Abstract
Abstract This paper clarifies and discusses Imre Lakatos’ claim that mathematics is quasi-empirical in one of his less-discussed papers A Renaissance of Empiricism in the Recent Philosophy of Mathematics. I argue that (1) Lakatos’ motivation for classifying mathematics as a quasi-empirical theory is epistemological; (2) what can be called the quasi-empirical epistemology of mathematics is not correct; (3) analysing where the quasi-empirical epistemology of mathematics goes wrong will bring to light reasons to endorse a pluralist view of mathematics.
Highlights
1 Introduction In A Renaissance of Empiricism in the Recent Philosophy of Mathematics,1 Imre Lakatos claims that mathematics is quasi-empirical
What does Lakatos mean by this claim? Why does he think that mathematics is quasi-empirical? And most importantly, is this claim correct? This paper aims to investigate these questions
For Lakatos to develop the quasi-empirical epistemology of mathematics, it is crucial to figure out what the basic statements of mathematics are (Lakatos 1976, p. 202)
Summary
In A Renaissance of Empiricism in the Recent Philosophy of Mathematics, Imre Lakatos claims that mathematics is quasi-empirical. If mathematics is quasi-empirical, an immediate question “what are the falsifiers for mathematics?” arises Logical falsifiers are concerned with the consistency of the quasi-empirical theory. Given that the quasi-empirical epistemology of mathematics is not correct, in Section 4, I investigate what instead should be the correct picture of mathematics. I argue that truth-value injections and transmissions in mathematics do not carry the epistemic weight as Lakatos thinks. Lakatos’ quasiempirical epistemology does capture the idea of extrinsic justifications for axioms in mathematics, which are, roughly speaking, the justifications by the desirable consequences of having the axiom He is wrong to view it as the single methodology of mathematics and to attach significant epistemic values to the justifications
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