On 24 Sep 2011, at 08:12, Roger Granet wrote:


    Hi.  My responses are:

>Mathematical truth is in the mind of persons. And assuming we are machine, mathematical truth is in the mind >of numbers relatively to numbers. Of course we have to assume all elementary arithmetical truth, like "17 is ><prime". Do you doubt them?

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).

and humans created them as a way of describing physical things. But, as you know, many physicists and others think that mathematical and physical laws exist independent of all else. When they can show us where they exist, I'll be willing to accept their argument.

But why do you want that if something exists implies it exists somewhere? This is assuming physicalism, which has been shown incompatible with mechanism.

I'm not sure where you're getting that I don't accept truths like "17 is prime".

Where did I say that. On the contrary I was just asking you the question.

I didn't say that.

I didn't say that you did it.

All I'm saying is that these truths don't have independent existence outside of everything else that exists.

I agree with that statement also, but I guess for a diametrical reason. Mechanism makes not just physicalism false, it makes this in a constructive way: it explains where the appearance of the physical reality comes from. So by assuming things easy things like the laws of addition and multiplication of the natural numbers, we can explain where both the quanta and the qualia arise. To explain the numbers from physics does not work, if only because all physical theory has to assume the numbers (which of course is almost never made explicit by the physicists).

If the truths exist, they're just one part of the overall set of existent things that is what we're all trying to figure out.

>To ask that a number should be somewhere is a category error. Numbers are not space-time object. It means >also that you assume space and time, which is a more complex notion than numbers.

Roger: See above.

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.

>So, while nobody can disprove the existence of these things, we can't really do much with them either it seems >to me. There just more of the things people claim to exist but can provide no evidence for. However, I admit >that I can also never directly prove my ideas about what used to be called "non-existence" because no person >or minds would be present there. All we can do is use our unprovable, but hopefully logical, hypotheses to >build internally consistent models that are consistent with known facts and that eventually can make testable >predictions. This is where I want to work towards because otherwise, it's all just talk.

>OK. But then you have to build a sufficiently precise theory, so that we can criticize it. The problem with >nothingness is that it is, a priori, just a word, indeed, and to make it precise requires some theory. For example, >the quantum vacuum needs the quantum theory. The empty set needs set theory, 0 needs number theory, etc.

Roger: This is what I just said in the comment you were responding to.

I know. We agree on that. But then you seem to derive from this that a physical reality exist *primitively*, and that we have to assume time and space, etc. Then what I say, is that for such a physicalism/ materialism to be true, you need to make brain and mind both substantial and infinite.

>In regards to consciousness, I feel pretty much the same. Consciousness is just the output of all the neurons, >neural circuits, ion gradients, etc. in your brain.

>This is extremely ambiguous. But from the UDP (the universal dovetailer proof), or UDA UD Argument, >either the neurons, neural circuits, ion gradients, etc. in your brain, are Turing emulable, and in this case >physicalism is refuted, or there are not, in which case you are developing a non mechanist theory (which is >something I respect, although I expect such theories to be very complex one, and quite different from >everything we know from observation and logic).

Roger: How is this ambiguous? No one yet knows exactly the biochemical mechanisms that produce consciousness, but it's clear to most biochemists, at least, that consciousness is a product of the physical stuff inside the head.

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.

> Again, if it's something else, I'd say: Show me where this consciousness/mind is that's not in the brain.

It leaves on the border of the arithmetical truth, or on the frontier between the computable and the non computable. The notion of "where" is an indexical based on the notion of "here", which is also an indexical.

>It belongs, assuming mechanism, to the infinite number relations that you can derive from addition and >multiplication alone.

Roger: Hmm

This is a logical consequence of the assumption that "my" brain can be approximated at a digital level, so that I would not feel any difference if a digital device is substituted fro my brain at that level. To assume this false, you have to make the brain infinite, or to assume consciousness in the components of the brain.

>For trying to think of why there is something rather than nothing, I don't think there can be any postulated >conscious observer other than some physical property intrinsic to whatever existent state we're considering. > >Otherwise, that doesn't explain where the observer comes from.

>I am afraid you are begging the question by assuming something physical. Where does *that* come from. >What is it. Mechanism can explain were both matter/space/time, and subjectivity arise come from. They are >derived from the addition and multiplication laws of natural numbers. The origin is not direct, nor physical in >any sense, but is made possible by the self-referential ability that some numbers display. The details of that >explanation needs some amount of theoretical computer science. But the argument showing the incompatibility >of mechanism and weak materialism (the doctrine saying that primitive matter exists) is accessible to anyone >with enough patience + a passive understanding of Church thesis.

>You might try to understand the 8 steps proof given >here 

Roger: I don't have time to read your whole paper, but from near the beginning, it looks like it's based on the comp idea which assumes arithmetical realism:

"This is the assumption that arithmetical proposition, like ‘‘1+1=2,’’ or Goldbach conjecture, or the inexistence of a bigger prime, or the statement that some digital machine will stop, or any Boolean formula bearing on numbers, are true independently of me, you, humanity, the physical universe (if that exists), etc."

As above, I'd say this is possible, but show me where these arithmetical propositions are that are independent of everything else. As you say, it's just another assumption.

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.

Overall, I don't think it really matters if it's physical stuff or mind, machine psychology, or arithmetical propositions that are the basis of our existence. Whatever it is that's the basis, it exists, and the whole point of this thread was about trying to figure out why it exists instead of not existing.

I can answer this. We don't know, and if we are machine, we will never know. The reason to start from arithmetic, is that it can be proved that there is no theory capable of explaining where arithmetic come from. We can only assume it. If you assume any theory in which you can derive the laws of addition and multiplication of the natural numbers, then it can be proved you assume a logically equivalent or stronger theory. So, the natural numbers is the only mystery which remains, but assuming them, we can explain why we cannot explain them. This is "well known" by logicians. In a sense, arithmetic is the simplest (turing universal) theory. From it you can explain why the numbers develop stable belief in consciousness and physical realities, and that the first one is fundamental, and the second one derived from the first one. It is big, in the sense that it shows that the platonist theologians are more rational than the aristotelian theologians (atheists and christians, notably). We might have to backtrack 1500 years, in the fundamental matter.



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