which may not reveal a regularity behind it, or conversely may trick us with an appearance of regularity that is not actually there (like in the case of the fine structure constant). Quantum mechanics is, of course, an example of a theory that was developed, first of all, on the shoulders of previous successful theories, and second, with the help of numerous independent lines of evidence, so we should feel pretty safe here.
AFAIK the Schrodinger equation's time evolution is deterministic, but that doesn't make the states deterministic. The states are samples from probability distributions [hide=*](generalisations of probability distributions I guess? I vaguely recall that they break a few rules)[/hide]. It might be that someone can declare some aspect of the randomness "unphysical" and salvage a global determinism (if only we had (blah) we'd determine the output states!). I don't really know enough about it.
Quoting SophistiCat
I'm reading this as a claim that there's some source that determines the observed quantum states deterministically, it's simply that we don't (or cannot) know the behaviour of the source? Analogously, Pi's digits pass tests for statistical randomness, but they're determined given a way to arbitrarily accurately evaluate Pi.
If you were looking for something profound, you've come to the wrong person. I was just pointing out the mistake of those who say that "2+2" and "4" refer to the same thing. It's really quite trivial, but some people seem to act like I'm attacking their God. Perhaps it was the behaviour of others which made you think I might be saying something profound.
By the way, in case I didn't make this clear last time, I consider "different expressions of the same value" to be ambiguous nonsense, and "different ways of expressing the same value" does very little to clarify what you could possibly mean. Do you even know what "value" means? It refers to the desirability of a thing, or what a thing is worth. How do you apprehend "2+2", or "4", as an expression of what a thing is worth?
Perhaps you are unaware that a word can have more than one meaning or use. You seemed to have little difficulty understanding what I was talking about when I spoke of “value or quantity”. I also assume you were not talking about value as “the desirability of a thing” when you said:
Quoting Metaphysician Undercover
That's because we qualified value with "quantitative" value. But your assertion "different expressions of the same value" does not show that qualification. Hence the ambiguity. And I know the way you argue through ambiguity, I've been exposed to it too many times. So I would not accept an ambiguous proposition from you.
Do we agree that "value", being inherently subjective, is not a thing?
"We calculated the value of the national carbon footprint for last year to so-and-so."
"I greatly value a cold beer on a hot summer night."
I'm guessing the use here is like the former. Contextual reading matters.
Yes, because our discussion was in the context of mathematics. Or do you think that mathematics is all about monetary value (i.e. desirability/worth)? Don’t be daft.
The more traditional interpretations treat the equation as only one component that is needed to determine the actual physical state - position, momentum. Everett just reads it literally as the equation of state, sacrificing some of our traditional notions of what a physical state is.
Quoting fdrake
With some effort we could interpret, for example, the spigot algorithm for calculating the digits of pi as some exotic physical process. Looking at it from the other end, if we were performing physical measurements, would we be able to figure out the underlying mechanism? Not without more context; taken on their own, measurements would appear quite random. Or take a chaotic Newtonian system: an observation that is limited to setting up the system, letting it run and then performing a measurement would lead us to conclude that it is aleatory. My point is that we need to probe nature not just many times, but in many different ways, in order to establish the causal mechanism with reasonable confidence (and always with the assumption that nature is not much trickier than we think it is, but that assumption is part of what goes into "reasonable confidence").
The use of "value" in the first statement is extremely ambiguous because it is not related (grounded) to anything. The supposed "value of the carbon footprint" needs to be substantiated by a scale of some sort in order to have meaning. Without that scale the supposed "value" is meaningless. In the second case, "I" substantiates the value, with personal beliefs and a personal hierarchy. So the meaning of "value" is revealed by your use of "I".
Quoting Luke
So, back to my point then. If it is true that "4" expresses a value, then "2+2" does not express a value. The latter expresses a mathematical operation which is a different type of expression than an expression of value. Do you see the difference? Do you see that if "4" is an example of an expression of value, then in "2+2" there are two distinct values expressed, "2" and "2" whereas only one value "4" is expressed with "4"?
2+2=4. You said that you don't deny this equation. How can "2+2" and "4" be equal if "2+2" does not express a value (i.e. a quantity, number, amount)?
Quoting Metaphysician Undercover
What does '+' do?
Really? And yet you understood it fine? And well enough that you could, say, go look up annual carbon footprints and such...? (I could start listing examples ... maybe another day)
I don't see how this can be so difficult for you.
Let's assume "4" represents an amount, number, or quantity. And we can also say that "2" represents an amount, number, or quantity. Doesn't "2+2" represent two distinct amounts, numbers, or quantities, related to each other with "+"? If "2" represents an amount, number, or quantity, how can you not see that there are two such amounts, numbers or quantities represented by "2+2"?
So, "2+2" does not represent a value, it represents two distinct values related with "+", and we say that this is equal to the value of "4". Here's an example, go to the store, and pick out three items. Now you have item number one, item number two, item number three, each has a distinct value. Place a plus sign between them and you have the cost of item number one plus cost of item number two plus the cost of item number three. Clearly what is represented here is three distinct values being added together. And we say that this is "equal" to one value, which is the sum of the three.
Therefore, a phrase such as "2+2", which does not express a value, but expresses a multitude of values in a specific relation, can and does, equal "a value".
Quoting jorndoe
I really can't say I understood it at all. I have absolutely no idea what "the value of a national carbon footprint" is. Examples would not help. As I said, you need a scale of some sort.
“2+2” is equal to a value of 4. I don’t see how this can be so difficult for you.
You are no longer arguing about identity. You are now arguing against the mathematical equation which you formerly said you did not deny. I have no interest in trying to teach or convince you of basic mathematics that most children can master.
