A few remarks on the (meta)philosophy of mathematics

Abstract

The present essay deals with the problem of how to choose the correct method of doing philosophy of mathematics taking into account the importance of technical mathematical results for philosophical analysis. After a short historical introduction presenting the formation of the present mathematical paradigm, it is pointed out that the current mathematical praxis has, in principle, no connection with philosophical investigations. Two radically different approaches to philosophy of mathematics are outlined. Basing on selected examples it is argued that the correct method of doing philosophy of mathematics should take into account both technical results obtained by mathematicians (which often throw a new light on old philosophical questions) and the autonomy of philosophical method.