On 7/26/2015 12:33 PM, Patrik Eklund wrote:
Philosophy of mathematics is still philosophy and has nothing to do with mathematics, since philosophy does not adhere to any mathematical principles.
Philosophy of logic is the same, since philosophy does not adhere to any logical principles.
By an argument such as this, it would appear that you could say that bacteriology has nothing to do with bacteria, because you cannot grow bacteriology on a Petri dish or sequence its DNA -and obviously this would be absurd. I think the source of the confusion here is that mathematics is reflexive in a way that bacteriology isn't: mathematics/logic _does_ feed back into itself and become a tool for doing more mathematics/logic. It's thus tempting to think that anything outside this loop is not part of mathematics/logic. However, the loop is not closed, and cannot be. There are questions which are legitimate parts of mathematics/logic that cannot be answered internally. I'm not talking about Goedel incompleteness here (though one might), but about why we do what we do. If we want to say what constitutes mathematics worth doing - to say why Fermat's Last Theorem or the Riemann Hypothesis are more important that the (3n+1) problem or finding palindromic sequences in the decimal expansion of pi - we cannot do this by calculation and proof. This is an example of a place where philosophy of mathematics can have a genuine connection. -Robert Dawson [For admin and other information see: http://www.mta.ca/~cat-dist/ ]