No, I'm not arguing against the notion that 2+2=4. And, the fact that I've explicitly stated this numerous times, and explained that what I am arguing is the difference between being the same and being equal is a clear indication of this. It appears like you have not a good capacity to read English, because you intentionally interpret ambiguous words in a way which is inconsistent with what I've explicitly stated I am arguing, such that they mean something inconsistent with what I am arguing, when it is possible to interpret them in a consistent way.. This is why I did not want to follow you down this road of ambiguity, into discussing the meaning of "expressing a value", because I am familiar with this mode of argumentation of yours. You intentional misinterpret another person's writing, just for the sake of saying "see you've contradicted yourself". But the apparent contradiction is just intentional misinterpretation for the straw man purpose, which is a symptom of bad interpretation. .
If you cannot see the difference between representing the value "one dollar", (which is represented as $!), and representing something equal to a dollar ("four quarters", or "ten dimes"), then I think you've got a problem. Or, as fishfry seems to do, you do recognize the difference but deny that it's a difference, as if it's a difference which does not make a difference, or something like that..
Feel free to explain the difference between "representing the value one dollar" and "representing something equal to a dollar" to anyone who cares to listen.
You can't be serious.
"Based on those samples we calculated an average value of so-and-so."
My young nephew and niece understand what's meant in the English language. If you can't, then you're missing something.
I just did. This is how I represent "one dollar", like that or like this, $1. Something equal to a dollar is "ten dimes", or "four quarters". I really do not believe that you can't see the difference, I think you're in denial.
I explained the difference, in reference to "2+2+4" and I will explain it again. "One dollar", just like "4", says something very general. It allows for "four quarters", "ten dimes", or whatever, just like "4" allows for "2+2", "3+1", 6-2", whatever. However, "ten dimes" refers to something specific. It cannot be represented as "four quarters", or anything else, because the particular form, "ten dimes" is specified, and ten dimes is not four quarters, though they both equal a dollar. Likewise, "2+2" represents something specific, and though it is equal to "6-2", we cannot represent "2+2" as "6-2". They have distinct meaning, just like four quarters has a meaning distinct from ten dimes.
Do you understand that "four quarters" represents something different from "ten dimes"?
Last time I explained this to you, just above, you completely ignored it and made no indication whether you understood what I said or not, arguing that in terms of value, they say the same thing. Sure, that's why they are equal, but 'the whole point is that say they are equal in terms of value does not mean that they represent the same thing.
Quoting Metaphysician Undercover
So please, before you proceed, give me some indication that you've understood what I have said here.
Quoting jorndoe
Sure, I'm missing something, I do not know what a national carbon footprint is. There's more than samples involved here, there's principles and a scale. Of which I have absolutely no understanding. Do you know how they take some samples and produce "the value of a national carbon footprint" from them? You might explain it to me, but I don't see how it's relevant.
Redacted. No point in talking with Meta.
I see. You are emphasising the difference in representation. This is no different to what I mean when I say that they are different expressions of the same value. The point is that both sides of a mathematical equation have the same value (again: the same quantity), despite being different "representations" of that value.
You seem to think that the law of identity has some bearing on mathematics, or that A=A is somehow relevant to mathematical equations. I fail to understand what the relevance is. There would be little point using mathematical equations to state, e.g., 4=4. It seems that you just enjoy the confusion you create by treating the law of identity like a mathematical equation, or vice versa.
OK, good, you are clarifying what you mean by expressions of value. MY point is that "different expressions of the same value" refer to different things. "Ten dimes" refers to something different than "four quarters".
Quoting Luke
Fishfry has been insisting for months now, that what you call "different expressions of the same value" refer to the very same thing. It is claimed that each side of the equation, "2+2", and "4", both refer to the same mathematical object. I believe this idea is derived from the axiom of extensionality.
You repeat the confusion. "Different expressions of the same value" are different wrt their expressions (or "representations"), but the same wrt their value.
Quoting Metaphysician Undercover
Yes, but "ten dimes" and "four quarters" have the same value; they both "refer" to a value of one dollar. You have already demonstrated how problematic and confusing this becomes with an example such as "2+2=4".
Edit: There is no philosophical significance in pointing out that a dime is different to a quarter, or that "2" is different to "4". It goes without saying. You clearly exploit those cases where the values are the same (but the expressions are different) merely to provoke a response.
Quoting Metaphysician Undercover
Quoting Metaphysician Undercover
There's the English language, and its use of the word "value". Everyone else understanding should tell you something. Yet, your response suggests that you do after all. Odd. By the way, you may also want to think of the word "variable" (as in, variables may take on sets of values, and be represented by symbols). But please don't make this a sixth term.
You're missing something, what the expression represents, it's meaning. So there are three layers, the expression "four quarters", what it represents four twenty five cent pieces, and a third thing, the value we give that collection of coins, one dollar. Likewise, the expression "2+2", what it represents, the number two added to the number two, and the third thing, the value, four.
In each of these expressions, "ten dimes" and "four quarters", what the expression represents is different, not the same, regardless of whatever value you assign. The "value" is something else assigned to it through some principle of equality, or equivalence. Notice that this principle is not stated in either of the expressions. So the expression "four quarters" does not say "one dollar". You only conclude that value by applying that principle.
Quoting Luke
No, they do not "refer" to a value of one dollar. That's a false assumption. That four quarters has the value of a dollar is a conclusion produced by a logical process. Neither "four quarters" nor "ten dimes" refers to a dollar, but you can take what is referred to, and infer one dollar, when the logical process is applied. Do you see the difference between what an expression refers to, and what can be inferred from what is referred to by the expression, through a logical process? The implied conclusion requires further premises (often taken for granted) which are not stated in the expression, nor referred to by the expression. So, that four quarters is equal to a dollar, is a logical conclusion which requires a further premise not stated within the expression "four quarters".
