Archive for January 2nd, 2015

January 2, 2015

Intuition and philosophy

by Neil Rickert

This is mostly a reaction to a recent post at Scientia Salon:

Apparently some philosophers, including the author Massimo Pigliucci, are seriously arguing that philosophy does not depend on intuition.

I had to check my calendar.  It seems far to early in the year for an April Fools joke.  The argument presented seems to suggest a staggering lack of self-awareness among philosophers.

Mathematics and intuition

I’ll start with where I see intuition as important.  And, quite frankly, I could not do mathematics or science without intuition.  Skeptics often criticize the use of intuition, but I’m inclined to think that when I am expressing skepticism, that skepticism is partly based on intuition.

Mathematics can be said to have a formal structure that is independent of intuition.  We make definitions and prove theorems based on those definitions.  Thus the conclusions are formal consequences of the definitions and other assumptions, so technically they are not dependent on intuition.

However, in order to do mathematics without any intuition, I would  be forced to rely on a mathematical philosophy of formalism.  Yet mathematics, seen as logical manipulation of formal symbols, seems sterile.  Almost everything that I value about mathematics depends on intuition.  My ability to use mathematics to solve real world problems depends on intuition.  My ability to think of numbers as if they were actual entities rather than formal meaningless symbols, is dependent on mathematical intuition.

read more »