(June 11, 2012 at 9:43 pm)apophenia Wrote: I'm not of the opinion that there's anything ontologically distinctive about math and numbers, but then I wouldn't lean towards Quine's belief that mathematical concepts are derived empirically either. Philosophy of math gets into some serious shit, and like many of the purely theoretical sciences, there are more dead ends than hopeful avenues. Whatever, it's beyond me. I would lean toward a Kantian, underdetermined functionalism — numbers and math are abstractions built into our cognitions to allow us to map input behaviors to output behaviors in a probabilistic manner, without us having to figure out how the mathematical relationships between the environment and the life form actually work. In that sense, a number like '4' is a reference to a number of behavioral invariants, such that the invariants, like composition of functions, yields appropriate behaviors in response to contemplation of, and combination of, concepts.
Don't get too far off subject to think that the topic of discussion has shifted to mathematic philosophical quandries. But, with that in mind, I do believe the statements quoted above warrant a responce.
I don't know if you contradicted yourself or if you misinterpreted Quine's empirical take as being in opposition to the Kantian "intuit" of math. The two don't conflict with one another, but, if I can take your statements at face value, are very complementary.
Intuition is derived from nature. We evolved in such a way as to adopt certain intuitions, and so did many animals, and, if a looser definition of intuition is applied, all living things.
Bees are born to carry out their task, to bring pollen to the hive. This is the purpose of their existence. They too have the Kantian interpretation of math "installed" into them, so to speak, as intuition. Well, I shouldn't be so assertive. We can only gauge that from the animal's interaction with nature. But isn't that true with all thinking creatures?
In any case, the bee and the human are both capable of taking in sets and digits as data and having it displayed as probability in their minds. If math is represented as abstractions and manifested in the living as intuition, then it follows that math is a description of nature just like all life within nature.
After all, life in itself is descriptive of nature. That was Darwin's starting premise when advancing the theory of evolution and is the basis of modern biology, is it not?
My conclusion is that there is no reason to believe any of the dogmas of traditional theology and, further, that there is no reason to wish that they were true.
Man, in so far as he is not subject to natural forces, is free to work out his own destiny. The responsibility is his, and so is the opportunity.
-Bertrand Russell
Man, in so far as he is not subject to natural forces, is free to work out his own destiny. The responsibility is his, and so is the opportunity.
-Bertrand Russell
