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Volume 36 Issue 2 - Special Issue: Lakatos’ Undone Work: The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science; Guest Editors: Sophie Nagler, Hannah Pillin, Deniz Sarikaya

June 2022

Issue of KRITERION – Journal of Philosophy

Contents
Journal Overview

Publicly Available November 11, 2022

Frontmatter

Page range: i-ii

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Introduction

Open Access April 22, 2022

Introduction to the Special Issue on Lakatos’ Undone Work

Sophie Nagler, Hannah Pillin, Deniz Sarikaya

Page range: 113-122

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Abstract

We give an overview of Lakatos’ life, his philosophy of mathematics and science, as well as of this issue. Firstly, we briefly delineate Lakatos’ key contributions to philosophy: his anti-formalist philosophy of mathematics, and his methodology of scientific research programmes in the philosophy of science. Secondly, we outline the themes and structure of the masterclass Lakatos’ Undone Work – The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science , which gave rise to this special issue. Lastly, we provide a summary of the contributions to this issue.

Research Articles

Open Access January 10, 2022

Degeneration and Entropy

Eugene Y. S. Chua

Page range: 123-155

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Abstract

Lakatos’s analysis of progress and degeneration in the Methodology of Scientific Research Programmes is well-known. Less known, however, are his thoughts on degeneration in Proofs and Refutations. I propose and motivate two new criteria for degeneration based on the discussion in Proofs and Refutations – superfluity and authoritarianism. I show how these criteria augment the account in Methodology of Scientific Research Programmes , providing a generalized Lakatosian account of progress and degeneration. I then apply this generalized account to a key transition point in the history of entropy – the transition to an information-theoretic interpretation of entropy – by assessing Jaynes’s 1957 paper on information theory and statistical mechanics.

Open Access January 12, 2022

Showing Mathematical Flies the Way Out of Foundational Bottles: The Later Wittgenstein as a Forerunner of Lakatos and the Philosophy of Mathematical Practice

José Antonio Pérez-Escobar

Page range: 157-178

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Abstract

This work explores the later Wittgenstein’s philosophy of mathematics in relation to Lakatos’ philosophy of mathematics and the philosophy of mathematical practice. I argue that, while the philosophy of mathematical practice typically identifies Lakatos as its earliest of predecessors, the later Wittgenstein already developed key ideas for this community a few decades before. However, for a variety of reasons, most of this work on philosophy of mathematics has gone relatively unnoticed. Some of these ideas and their significance as precursors for the philosophy of mathematical practice will be presented here, including a brief reconstruction of Lakatos’ considerations on Euler’s conjecture for polyhedra from the lens of late Wittgensteinian philosophy. Overall, this article aims to challenge the received view of the history of the philosophy of mathematical practice and inspire further work in this community drawing from Wittgenstein’s late philosophy.

Open Access January 10, 2022

HYPER-REF: A General Model of Reference for First-Order Logic and First-Order Arithmetic

Pablo Rivas-Robledo

Page range: 179-205

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Abstract

In this article I present HYPER-REF, a model to determine the referent of any given expression in First-Order Logic (FOL). I also explain how this model can be used to determine the referent of a first-order theory such as First-Order Arithmetic (FOA). By reference or referent I mean the non-empty set of objects that the syntactical terms of a well-formed formula (wff) pick out given a particular interpretation of the language. To do so, I will first draw on previous work to make explicit the notion of reference and its hyperintensional features. Then I present HYPER-REF and offer a heuristic method for determining the reference of any formula. Then I discuss some of the benefits and most salient features of HYPER-REF, including some remarks on the nature of self-reference in formal languages.

Open Access January 12, 2022

The Quasi-Empirical Epistemology of Mathematics

Ellen Yunjie Shi

Page range: 207-226

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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.

Open Access April 21, 2022

Lakatos’ Quasi-Empiricism Revisited

Wei Zeng

Page range: 227-246

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Abstract

The central idea of Lakatos’ quasi-empiricism view of the philosophy of mathematics is that truth values are transmitted bottom-up, but only falsity can be transmitted from basic statements. As it is falsity but not truth that flows bottom-up, Lakatos emphasizes that observation and induction play no role in both conjecturing and proving phases in mathematics. In this paper, I argue that Lakatos’ view that one cannot obtain primitive conjectures by induction contradicts the history of mathematics, and therefore undermines his quasi-empiricism theory. I argue that his misconception of induction causes this view of Lakatos. Finally, I propose that Wittgenstein’s view that “mathematics does have a grammatical nature, but it is also rooted in empirical regularities” suggests the possibility to improve Lakatos’ view by maintaining his quasi-empiricism while accepting the role induction plays in the conjecturing phase.

About this journal

KRITERION - Journal of Philosophy provides a forum for rational discussion in any field of philosophy. As dedicated to the analytic tradition, it publishes highly understandable and criticisable work making use of clear and thorough argumentation. We believe that this is the only possible way of contributing to progress in philosophy, which is the journal's main objective.

The journal was founded in 1991. Since 2021, it is published and distributed as an open access journal by De Gruyter. We are convinced that this collaboration will further increase the quality and visibility of the journal.

KRITERION - Journal of Philosophy accepts contributions in English language. All contributions go through a double-blind peer review process. Since we especially want to encourage early career authors, the journal's policy is to reach a decision on every submission within five weeks of receipt. The journal is known for providing friendly and helpful reviewer comments and suggestions of how to improve manuscripts. This becomes manifest also in our current statistics: The initial acceptance rate is 5%, the overall acceptance rate is almost 30%, and over 90% of authors receive reports from external reviewers.

KRITERION - Journal of Philosophy also publishes special issues and monographic sections. For more information on guest-editing a special issue or monographic section, please see the supplementary material below.