Against Set Theory.mellel

Since the rise of modern science in the seventeenth century, philosophy has suffered from a need for legitimation. If it is science that provides us with our advanced knowledge of the world, what role is there left for philosophy? Several answers have been given. One answer is that of Wittgenstein. Philosophy is not in the knowledge business at all. In a world in which no one misused language, there would be no need for the restorative activity called ‘philosophy’. Philosophy, like medicine, is a response to imperfection. Among the positive answers are three. One assimilates philosophy to natural science and denies there is any sharp distinction. We find this among empiricists such as Mill, Quine and Armstrong. Another attempts to discern some special subject matter and/or method for philosophy, inaccessible to and prior to science. Kant’s critical philosophy, Husserl’s phenomenology and some strains of linguistic-analytic philosophy are like this. Finally there are those who would assimilate philosophy to the formal sciences of mathematics and logic. This was most popular among seventeenth century rationalists who attempted to do philosophy more geometrico but has its modern echoes in philosophy in the phenomenon we may call ‘math envy’. Applying set theory promises the philosopher partial relief from math envy, because it can be used to convince sceptics that philosophy too can be hard science. This paper is about why philosophers should stand up on their own and overcome their besottedness with sets.