Here's another example. If you have a red car, and I say, "the roof of my house is red", you could infer that the colour of my roof is the same as the colour of your car. But in no way am I talking about the colour of your roof. Likewise, if I say "I have four quarters", you could infer that I have a dollar, but in no way am I talking about having a dollar. And, if I say "2+2", you could infer that I am taking about the quantity represented by "4", but in no way am I talking about the quantity represented by "4". You simply apply some logical premise and make that conclusion. But applying a further premise, not stated by the expression, and making a logical conclusion from this premise, to insist that this is what the expression is saying, is faulty interpretation. It is not what the expression is saying, it is a logic conclusion that you've derived from what the expression is saying, through the application of a further premise.
Quoting Luke
What are you talking about? That a dime is different from a quarter is obvious. What I am stating ought to be just as obvious, that ten dimes is different from four quarters, regardless of whatever value you assign to these things. Do you accept this fact, or are you in denial of the obvious, like fishfry? Do you believe that four quarters is the very same thing as ten dimes, just because you can apply some logical principle which makes them equal?
If having the same value meant being the same as, we could assign any random thing the same value as any other random thing, and conclude therefore that they are the same thing. That's nonsense.
Quoting jorndoe
Well jorndoe, it seems very obvious from this thread that many people misunderstand. Jgill seems to be about the only one who does understand. Maybe you need to change that statement, and your perspective.
There is no "logical premise" involved; that's simply how we use mathematical equations: the equals sign means that the value on the left is equal to the value on the right. "2+2=4" is a mathematical equation. To make the case that each side of the equation is different in a way which is unrelated to their values, i.e. in their symbols, or in what those symbols refer to, is just being a troll. Obviously, they are different in that sense; just look at the bloody symbols. That difference does not need to be pointed out. You are trolling for a response, and I won't oblige you any further.
Do you not understand that a logical principle is required to say that ten dimes is equal to a dollar? Suppose that you had not learned any arithmetic and some one showed you ten dimes and taught you how to count the dimes, such that you knew there was ten dimes. How would you know that the ten dimes is a dollar unless you learned this further principle? Likewise, if someone just taught you how to count, and then said now take one two and add it to another two, you would not know that this is four. You need to know the further principle of addition to know that two plus two is equal to four.
Therefore, you cannot say that it is the equals sign between "2+2" and "4" which makes these two equal, nor can you even say that the equals sign means that they are equal. It is by means of that logical principle that they are equal. Otherwise, I could write "3+2=4", and the equals sign would mean that the value on the left is equal to the value on the right. But this is not true, because the logical principle of addition is not followed and adhered to, in this representation.
Quoting Luke
Call it "being a troll" if you like. I look at it as a trivial matter. The problem is that the difference needed to be pointed out, because fishfry kept insisting that the very same thing is represented on the left side as the right side of the equation. And when fishfry ceased arguing this, you took up that position. Therefore, I was obliged to point this out to you as well. If you now realize how obvious this is, I am amazed that it took you so long, because I stated very explicitly what I was pointing out, over and over again.
It really seems more like you were trolling me, arguing against me just for the sake of arguing against me, until you realized that what I am arguing is an extremely obvious truth. Now you accuse me of trolling, for making you look like a fool for arguing against something so obvious. But you engaged me, so you really trolled yourself.
You mean it doesn't make the states stable or uniform. Determinism is commutative, but results can be unstable or changeable.
It's not trivial. Refine your claims -- this is what I gather from Luke's pleas. Whenever one invokes a mathematical equation, he or she is bound by a mathematical conclusion. In a game of chess all moves are determined and defined and understood.
Instead of arguing pages after pages of the same thing without changing one variable in your claim (you are engaging in futility, which amounts to nonsense) --
use the theory of meaning if you want to make a point on the the distinction between "2+2" and the number 4. Please start there.
Af far as I can see, you're the only one that don't understand typical use of "value" (e.g., as in variables that may take values, like some/any proposition p in non-contradiction ¬(p ? ¬p)). I suppose, if you don't even (want to) try, then so be it.
This is a good example. To be fair, values can also be invalid.
But I think Metaphysician's difficulty here, and other points on this thread, is the context or application of theory. I think MU is not trying to argue about equivalence --> 2+2 = 4, a mathematical proof, rather it is referent that's being invoked here.
Right, I've said this numerous times already in this thread, there is no question of whether or not 2+2=4. It does, without a doubt. What is at issue is whether "2+2" refers to the same thing, or even has the same meaning, as "4".
Some here seem to believe that "having the same value" implies "being the same mathematical object", such that "2+2" represents the same mathematical object as "4" does. I have argued that since "2+2" represents a more specific configuration of the four things indicated, it does not refer to the same intelligible object as the more general "4".
I just can't see how the fact that a specific variable can be assigned different values, is at all relevant. That's simply the nature of a value, because value is relative there is a degree of arbitrariness. One dollar appears to be a constant value, but when considered within the context of the international market, it is variable. This arbitrariness of "a value" is just further evidence that having the same value does not imply being the same intelligible object. Otherwise I could arbitrarily say that a chair and a table have the same value to me, therefore they are the same intelligible object.
You don't seem familiar with the mathematical use of the term "value", which can describe any number or any result of a calculation (such as "2+2"). If you are familiar with this term, then I don't understand why you would describe this type of value as being "relative" or "arbitrary". Nobody else is talking about "value" in terms of worth.
