The Use of Symbols in Mathematics and Logic

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Book Chapters


Essays on the Foundations of Mathematics and Logic, Polimetrica Publisher, Volume 2, Italy, p.99–120 (2005)



Foundations of Mathematics and Logic, Philosophy of Mathematics and Logic


It is commonly believed that the use of arbitrary symbols and the process of symbolisation have made possible the discourse of modern mathematics as well as modern, symbolic logic. This paper discusses the role of symbols in logic and mathe- matics, and in particular analyses whether symbols remain arbitrary in the process of symbolisation. It begins with a brief summary of the relation between sign and logic as exemplified in Indian logic in order to illustrate a logical system where the notion of `natural' sign-signified relation is privileged. Mathematics uses symbols in creative ways. Two such methods, one dealing with the process of `alphabetisation' and the other based on the notion of `formal similarity', are described. Through these processes, originally meaningless symbols get embodied and coded with meaning through mathe- matical writing and praxis. It is also argued that mathematics and logic differ in the way they use symbols. As a consequence, logicism becomes untenable even at the discursive level, in the ways in which symbols are created, used and gather meaning.


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