The Nature of Number

[Bernard]

Maybe you are undervaluing the reality of ideas or reason, as if math were a rung above. And what if math/logic were perhaps a physical phenomena? There are physicists who like to think it is. Would that make it less real?

[Jonathan.s]

Julian Jaynes?

The image is a symbol referring to nothing but the sensual data that were incorporated in producing it.

But how do we know that? How is that judgement made? How do you go about breaking down the components of a logical inference into 'sensory data'? I say you can't do it. In order to even commence this line of investigation you need to exercise reason: 'if this, therefore that'. There is no need to justify every instance of logical inference of this type on the basis of a comparison between sense data, image, and object, without begging the question. What is begging the question? It is assuming what you set out to prove.

And what if math/logic were perhaps a physical phenomena? There are physicists who like to think it is. Would that make it less real?

The irony is that the more we have progressed in physics, the less real 'the fundamental constituents of matter' have turned out to be. Don't forget that the original meaning of the word 'atom' was 'indivisible'. Of course it hasn't meant that for a long time now, but the 'standard model' that has replaced it is very much an intellectual construction which can only be expressed in mathematical terms. The 'fundamental entities' of physics are highly ambiguous, from a common-sense point of view.

So I don't see how I am 'devaluing' maths in saying this. Actually I think maths belongs to a kind of higher-order reality than phenomenal objects. But so too did the whole rationalist tradition in Western philosophy.

[Bernard]

Well I thought you were perhaps overvaluing math by giving the sense that because it had perhaps no physicality, and yet was real, it was a rung above ideas, which, as you said, maths was can be more real than. This led me to think that you were of an inclination to feel that reason/ideas belonged more to a base physical reality than does math. However, in light of what you say about the indeterminancy of matter, I'm of a mind to regard that you consider math in mystical terms that are more pronounced, or of a greater filigree of the same substance as that which produces ideation.

I don't see physics as having arrived at greater ambiguity compared to any place it has already been. Certainly, it takes more time to familiarize oneself as a layman with current nomenclature and schools of thought, but the basics seem more in place than ever. For instance: the definition of mass as resistance to acceleration is still that apple hitting that guy on the head. The commonsense understanding hasn't been lost but has just been seen in more and more refined ways. The integrity doesn't dissolve with use. That said, the more refined commonsense becomes the more refined ambiguity in relation to physics becomes (as a way of constructing a description of reality), but still that ambiguity is not less or more - its just more talked about, and therefore evaluated, which is inevitable for anything that talk gives so much time to.

[Satyr]

Julian Jaynes?

Yes: Origin of Consciousness

But how do we know that? How is that judgement made? How do you go about breaking down the components of a logical inference into 'sensory data'? I say you can't do it.

What a negativer chap you are.
I think it's because you wish to preserve the idea that reason is something mystical or that exists outside the brain.

The brain uses agencies.
Consciousness is a part of existence perceiving the rest; self-consciousness is a part of consciousness perceiving the rest....there are agencies controlling, overseeing, processing the data from other agencies.
The brain is a self-referential loop,if it were not for the imposition of sense data.
It is the sensory input streaming into the brain from sources outside the brain which intervene in this mental loop.
This is why the concepts are prone to being self-supporting mechanism based no a starting proposition which is taken as self-evident....like the logic of math.
Even God, the concept of it, is that of a self-referential, self-maintaining, self-determining solipsist.

It is this sensory input, this empiricism, which invades the mind and challenges it. This is why consciousness is an ongoing, self-correcting process...if it is not corrupted by illness or by some genetic failing.
Consciousness does not need self-consciousness. In fact the latter inhibits consciousness in many ways.
When you listen to music you are totally engrossed by the conscious perception of it; self-consciousness would break your spell and make your consciousness of the music less clear.

In order to even commence this line of investigation you need to exercise reason: 'if this, therefore that'. There is no need to justify every instance of logical inference of this type on the basis of a comparison between sense data, image, and object, without begging the question. What is begging the question? It is assuming what you set out to prove.

Then begin with the simple.
You have sense input...an interaction of a medium with a phenomenon which then interact with your sense organ.
This information in its most primal forms of consciousness, is processed using simple binary judgments: edible/not edible or threat no-threat.
Some reactions to stimuli are automatic: the blinking of an eye....getting an erection when you see a beautiful female, salivating when you smell food, your autoimmune system, your heart beating, you breathing etc.
All of this has been automated, naturally, and requires no consciousness.

[Jonathan.s]

A current story on the Higgs boson, from the Huffington Post:

Amazingly, the Higgs boson was predicted to exist not for any physical reasons, but on strictly mathematical grounds based on arcane symmetries usually studied in "pure" mathematics.

.... it all goes back to the pure mathematics of continuous symmetries and the idea of a group developed by Galois and originally proposed in order to understand why some equations can be solved and others not.

Of course, all the theory is beyond me, but I find the 'mathematicism' interesting.

[Bernard]

Indeed, its fantastic - expecting brains to do the amount of work that needs to be done to make these type of predictions, without the use of formulae, would be like trying to get to Mars with a donkey.

[Bernard]

Impessive at the other end of the scale as well.


http://apod.nasa.gov/apod/ap120813.html

[Kuznetzova]

The two incompleteness theorems are Platonic. If man were truly the measure of all things, then we should be able to make up any mathematical system we want, which does not appear to be the case.

I interpret Godel's theorems to say exactly the opposite of what you just wrote here.
To me they (strongly suggest) that mathematics is merely a language that human beings created to communicate ideas.

The theorems definitely suggest that humans could create any system of math. In fact the theorem requires the reader realize that there are many many different reduxes of deductive systems. Any deductive system (so conceived) which is capable of depicting arithmetic will be either incomplete or inconsistent. Look at the leading phrase on that sentence, "Any deductive system which..."

[ForgedinHell]

The two incompleteness theorems are Platonic. If man were truly the measure of all things, then we should be able to make up any mathematical system we want, which does not appear to be the case.

I interpret Godel's theorems to say exactly the opposite of what you just wrote here.
To me they (strongly suggest) that mathematics is merely a language that human beings created to communicate ideas.

The theorems definitely suggest that humans could create any system of math. In fact the theorem requires the reader realize that there are many many different reduxes of deductive systems. Any deductive system (so conceived) which is capable of depicting arithmetic will be either incomplete or inconsistent. Look at the leading phrase on that sentence, "Any deductive system which..."

The author of the two theorems would have strongly disagreed with you. I think the person who wrote them knew their significance. The reason is that if math were something people made up, then there is no reason why they could not be complete. The fact the systems are constrained, no matter what we dream up, means that "man is not the measure of all things." Godel was a good friend of Einstein, and both had a Platonic view of math.