Enakshi Ray Mitra: Later Wittgenstein on Language and Mathematics: A Non-foundational Narration
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Enakshi Ray Mitra: Later Wittgenstein on Language and Mathematics: A Non‑foundational Narration Indian Institute of Advanced Study, Shimla, 2017, 351 pp, Rs. 745/Ramesh Chandra Pradhan1 Published online: 9 January 2019 © ICPR 2019
The book by Dr. Enakshi Ray Mitra is on Wittgenstein’s later philosophy of language and mathematics. It is an exhaustive study of the Wittgenstein’s later views on language and mathematics with a view to provide a non-foundational narrative of the entire corpus of the concepts dealt with by Wittgenstein in his later writings. Dr. Ray Mitra has built up a narrative around some of the central themes of Wittgenstein’s later philosophy such as language games, forms of life, family resemblance and aspect seeing which have a direct connection with his philosophy of mathematics. For Wittgenstein, mathematics goes the same way as language because the language of mathematics is no different from language per se having no foundations on which to stand. If language is a form of life, so is mathematical language which depicts how the human beings engage in the use of the mathematical concepts such as number, addition and division. With a number of illustrations, Dr. Ray Mitra has explained the characteristic nature of the mathematical activities to prove that mathematics has no foundations other than the way it is practiced by the human beings in their day-to-day life.
Non‑foundationalism The central argument of Dr. Ray Mitra is that, according to the later Wittgenstein, mathematics has no foundations and that there is a non-foundationalist streak in Wittgenstein’s later writings on language and mathematics. Wittgenstein’s nonfoundationalism is evidenced by his repeated attack on the Augustinian model in language use and the use of the mathematical concepts. From the Philosophical Investigations to the Remarks on the Foundations of Mathematics, Wittgenstein consistently argues against the Augustinian model of language by exposing the * Ramesh Chandra Pradhan [email protected] 1
IIAS, Shimla, India
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Journal of Indian Council of Philosophical Research (2019) 36:211–214
limitations of such a model. This model has its origin in the idea that language use is based on the name–object relationship quite popular among the atomist theorists of language. This model has its impact on the theories of mathematics such as logicism, realism or Platonism and to some extent on intuitionism. Dr. Ray Mitra finds the shadow of the Augustinian model in the available theories of mathematics thus smacking of foundationalism of some sort or other. Wittgenstein was no doubt against Frege–Russell’s logicism because the move to convert all mathematics to logic is itself an ambitious and ultimately a failed project because both logic and mathematics have their own spheres of operation which refuse to be assimilated into each other. Wittgenstein did expose the limitations of the logicist account of mathematics not only in his early philosophy but also in his later writings. The reas
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