A mathematical value is a type of "worth", it is the value which something has (what it is worth) within that mathematical system. Therefore that value is "relative" to that system. Evidence of this is the fact that if a person has not learned the system they will not be able to assign the proper value to the thing. The principles that the system is based in, the arbitrariness of the system, is a further matter.
This appears quite different to your previous comments, where the value was not relative to a mathematical system, but instead relative to you:
Quoting Metaphysician Undercover
You also demonstrated the same misunderstanding about "value" previously, where you asked and asserted:
Quoting Metaphysician Undercover
It is clear that you have had this meaning of "value" in mind the entire time, and have misunderstood the meaning of "value" as used in mathematics, and by most of us here.
Quoting Metaphysician Undercover
A "further matter" that you don't care to explain? You didn't claim that it was "the principles that the system is based in" which were arbitrary; you claimed that it was value itself. You said:
Quoting Metaphysician Undercover
In what sense is a mathematical value arbitrary? There's no need to answer, because you clearly weren't referring to mathematical value when you said this.
The point is that it is relative to something. Whether it is relative to my own personal decision, or agreed upon decision (convention), does not change the nature of what a value is, itself.
Quoting Luke
No, there you go again with your uncharitable interpretation for the sake of straw manning. You, yourself, introduced ambiguity onto the meaning of "value", trying to distance your use of "value" from my use of value, for the sake of your straw man, when no such separation is warranted.
Quoting Luke
Exactly as I explained. The value exists only relative to the system of evaluation. The system of evaluation may be entirely arbitrary if it is not grounded by something substantial. Look, it is completely arbitrary that the symbol "2" represents the quantitative value which we call "two". To remove the arbitrariness we might assume an object, a number, which "2" and "two" refer to. The reality of this object, the number two, must be substantiated in order that the arbitrariness be truthfully removed. This is the meaning of "2", which is to signify two distinct things that are not the same thing. Without this meaning of "2", what "2" refers to, the value associated with that symbol is completely arbitrary.
The important thing to notice, which is relevant to my argument, is that the two distinct things referred by "2" are necessarily distinct and different things, or else there would not be two distinct things, and the meaning of "2" would be lost. So when we say "1+1=2", or proceed in the act of counting, by adding another "1", to say 1,2,3,4,etc., each "1" must represent a distinct thing. Therefore each time "1" is used we must allow that this symbol may represent a distinct thing, and not necessarily the same thing (such as the number one). To claim that the symbol 1 represents the number one, or that the symbol 2 represents the number two is a false claim, because if it were true, then the fundamental use of these symbols in the act of counting would be invalid, "2' would not represent two distinct things, it would represent two instances of the same thing, the number one, which is only one thing, not two.
Therefore this attempt to remove the arbitrariness, which assumes that "1" refers to a number called "one", and "2" refers to a number called "two", is unacceptable, and the arbitrariness of the mathematical system of evaluation cannot been overcome in this way. Finally, the arbitrariness of the mathematical value system can only be overcome by grounding, or substantiating it, in principles which establish separation, individuation, difference between things, rather than an assumed sameness or equality of things. That two distinct things are equal, and therefore have the same value, is inherently arbitrary, but that they are distinct individuals, allowing us to number, or count them individually, is grounded in real difference.
How is, e.g. the set of natural numbers, relative to your own personal decision? Also, how can it be relative if your decision "does not change the nature of what a value is, itself"? You're talking out of both sides of your mouth.
Quoting Metaphysician Undercover
The ambiguity exists in the language because the word "value" has more than one meaning. If you think that mathematical value, or the set of natural numbers, has anything to do with "the desirability of a thing", then you are plainly incorrect.
Quoting Metaphysician Undercover
That's an arbitrariness of the symbols used to denote a value, not an arbitrariness of the value itself. For example, the different expressions "2+2" and "4" both have the same mathematical value: 4.
Quoting Metaphysician Undercover
You're aware that we can count independently of counting things, right? The arbitrariness you seem to be referring to is in what things we consider to be the same, not in the numbering system.
It's relative to human convention, or agreement. Whether it was your idea, or mine, or someone else's is not relevant
Quoting Luke
I don't see how you construe this. Value is relative to human decision, whether it's your decision, my decision, agreement between us, or an enforced law, doesn't change the fact that it is relative to human decision. Therefore these issues of who's decision it actually is, are irrelevant to the fact that "value" is relative to human decision. There's no "both sides of the mouth" here, it's human decision plain and simple. You just seem to think that whose decision it was is somehow relevant.
Quoting Luke
No, that's clearly wrong, mathematics has to do with the desire to count and measure things. Counting and measuring are desirable things. Therefore contrary to your ignorant assertion, assigning a quantitative value to things is the result of the desirability of something, counting and measuring, because these are desirable things to do, there's a purpose to them.
Quoting Luke
Oh yeah!, Finally you've gotten to the point. What exactly is a count, independent of counting things? It's just an arbitrary ordering of symbols. If we learned how to count, without actually counting things, we'd just be learning an arbitrary ordering of symbols. And as I explained in the last post, if "1" refers to an object called "a number", then "2" cannot refer to two distinct occurrences of that same number, or else we would not have two, but only one still. So in the act of counting, if it were independent of counting things, the symbols would refer to nothing, because they cannot refer to "a number", or else the count would be invalidated. Therefore that act of counting independent of counting something, is just an exercise in remembering an arbitrary ordering of symbols. If, on the other hand, you claim that three is one more than two, then there must be something which is being counted to validate this claim. It cannot be numbers which are being counted because each "one" being added which makes three one more than two, and four one more than three, must represent a distinct object, or else the count is invalid. So "one" cannot represent a number, nor can any of the other numerals represent a number because this would invalidate simple arithmetic. Therefore the act of counting, independent of counting things, is nothing other than an arbitrary ordering of symbols.
