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Chapter 7 - Wittgenstein and the covert Platonism of mathematical logic
from Part I - The Main Positions
- By Mark Steiner
Edited by Penelope Rush, University of Tasmania
Book:

The Metaphysics of Logic

Published online:

05 October 2014

Print publication:

16 October 2014, pp 128-144
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Summary

This chapter discusses a kind of relativism or pluralism concerning logic. It explores a core metaphysical issue concerning logic, the extent to which logic is objective. The chapter adopts a Hilbertian perspective, either the original version where consistency is the only formal, mathematical requirement on legitimate theories, or the liberal orientation where there are no formal requirements on legitimacy at all. It explores the ramifications for what the author takes to be a longstanding intuition that logic is objective. This chapter explains the matter of objectivity with the present folk-relativism concerning logic in focus. Sometimes it concentrates on general logical matters, such as validity and consistency, as such, and sometimes it deals with particular instances of the folk-relativism, such as classical validity, intuitionistic consistency, and the like. The chapter limits the discussion to Wright's axes of epistemic constraint and cognitive command.