Read my Bengali article on Philosophy of Mathematics

Starting from the work of Gottlob Frege and the success and failure of the logicist trend in the philosophy of mathematics, and then having a brief look at Zermelo-Frenkel set theory, I address a few basic issues in Mathematical Realism, also termed Platonism in mathematics. While prominent names in mathematics are known to have adopted the Platonist position, the latter is not free of problems of interpretation rooted deeply in our view of what mathematical truth is all about. I then counterpose the intuitionist view of mathematics against the Platonist view and briefly outline David Hilbert's project of looking for the consistency of Mathematics, aiming to reconcile the finitary approach with the Platonist point of view. This also engendered the possibility of a resolution between the realist and the intuitionist points of view, but that possibility was thwarted to a considerable extent by Goedel's incompleteness theorems. This leads to the position that different trends in mathematical practice can coexist beside one another without compromising the precision and universality of any one of these. 

Indeed, mathematics is all about various possible combinations of concepts in our conceptual world, hanging together by consistency requirements, and of possible relations between concepts, among which the relation of analogy holds a crucial position of relevance. This is consistent with the broad framework of mathematics that category theory offers, where the concept of 'basic' mathematical objects, inherent in the realist approach, loses much of its relevance. Finally, I introduce a number of observations made by Wittgenstein that speak of the danger of too rigid a philosophy of mathematics.

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