Quoting Metaphysician Undercover
So you've really managed to confuzzle value up good and well.
Did you even look at the Wikipedia page I linked to earlier on Value (mathematics)? It's quite short; here's most of it:
A mathematical value can be a number, like 8 or 163 or pi. A set of numbers, e.g. the set of natural numbers, is a set of values. The meaning of "value" in this sense is completely different to the meaning of "value" in the sense of "desirable things". There is a value in using numbers, no doubt, but there are also the numbers themselves, each of which can be called a "value". These are different meanings of the word "value". You were clearly not aware of this.
Quoting Metaphysician Undercover
1+1=1?
Quoting Metaphysician Undercover
Right, sort of like remembering the alphabet. Are you claiming it's not possible? Just because we can count (and do simple arithmetic) independently of "things" does not imply that we cannot count things or that we never count things.
This is what I object to. In no way can a value be an object. Otherwise any count would be invalidated, as I explained. That there's a cult of mathematicians who believe that values are objects, when in actual usage value is really something predicated, indicates that these people believe falsity.
Quoting Luke
If "1'" refers to an object called a number, then "1+1" indicates two distinct instances of the same object, which is still just the same object. So "1+1" would signify only 1 object if this were the case. However, in common usage it is correct to say "1+1=2". Therefore, to remain consistent with common usage and adhere to true principles of numerology, we must accept the conclusion that "1" does not refer to a mathematical object called a number because this would allow the representation of two distinct instances of the same object "1" to be the same as "2". But according to common usage in counting, "2" cannot refer to a second instance of the same thing.
Quoting Luke
What is not possible, is the notion that counting is a completely arbitrary ordering of symbols. If it were then mathematics would not be as useful as it is. So we can conclude that there is some meaning to these symbols, and learning to count is not a simple matter of learning an arbitrary ordering of symbols. It is a matter of learning the meaning of the symbols. Likewise, learning the alphabet is not a simple case of learning an arbitrary ordering of symbols, it is a matter of learning the sounds represented by the symbols.
The point I am making, is that if in learning how to count (learning the meaning of the symbols), we learned that one represents an object called a number, and two represents an object called a number, then we could not proceed from this understanding toward learning simple addition for the reasons described. However, this is not what we learn when we learn to count, we learn that "2" represents two distinct objects, not an object with equal value to two instances of the object represented by "1". Therefore, if someone comes along at a later time, after we've learned how to count, and tries to convince us that "1" represents a mathematical object, and "2" represents a mathematical object with the value of two distinct instance of the number named "1", we ought to reject this as a false representation of how we've learned to use numbers, and therefore a false premise. .
How can "two distinct instances of the same object" amount to only one object?
Quoting Metaphysician Undercover
This is like arguing over the rules of chess with someone who doesn't know the rules. I'm done.
Isn't this obvious to you? If I count the object as "1" at time x, then I count the very same object as 2 at time y, this is a faulty count, counting the same object twice. Two instances of seeing the very same object, therefore a faulty count if I say there's two objects.
I should be asking you the opposite question, how do you think that two distinct instances of the very same object qualifies as two objects?
Quoting Luke
That's a sad analogy. Any time someone is going to argue with you over the rules of chess, you're going to insist that they do not know the rules, or else they wouldn't be arguing with you about them. Now I argue the rules of counting with you, and of course, you think that I do not know the rules of counting. Obviously it's you who doesn't know the rules of counting, because you think that the same object can be counted twice, for a count of two. Rule number one, you must count distinct objects, you cannot count the same object twice. No matter how many times the same object appears in front of you, you still only have one object.
But what is an "object"? And what is a "metaphysical object"? Is there an overlap? :chin:
I would say that since metaphysics is the discipline which addresses the issue of what is an "object", and metaphysics therefore determines the meaning of "object", there is no difference between "object" and "metaphysical object". Where I see a problem is that "mathematical object" as people on this thread have proposed, does not seem to be consistent with acceptable metaphysical principles. In other words, it appears to me like mathematicians have posited a type of "object" which is metaphysically unacceptable.
So we can’t add 1+1 - is that your argument? Because “1” is identical to itself? All mathematicians are wrong? How is “1” an object anyway? I note this is your first introduction of time into the scenario. I thought you meant the same type of object, not the same object counted again some time later. Like how we count three apples; they’re three of the same type of object counted on one occasion, not one object counted on three different occasions. But how we got to this point was that you stated:
Quoting Metaphysician Undercover
So your argument is about numbers, not objects. This implies we can’t even add 1+1 because there is only one “object” which is the number “1”. Okay pal, whatever.
No, "1" is a symbol. So long as each 1 represents a different object there is no problem to add 1+1 and get 2. But if both 1s are supposed to represent the same object I don't see how you could get two out of that.
Does “1” refer to an object called “a number”?
From Wikipedia: "The strong, classical view assumes that the 'objects' studied by metaphysics exist independently of any observer, so that the subject is the most fundamental of all sciences. The weak, modern view assumes that the 'objects' studied by metaphysics exist inside the mind of an observer, so the subject becomes a form of introspection and conceptual analysis."
No, of course not. That is the mistaken description of how "1" is used which I am trying to expose. If "1" referred to an object called a number, then we could not use "2" to refer to two distinct objects.
That is relevant to this thread because if someone takes it as the basis for an argument about infinity and the infinite, that 1 refers to a mathematical object called a number, it's a false premise. To assume that it does, for the sake of saying something about infinity, is to base what you are saying about infinity in a falsity.
We may disagree on what "the objects studied by metaphysics" refers to. Metaphysics must study all objects in order to have the capacity to distinguish objects existing only within the mind (imaginary and fictional objects) from objects which exist independent of an observer.
