DTLarca

04-05-2013, 01:08 AM

I have learned this week that there is an area of philosophy that I am almost certainly not interested in. That is the philosophy of mathematics.

After reading the first few chapters with close attention I then skimmed quickly to the end over the next short period of about just 3 hours.

I agree with all his conclusions found on page 217 and 218.

For instance... and I quote conclusions 6, 7 and 8 only...

6) ...diagrams can be rigorous proofs.

7) Mathematics is wedded to classical logic?

"One god, one flag, one logic", said Whitehead. Well, he was at least right about logic, and it is classical.

8) Mathematics is independent of sense experience?

Right again. This is the sense in which mathematics is a priori. It is not infallible, however. Experimental mathematics, it must be stressed, should not be confused with mathematics based on sensory evidence - there's no such thing.

http://www.amazon.co.uk/Philosophy-Mathematics-Contemporary-Introduction-Introductions/dp/0415960479

And of course logic (including math) has to be a priori, has to be analytic, because otherwise something else would have to be.

The implications of that all pervasive problem of the criterion surely entail that the logics are all a priori.

"How can any criterion of reliable knowledge be chosen unless we already possess some reliable criterion for making that choice?"

If we are to even begin judging the world we have to already have an innate means, axioms, theorems etc, according to which the world can be judged.

How could we possibly even begin to conceive of the world without an a priori established, or given, conceptual framework? (Immanuel Kant).

After reading the first few chapters with close attention I then skimmed quickly to the end over the next short period of about just 3 hours.

I agree with all his conclusions found on page 217 and 218.

For instance... and I quote conclusions 6, 7 and 8 only...

6) ...diagrams can be rigorous proofs.

7) Mathematics is wedded to classical logic?

"One god, one flag, one logic", said Whitehead. Well, he was at least right about logic, and it is classical.

8) Mathematics is independent of sense experience?

Right again. This is the sense in which mathematics is a priori. It is not infallible, however. Experimental mathematics, it must be stressed, should not be confused with mathematics based on sensory evidence - there's no such thing.

http://www.amazon.co.uk/Philosophy-Mathematics-Contemporary-Introduction-Introductions/dp/0415960479

And of course logic (including math) has to be a priori, has to be analytic, because otherwise something else would have to be.

The implications of that all pervasive problem of the criterion surely entail that the logics are all a priori.

"How can any criterion of reliable knowledge be chosen unless we already possess some reliable criterion for making that choice?"

If we are to even begin judging the world we have to already have an innate means, axioms, theorems etc, according to which the world can be judged.

How could we possibly even begin to conceive of the world without an a priori established, or given, conceptual framework? (Immanuel Kant).