On 25 Sep 2011, at 09:05, Roger Granet wrote:



>Roger: When you say "Mathematical truth is in the mind of persons", this was the very point I was making. I don't >think there can exist mathematical truths in some platonic realm somewhere. They're in the mind, which is a physical >thing,

>This is something you assume. It is not obvious, and provably false if we assume that brains are Turing emulable at >some level such that we would survived through such an emulation. (this is not entirely obvious, and I explain this from >times to times on the list, but you can also take a look on the papers in my url).

Roger: I agree that this is an assumption; although, I'd say it's also an assumption that mathematical truths exist somewhere outside of all other physically existent things.

When a mathematician assume something, like (x ≠ y -> s(x) ≠ s(y), say. He is neutral on the interpretation of x, s(x), etc. So it is not part of the assumption made by the mathematician, that mathematical truth is in or outside some other object assumed, or not, by some other people.

In cognitive science, or in theology, we don't have to postulate that a mathematical truth, like "17 is prime" is outside of physical things. We might just NOT postulate physically existent thing. And remains agnostic on that question until further clarifications appear.

I realize now from later in your email that you also don't think these truths exist separate from all other physically existent things (?), but it seems like many physicists and mathematicians do think they exist outside of all other physical things.

>I don't see how you answered this above. I do see that you assume a physical reality. But I don't see how you explain >the numbers from that, still less the mind.

Roger: While I admit explaining the numbers isn't the area I think about the most, it seems like if you have a set of existent states in which some intelligence developed, this intelligence would see the presence of a single existent state and could equate that to the number 1, the existence of another one next to it to a total of two, etc.?

All right. But set of existent state already exists in many mathematical structures. You explain well how intelligence might develop from such state and BET on the presence of a single state, and conceptualize through it the idea of number 1. I don't see anything physical here. You are using Aristotle idea that seeing is sort of proof of existence, a bit like animals are programmed to do (it pays in the short run). Platonist took distance with that idea. They better remember their dreams, I guess, so that they stop to consider that seeing, or measuring, observing, is a proof of existence. They take "seeing" as an opportunity to bet on something which would explain the seeing, and which is not necessarily made of what is seen.

>But biochemical activity is explained by quantum mechanics, which is Turing emulable, and so this, by the UDA result, >makes phsyicalism wrong. In fact QM can be (and, assuming we are machine, has to be) explained by addition and >multiplication. That has been partially done. Contrariwise, nobody has been able to explain how consciousness can be >the product of anything described by third person notions.

Roger: But, many question whether or not quantum mechanics is the one theory that can explain all of reality, so I'm not convinced that all biochemical activity is explained by quantum mechanics.

I mentioned QM only to mentioned a computer emulable theory of molecules. I find quite possible that QM explains biochemistry, given the incredible theory of chemistry the SWE equation allow (molecules and the electronic shape of atoms is really what QM explains the most elegantly and successfully, but this is besides my point).

But you are coherent: if you want materialism, you will need a non turing emulable theory of matter, and of mind. Good luck, because it needs already some amount of work to conceive something not Turing emulable in math, and in physics, it is even more difficult. But it is logically possible, and the study of computer science is the must, for those who hope to succeed in going beyond. But the universal machine is good in defeating such arguments, already.

>But that assumption is used commonly in physics. If "1+1=2" can be derived from physics, without assuming it, then >please show this to me. You might begin to give me a physical definition of what is 1, without assuming the usual >arithmetical meaning of 1.

Roger: I'm not clear how the existence of a single physical object/ existent state can't be described by an intelligence as the number 1.

I' not clear how the existence of a single biological organism/ existent state can't be described by an intelligence as the number 1. Would you infer from that 1 is biological? A single physical object can only be an example of an instanciation of the idea of one. Actually you already need the notion of 1 to single out that single physical object.

Then the existence of another object next to it, and that intelligence can get 1+1=2. But, I'd agree that you need the intelligence to make up this addition system. I guess where we disagree is in that I think intelligence/mind is entirely made of these physical objects, and you don't?

Not really. I am a logician, and I try to hide what I think. (I confess I can change my mind easily on so deep question, and that is why I focus on what follows from assumptions). I am just trying to explain (prove) that IF some rational agent believes that he can survive with an artificial digital body/brain/ universe, THEN, if he can be 100% honest with itself (ideally correct), he will soon or later understand that, as far as he is correct in its mechanist beliefs, the laws of physics arise from a self-reference ability of the numbers. And this leads to a way to derive physics from number theory (intensional number theory, for the detail), making the mechanist thesis refutable by observation. In fact my point is that mechanism leads to sort of theology which is scientific in the sense of being refutable.

In my youth I tended to believe in mechanism by looking at amoebas and tiny animals and plants. That feeling in favor of mechanism has been multiplied by a lot, when I read James Watson's book "Molecular biology of the gene", and I like very much biochemistry. But then I studied QM, to see how macro and micro molecules "really work", and I got permanently (like many) stumbling on the "nonsense" of it, and I begun to doubt seriously about mechanism, despite my theoretical interest continue to grew (especially through the study of Turing, Gödel, Post, Church, etc.) Then I read Everett, and now I consider that Everett *formulation* of QM (= the usual one without collapse); might be, like Gödel's theorem, an incredibly strong evidence for mechanism. My work goes in that direction by showing the hardness to refute mechanism.

But who knows? If we are machine, then it is a theorem that we will never know that mechanism is true for sure.

Overall, thanks for all the interesting things to think about in my physical brain! :-)

In your dreams :)

Thanks for sharing the pleasure to muse and dig on deep questions.



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