The problem is that the existence of each of these types, as a proposed type of object, is difficult to validate, substantiate, or ground, in real principles, without reference to objects of the other type. So there's generally a type of circularity involved in substantiating "existence". That's one reason why dualism has been a prominent metaphysics in the past. My position is that we cannot take the existence of objects, of any type, for granted. Therefore the concept of "object" wherever it is used, must be justified.
So "1" is not a number? Or, is it specifically that "1" is not an object called "a number"? Who is claiming that "1" is an object?
The point is that there is no need to posit "a number" as existing between the symbol "1", and what the symbol refers to in a particular application of mathematics. This is unnecessary obfuscation, like positing "an idea" as existing between my car, and my usage of "car" to refer to it. To posit such an ideal object as existing between the symbol, and what the symbol refers to in application, is a misrepresentation of what is really the case. There is some thinking which occurs as a medium between my use of the word, and the object referred to, but it's incorrect to say that there is a thing, called "an idea" which exists there.
Quoting Luke
From your Wikipedia post above:
Once it is established through an axiom, that a number is an object (mathematical object), it becomes a thing which can be counted. In reality, counting numbers is nonsense, as I explained, it's just arbitrary play with symbols.
Different numerals can represent the same number (or value), such as "4" and "IV". Also, different expressions can represent the same number (or value), such as "2x2" and "1+3". This indicates "a number as existing between the symbol(s)...and what the symbol(s) refer to".
Quoting Metaphysician Undercover
I don't see how you can count (anything) unless you can count numbers.
I have no problem with saying that a numeral represents a value. That is how we establish equality, by giving different things the same value. I do have a problem with saying that a value is an object. Value is something which is predicated. And if we say that value is a predication of the symbol instead of the subject or object which the symbol represents, that is a category mistake. So anytime we say that a numeral represents a value, this is a simplification, and we ought to understand that the value only exists in application. It's like when we state logical expressions using symbols,.to make an example of how to use such symbols. The symbols only have a "value" if they represent something, and the logic is being applied.
Quoting Luke
So in this instance, when "2+2" is applied, and "3+1" is applied, there is an equality between the value of the objects represented by both. Without those objects, which only exist in application, when the numbers actually refer to something, "2+2" and "3+1" are just symbols which cannot be said to have any particular value, or refer to any particular value.
Quoting Luke
No such "number" is indicated. "2+2=3+1" is just an expression of symbols, demonstrating how to use mathematical symbols, just like we make demonstrations in other forms of logic, in which the symbols refer to nothing. It is an expression of "form}, which demonstrates how to proceed with the logic. There is nothing referred to by the symbols because the logic is not being applied. It is simply a representation of form. To imagine that there is an object called "a number" referred to by "2", or "3", or another type of mathematical object referred to by "2+2", or "3+1" is just an imaginary fiction, which might be useful for the purpose of teaching, but it is a fiction nevertheless.
Then you must concede that there exists an intermediary between a symbol (numeral) and an object: a value. A value is a number.
Numerals represent numbers which are predicated of objects. But a numeral or a number can also be an object. We can speak of three numerals or four numbers, for example.
Quoting Metaphysician Undercover
Both expressions have a value of 4. A child could tell you that.
Quoting Metaphysician Undercover
Forget those expressions, then. You have accepted that the symbols "4" and "IV" both represent a value of four, and a value is neither an object nor a symbol; it is a number. A number is an abstract concept.
Quoting Metaphysician Undercover
You still need to explain how you can count objects without first being able to count numbers.
Hold on here, you're jumping ahead of yourself. An object is one, so you cannot predicate any number other than one of an object. If you have a group or set of objects you can count them, assign a quantity or number to that group or set, but take notice that number, or quantity is actually predicated of the group or set, not of the objects themselves.
Quoting Luke
Clearly a numeral is an object, as a symbol. But I do not see how a number can be an object. Number, or quantity is something predicated of a group or set of objects, so how can a number itself be an object?
Quoting Luke
This is the ambiguity you tried to introduce earlier. The expression isn't what has the value, it's what the expression refers to that has the value. The numeral "4" does not have the value, of 4, Whatever it is that we refer to with "4", in application, is what is judged to have that value. So "4" is used to refer to that group of objects which is judged to have the value of 4.
Quoting Luke
We went through this already. 1 refers to one object, add another and it's "2" objects, another, and it's "3" objects. It's how I learned to count, I don't know how you learned to count. Memorizing an order of symbols, 1,2,3,4, etc. is not learning how to count anything, just like learning to recite the alphabet is not learning how to spell anything.
We do say that reciting the numbers in order is counting, but when we learn how to do this it's definitely not a matter of learning how to count numbers, because at that age we are not told that there are abstract numbers, Platonic ideas which the numerals refer to. It's just learning how to count, and this is a distinct meaning of "count" from counting something, which is to determine an amount. Clearly, when we learn how to recite the numerals in order, i.e., learn how to count in this sense of the word "count", we are not told that we are counting (determining the amount of) some abstract ideas called "numbers". This would only confuse the child. In my experience, I learned how to count objects, and recite the symbols, long before I learned that there was supposed to be numbers which the numerals refer to. That would have confused me immensely. It still does.
First you claim that there is no intermediary between symbols and objects, but now you claim that there are both numbers and sets between them? Make up your mind.
Quoting Metaphysician Undercover
Yes, I expressed this poorly. I simply meant that numbers can also be predicated of numerals and numbers themselves.
Quoting Metaphysician Undercover
Right, the expression [e.g. “2+2”] is a set of symbols. I was drawing a parallel between this and numerals.
