On 08 Sep 2012, at 06:19, meekerdb wrote:

On 9/7/2012 8:43 PM, Jason Resch wrote:
Platonism (or mathematical realism) is the majority viewpoint of modern mathematicians.

In a survey of mathematicians I know it is an even division. Of course they are all methodological Platonists, but not necessarily philosophical ones.

Computationalism (or functionalism) is the majority viewpoint of cognitive scientists and philosophers of mind. Thus the scientific consensus is that infinite (mathematical) truth

Except mathematical truth is just a marker, T, whose value is preserved by the rules of logic. Whether a proposition that has T corresponds with any fact is another question.


Be careful to distinguish a true sentence (like T) with the notion of truth or of arithmetical true sentence, which is not even definable in arithmetic, and can be meta-defined in some set theory or second order arithmetic, at the meta-level. God can be arithmetical truth, but God can't be just T.




is the self-existent cause and reason for our existence.

That is very far from a scientific consensus. I'd say majority the opinion among scientists who are philosophically inclined is that mathematics and logic are languages in which we create models that represent what we think about reality. This explains why there can be contradictory mathematical models and even mutually inconsistent sets of axioms and rules of inference.

Yes, but this makes sense only for people agreeing on elementary arithmetical truth. If not, the notion of axioms and rules of inference don't make sense.

Nobody serious disagree on elementary arithmetic. I have never seen someone doubting the meaning of (N, +, *), except philosophers. Bad philosophers, I would say, when they are in desperate needs to demolish some argument, or to look original or something. We need assess arithmetic to make sense of doubting arithmetic, and so, doubting arithmetic does not make sense, in fact.

Bruno



Few people today have realized that this is inevitable conclusion of these two commonly held beliefs.

Not only that a few people have rejected it.

Brent

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