Philosophy Reading Group / Kant & Math

[JoeDawg]

Could you tell if you had more than one thought?

I think this is one of the problems faced by those who want to create an AI. I think our consciousness is a function of interacting experiences from multiple stimuli. Creating a brain in box, or brain in a vat, means there is really only one source of stimuli. If we want to mimic intelligence, I think we need to include a variety of input sources. A robot with eyes, ears... a sense of touch...etc..

But to answer your question, I think you would have to have a need to distinguish between thoughts, and that need would undoubtedly rely on an external influence.

 

[wofsy]

A pretty big problem from what I have read. I think you're idealizing mathematics, like the ancient greeks did with geometry. It all happens in the human brain. And different cultures have developed different mathematical systems. Ours has simply absorbed all the aspects we find most useful.

Math is in large part analytic, but its axioms and basic logic are derived from experience. All logic comes from how we see the world working. Math is just a way to represent and predict experience using highly abstract language.

Axioms are little more than assumptions, or constraints. And those constraints are based on our experiences in the world.

A couple unrelated thoughts: They are meant as talking points not as assertions of anything that I believe.

- in some sense everything happens in the human brain. Mathematics and experience are inescapably unified.

- Logic is intrinsic. If it were not we would not be able to think.

- "Derived from expeience" is a vague idea. Derived has no rigorous definition.

- Math is not "just" a way to represent and predict experience". Here is a quote from Felix Klein's introduction to his book, Riemann's Theory of Algebraic Functions and their Integrals."

"He(Riemann ) had in mind far more general methods of determination than those we employ in the following pages;methods of determination in which physical analogy ...fails us."

- Experience suggests an underlying mathematical reality but that reality supercedes direct experience

 

[apeiron]

A couple unrelated thoughts: They are meant as talking points not as assertions of anything that I believe.

- in some sense everything happens in the human brain. Mathematics and experience are inescapably unified.

- Logic is intrinsic. If it were not we would not be able to think.

- "Derived from expeience" is a vague idea. Derived has no rigorous definition.

- Math is not "just" a way to represent and predict experience". Here is a quote from Felix Klein's introduction to his book, Riemann's Theory of Algebraic Functions and their Integrals."

"He(Riemann ) had in mind far more general methods of determination than those we employ in the following pages;methods of determination in which physical analogy ...fails us."

- Experience suggests an underlying mathematical reality but that reality supercedes direct experience

If you want to demystify and make rigorous the relationship between minds and worlds, Rosen's modelling relations work serves as a good template...

http://www.panmere.com/?page_id=18

http://www.osti.gov/bridge/servlets/purl/10460-5uGkyu/webviewable/10460.pdf