Quoting Metaphysician Undercover
Exactly my point. So you need to review your claim that “ there is no need to posit "a number" as existing between the symbol "1", and what the symbol refers to”. “4” refers to neither the symbol nor the objects themselves, but instead to an abstract feature/grouping of those objects: a number.
You obviously have not understood what I said. Oh well, I'm tired of repeating the same thing over and over, only to have it interpreted in some odd way such that you perceive contradiction. I've already pointed to this problem which you have, and it would be appreciated if you could work on correcting it.
Quoting Luke
As I said last post, i don't see how a number could be predicated of a numeral. The symbol, and what the symbol mean, are two distinct things. You could only predicate a number of a numeral if the number was somehow a quality or property of the symbol.
Quoting Luke
A group of objects is not an abstract feature. Patterns are real, ontological. The value we give to the group "4", is an abstract feature, but it's a value, therefore a form of quality, not an object.. If you allow the grouping to be arbitrary, mathematics gets lost to randomness. This is why there must be a real ontological difference between two groups of two (2+2), and one group of four (4). Otherwise there would be no reason to refer to the one situation as "2+2", and the other as "4".
A value is a number. Do you acknowledge that?
Given your two claims above, it looks like you now accept that the “abstract feature” of a value/number exists between the symbol and what the symbol refers to. Otherwise you must think that a value/number is a symbol, or that an object is an “abstract feature”.
No! That's exactly what I've been arguing against for this entire thread. How can you not see that that is what I am arguing against, after all this time? There is a specific type of value, a quantitative value, which people have assigned the word "number" to. You have been working hard to disassociate "quantitative value" from all other forms of value, with the intention of claiming that quantitative value is grounded in an object called "a number", rather than the human subject. That argument disguises the true subjective nature of "a value" by making it appear to be an object called "a number".
Quoting Luke
I don't at all claim that there is nothing between the symbol and what it represents, that would be ludicrous, and that's why it's ridiculous and extremely frustrating that you would misrepresent what I said, in this way. Of course there is obviously a medium, which is a thinking human being, between the symbol and what it represents, as it is necessary that someone applies the symbol. But a thinking human being is better known as a subject, and is obviously not well represented as an object called "a number".
Your interpretation has taken what I've said about human thinkers applying numerals, and you have misrepresented as an instance of "value" and misrepresented a "value" as a number. So you have made a double misrepresentation.
That's the problem with this sort of Platonism, it takes the human activity of thinking, which is the medium between the numerals and what they refer to, and replaces that with Platonic ideals, "numbers". From this premise you can completely overlook all the mistakes within the principles of mathematics, insisting that there cannot be mistakes because mathematics is objective, the numerals refer directly to mathematical objects, numbers. Therefore it's impossible that there is mistaken value here because that sort of value is based in objects, "numbers", so it is objective. In reality there is the human thinking between the numeral and what it refers to, not an object called "a number", hence mistake is possible within mathematical principles. And that sort of Platonic realism is itself a mistake.
They are different meanings of the word "value", as demonstrated by the Wikipedia article I posted. If you can't accept this, then I wish you well.
My reply to your Wikipedia quote:
Quoting Metaphysician Undercover
That was four days ago. And, it's what I've been arguing for weeks. Did it take you this long to figure out that I really. mean what I say?
What does any of that have to do with numbers?
I assume you saw the phrase "mathematical object" in the Wikipedia article on value and now you want to argue over the meaning of "objects". No, thanks. Look it up: "A mathematical object is an abstract concept arising in mathematics."
Clearly our disagreement is not in the meaning of "objects", but in the meaning of "value". You want to disassociate quantitative value from all other sorts of value, claiming that mathematical values are something completely distinct and unrelated to any other type of value. But values do not exist in that way, They exist in hierarchical structures, one type of value receiving its worth from another, like a family tree, until the whole structure is grounded in a material desire or want. Aristotle explained this in his Nichomachean Ethics, one end is for the sake of another end, which is for the sake of another, until there is a grounding. Unless you recognize that values are tied together in this way and it is unrealistic, and a misunderstanding, to separate one type of value (quantitative value) from all others, we will always disagree.
Quoting Luke
Sure, but this does not settle our disagreement concerning the relationship between "value" and "abstract concept". You seem to think that value is a predicate of an abstract concept. I see a concept as grounded in a value, and emergent from that value. Therefore from my perspective the value that a concept expresses is prior to the concept itself. And if there is a new value derived from a concept, it is produced through application of the concept. This means that the value which "mathematical objects", or 'abstract concepts arising in mathematics' is grounded in cannot be a quantitative value at all, because "quantitative value is an abstract concept emergent from the application of arithmetic. Quantitative value has been produced from the application of mathematical concepts, and the sort of "value" which is responsible for the creation of mathematical concepts, and therefore underlying mathematical concepts, is a different type.
Mathematical concepts provide us with quantitative value, but they are produced from another type of value. So we cannot understand mathematical concepts simply through reference to quantitative value because this is circular. To escape this vicious circle which you have been trapped in for weeks now, you need to allow your inquiry to accept the values which lie behind an individual subject's application of abstract concepts, to be relevant in the creation of these concepts. In other words, you need to free yourself from your self-imposed restrictions on "value".
For god sake, man. There is a meaning of the word "value" which is a synonym for "number". I'm not talking about a type of value, as in the values that people hold or in what people value. It's just another word for a number, or the number represented by an algebraic term. That's it. It has absolutely nothing to do with any other meaning of "value". You can't accept that? Fine. I don't care.
