The Nature of Mathematical Truth: A Comparative Study of Frege, Mill, and Kripke

• Sharmistha Chakraborty

  Presidency University

  Author

  https://orcid.org/0009-0007-8792-2348

Philosophers have debated the question of what makes mathematical statements true. In the present paper, we explore three influential and contrasting perspectives on mathematical truth by John Stuart Mill, Gottlob Frege and Saul Kripke. For the empiricist MILL, mathematics is inductive, its truths being generalisations of repeated observation. This perspective links mathematics directly to science, but it has been criticised for failing to account for the necessity and universality of mathematical truths. For Frege, all mathematical statements are analytic a priori because they are true by virtue of meaning and logical structure, independent of experience. He aimed to reduce arithmetic to logic. Kripke introduced the concept of the necessary a posteriori and showed how some truths can be necessarily true yet known only through experience. This paper compares these three thinkers and considers their strengths and limitations. Ultimately, we agree and disagree with different parts of their views. It finally reaffirms the Fregean stance that mathematical truth is necessary and a priori, with analytic statements in arithmetic and synthetic statements in geometry.

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