The Quasi-Empirical Epistemology of Mathematics

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Ellen Yunjie Shi

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.

Author(s):  
José Ferreirós

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, the book uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, the book shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. It argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. It demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, the book challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.


Philosophy ◽  
2014 ◽  
Author(s):  
Brendan Larvor ◽  
Colin Jakob Rittberg

Imre Lakatos (b. 1922–d. 1974) was a philosopher of mathematics and science. Having left Hungary in 1956, he made his first appearance on the international stage with a series of four papers during 1963 and 1964 in the British Journal for the Philosophy of Science, later published together posthumously in Proofs and Refutations (1976), in which he discusses the formation of mathematical concepts by proof-analysis. This radical break with classical approaches to the philosophy of mathematics attracted sufficient interest that Kitcher and Aspray deem Lakatos to have started a new and “maverick” tradition in the field (“An Opinionated Introduction,” in History and Philosophy of Modern Mathematics, 1988). By 1959, Lakatos had become an assistant lecturer in the Department of Philosophy, Logic and Scientific Method at the London School of Economics and Political Science. This department was still under the direction of its founder, Karl Popper, and Lakatos’s evolving and ultimately antagonistic relations with Popper and the Popperians conditioned much of his work. The chief part of this work was a series of influential papers on the philosophy of science. These are included in the two books of his work that two of his former students, John Worrall and Gregory Currie, published after his death (Lakatos 1978a and Lakatos 1978b, cited under Posthumously Published). In 1974, Lakatos died of a heart attack, leaving his projects in philosophy of science and mathematics incomplete.


Author(s):  
N. N. Trakakis

The ‘problem of evil’—whether conceived broadly as the challenge of reconciling evil and imperfection with a commitment to ultimate justice, goodness, or harmony in the universe, or more narrowly in (say) theistic terms as the problem of reconciling the existence of an absolutely perfect being with the existence of sin and suffering—has a long and venerable history, exercising some of the finest minds from ancient to modern times. However, as will be discussed below, in recent philosophy of religion the debate seems to have reached a stalemate, where opposing camps rehearse tired and familiar lines of argument that remain singularly unconvincing to one another, giving the entire debate the character of what Imre Lakatos called a ‘degenerating research program’. In reaction to this, signs have begun to emerge that the problem of evil and the discipline at large are on the cusp of a breakthrough that promises to bring to the forefront a series of imaginative, suggestive, and innovative, though unfortunately neglected, approaches to the nature of divinity and its relationship to evil. The present collection of dialogical essays is put forward as a contribution to this renewal....


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