Hypothesis on mathematical realism.

2021 ◽  
Author(s):  
Jacinto Choza ◽  
Francisco Marqués
Keyword(s):  
Mathematical Realism

Inference to the best explanation and mathematical realism

Synthese ◽  
2006 ◽  
Vol 160 (1) ◽  
pp. 13-20 ◽  
Author(s):  
Sorin Ioan Bangu
Keyword(s):  
Mathematical Realism

Modal Realism and its Roots in Mathematical Realism

2007 ◽  
pp. 997-1022
Author(s):  
Charles S. Chihara
Keyword(s):  
Modal Realism ◽  
Mathematical Realism

scholarly journals Debunking, supervenience, and Hume’s Principle

2019 ◽  
Vol 49 (8) ◽  
pp. 1083-1103 ◽  
Author(s):  
Mary Leng
Keyword(s):  
Mathematical Realism ◽  
Mathematical Beliefs ◽  
Conceptual Truth ◽  
Hume’S Principle ◽  
Moral Beliefs ◽  
Debunking Arguments ◽  
Moral Facts

AbstractDebunking arguments against both moral and mathematical realism have been pressed, based on the claim that our moral and mathematical beliefs are insensitive to the moral/mathematical facts. In the mathematical case, I argue that the role of Hume’s Principle as a conceptual truth speaks against the debunkers’ claim that it is intelligible to imagine the facts about numbers being otherwise while our evolved responses remain the same. Analogously, I argue, the conceptual supervenience of the moral on the natural speaks presents a difficulty for the debunker’s claim that, had the moral facts been otherwise, our evolved moral beliefs would have remained the same.

scholarly journals Mathematical and Moral Disagreement

2019 ◽  
Vol 70 (279) ◽  
pp. 302-327
Author(s):  
Silvia Jonas
Keyword(s):  
Moral Realism ◽  
Moral Disagreement ◽  
Central Problem ◽  
Mathematical Realism

Abstract The existence of fundamental moral disagreements is a central problem for moral realism and has often been contrasted with an alleged absence of disagreement in mathematics. However, mathematicians do in fact disagree on fundamental questions, for example on which set-theoretic axioms are true, and some philosophers have argued that this increases the plausibility of moral vis-à-vis mathematical realism. I argue that the analogy between mathematical and moral disagreement is not as straightforward as those arguments present it. In particular, I argue that pluralist accounts of mathematics render fundamental mathematical disagreements compatible with mathematical realism in a way in which moral disagreements and moral realism are not.1

Mathematical Realism

1988 ◽  
Vol 12 ◽  
pp. 275-285
Author(s):  
Penelope Maddy ◽  
Keyword(s):  
Mathematical Realism

A Critique of Resnik’s Mathematical Realism

Erkenntnis ◽  
2005 ◽  
Vol 62 (3) ◽  
pp. 379-393
Author(s):  
Timothy John Nulty
Keyword(s):  
Mathematical Realism

scholarly journals Defending Mathematical Realism

2011 ◽  
Author(s):  
Brendan James Sheehan
Keyword(s):  
Mathematical Realism

The Case for Mathematical Realism

1999 ◽  
pp. 41-51
Author(s):  
Michael D. Resnik
Keyword(s):  
Mathematical Realism

Realism, Ontology, and Objectivity

2020 ◽  
pp. 13-34
Author(s):  
Justin Clarke-Doane
Keyword(s):  
Mathematical Realism ◽  
Epistemological Challenge

This chapter explicates the concept of realism, and distinguishes it from related concepts with which it is often conflated. It shows that, properly conceived, realism has no ontological implications, and that influential epistemological objections to moral and mathematical realism fallaciously assume otherwise. One upshot of the discussion is that it is no response to Paul Benacerraf’s epistemological challenge to claim that there are no special mathematical entities with which to “get in touch.” The chapter concludes with a distinction between realism and objectivity, a distinction which is central to Chapter 6. It uses the Parallel Postulate, understood as a claim of pure geometry, as a paradigm of a claim that fails to be objective, even if mathematical realism is true. Conversely, it explains how realism about claims of a kind may be false even though they are objective in a sense in which the Parallel Postulate is not.

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