PhilosophyAndMathematics

Quora Answer : Professionally speaking, a mathematician can become a philosopher through logic. Can a philosopher do the opposite?

Dec 9, 2016

Philosophy and maths have plenty on common. Both work by analysing the structure of ideas rather than empirically sampling the structure of the world. Philosophers care about logic. Most are pretty rigorous, for some value of rigour.

Some famous philosophers have also been professional mathematicians too. From Descartes and Pascal, to Gottlob Frege, Bertrand Russell, Alfred North Whitehead and Ludwig Wittgenstein.

But arguably philosophy is broader than mathematics. You CAN choose to be very concerned with formalisms and what you can derive from them in philosophy. But you can also choose very different styles of thinking and writing too. Philosophy is more free.

Also, it tends to be that mathematicians do their best work when young. It seems that there are few who make their first significant contribution older than their mid-30s. So it might be easier for someone who got famous in maths to shift into philosophy later in life and do good work (eg. Whitehead) than someone who got famous in philosophy to shift into doing significant maths later in life.

Quora Answer : What is the relationship between mathematicians and philosophers of mathematics?

Jan 10, 2017

I think there's quite a lot of overlap.

Mathematicians are people who explore the unfolding implications of particular sets of axioms or formal rules.

Sooner or later, they are going to become curious about why the rules / axioms should be what they are.

This question can be asked in a "mathematician's" way, of course ... by trying to abstract and find if those rules are cases of a more general set of rules. Or by tweaking an axiom and seeing how the implications would be different.

But it can also lead into full philosophy of mathematics. Such as asking metaphysical questions about what rules are or epistemological questions about how we can "know" them.

Quora Answer : What is the difference between philosophical logic & mathematical logic?

Oct 26, 2015

Both maths and philosophy are largely talking about the same logic.

But the job of mathematicians and philosophers is different. Mathematicians start with a set of rules and axioms and explore the implications of those rules and axioms. Sometimes they vary them, to see what they can find out about what it's like in the neighbouring worlds. But sticking to the rules is what's most important.

The job of philosophers is broader ... it's to talk about what thinking and reasoning are and why we should do them ... in the widest possible sense.

Philosophers will USE logic when they think that it's possible to represent an argument using this formalism. OTOH when they don't think that what they want to say can be usefully formulated in such a language, they'll look for a different way to make their argument. Perhaps one that doesn't have the formality and rigour.

For the mathematician, formality and rigour are everything. Anything that can't be formalized isn't worth thinking about (at least not during work-hours). For the philosopher, if formality and rigour aren't up to the job then poetry or something else will have to be used instead.