Sure there is, and that's your vicious circle, which I just pointed out. Define "value" as number, and define "number" as value. Claim that they are synonyms and live in your little bubble withou having a clue as to what a value or a number is. If you read my reply to jorndoe, a week or so back, I explained how a value is defined by a scale. The number just indicates a position relative to the scale.
Quoting Luke
This is incorrect. Any specified value is defined by a specific scale. So there are many different types of value, all relative to different scales. Therefore any value is a type of value and the type is determined by the scale. There is no such thing as a value which is independent from a scale of evaluation, and the scale determines the type of value. So unless you are talking about "value" in the most general sense, which you clearly are not, because you've been rejecting my talk of "value" in the most general sense, you are necessarily talking about a type of value. Therefore your claim that you are not talking about a type of value is false. You very clearly are talking about a type of value.
Quoting Luke
I already explained how the idea of "number" on its own, as a supposed medium between a numeral and things to be counted, does not make sense. When we count things, we apply the numerals right to the things being counted, in the process of counting. If you want to ground the existence of "number", in some type of value, then we need to refer to the evaluation scale to see what type of value it is. I already suggested that it is a quantitative value. Do you agree?
It's as though I am talking about the bank of a river and you keep telling me that I must be talking about a financial institution.
Quoting Metaphysician Undercover
What is ""value" in the most general sense"? A word can have more than one meaning. What basis is there for assuming that the word "value" can have only one meaning? I mean, just look in the dictionary.
I don't see the analogy. You appear to be avoiding the points I made.
I never suggested that it did. I said there are all different types of values. Obviously, each different type entails a different meaning for the word.
What basis is there for claiming that there is a meaning for "value" which refers to something completely independent from all other types of value, such that it cannot be called a type of value?
This implies the same meaning of the word "value" across all "types of values".
Quoting Metaphysician Undercover
The dictionary for one thing. My knowledge of different meanings/uses of the word "value" for another.
Google offers these different meanings of the word "value":
These aren't different "types of values"; they are different meanings of the word "value". Note that not all of these are synonymous with "the desirability of a thing".
That's nonsense, meaning is relative to context, usage. For example, there are different types of animals. When I talk about this animal here, my cat, "animal" has a completely different meaning from when I talk about that animal over there, my dog. The fact that all the things called "animal" can be classed together in one group, as animals, does not mean that whenever someone refers to one of those animals, "animal" has the same meaning. I am talking about this animal here now, my cat, do you see how the meaning of "animal" is completely different from when I am talking about that animal over there, my dog.
We can say the same thing about "value". There is a reason, or reasons why we categorize something as a value, just like there are reasons why we categorize something as an animal. I suggested, that a "value" is related to a scale, But this does not mean that when I talk about the value of a dollar, or the value of zero degrees Celsius, "value" has the same meaning. That would be ridiculous. The meaning is determined by the scale being referred to, just like the meaning of "animal" in my example, is determined by the creature being referred to.
These are the same meaning of the word "animal", with a definition such as: "a living organism that feeds on organic matter, typically having specialized sense organs and nervous system and able to respond rapidly to stimuli."
Quoting Metaphysician Undercover
It's not the same. Your example of "animal" uses the same definition and has the same meaning whether it's a cat or a dog. The Google definitions I provided for "value" are not the same and do not all have the same meaning.
In this discussion, all we've done is digressed, from the meaning of "number" to the meaning of "value", to the meaning of "meaning". I now think I see why it's so difficult for us to agree on anything, or make any progress in discussion, and all we do is digress.. We have a very deep difference in how we relate to what a word means.
If I'm talking about that animal lying on the floor over there, I believe that "animal" refers to the dog I am talking about, and that reference gives meaning to the use of "animal" in that context. You seem to think that when I am talking about that animal, there is some abstract idea, defined as you described above, which exists as an intermediary between the word, and my use of the word, constituting "the meaning" of the word. This is exactly what you've been arguing with numerals, that there is an abstract idea, "a number", which constitutes "the meaning" of the numeral, and is intermediate between the numeral and its usage. I thought you supported Wittgenstein, who dismissed all that Platonic idealism as nonsense.
Let's consider what really exists between the word "animal" and the way that I use it. I have had some education, and have developed some habits of usage, and I might refer to a dictionary or other sources like Wikipedia now and then. There is no specific definition, such as the one you offered, which constitutes "the meaning" of the word for me, which I reference every time I use that word. Sure, you might argue that every time I use the word "animal", it is consistent with your proposed definition, therefore your proposed definition is "the meaning" which the word has when I use it, but that is not a valid conclusion. That a thing is consistent with a description does not necessitate the conclusion that it is the described thing because the identity of the particular is within the particular itself (law of identity), and cannot be represented through universal terms which refer to more than one thing. Therefore the identity of the particular cannot be concluded necessarily through reference to the universal, or more general. The meaning of any particular instance of usage of symbols is specific to that particular instance, and cannot be expressed in universal terms. We must refer to the material substance of what is referred to in that particular instance of use, to determine the true meaning.
I believe that this attitude which you have toward meaning is the reason why you have such a hard time discussing these philosophical issues with me, and continually misinterpret me. You see my use of certain words, and instead of referring to the context of my usage, to derive the meaning of those words, you refer to some "idea" of "the meaning" of the word, which you have for that word, and this provides for you, the wrong interpretation, or meaning. Then you take this incorrect meaning (faulty interpretation) based in some supposed idea of "the meaning" of that word, instead of the meaning meant by me, revealed by the context of my usage, and insist that I've contradicted myself.
That's probably because you tried to argue that the word "value" has only one meaning, then I provided several other different dictionary definitions, and then you tried to change the subject.
I'm done with your twisting of the discussion. You're wrong.
Another example of pathetic interpretation.
Quoting Luke
It's not me who never learned how to read philosophy.