<abstract xmlns="http://www.w3.org/1999/xhtml">
				
				<p>In this paper I dispute the current view that intuitionistic logic is the common basis for the three main trends of constructivism in the philosophy of mathematics: intuitionism, Russian constructivism and Bishop’s constructivism. The point is that the so-called ‘Markov’s principle’, which is accepted by Russian constructivists and rejected by the other two, is expressible in intuitionistic first-order logic, and so it appears to have the status of a logical principle. The result of appending this principle to a complete intuitionistic axiom system for first-order predicate logic constitutes a new logic, which could well be called ‘Markov’s logic’, and which should be regarded as the true logical system underlying Russian constructivism.</p>
			</abstract>

In this paper I dispute the current view that intuitionistic logic is the common basis for the three main trends of constructivism in the philosophy of mathematics: intuitionism, Russian constructivism and Bishop’s constructivism. The point is that the so-called ‘Markov’s principle’, which is accepted by Russian constructivists and rejected by the other two, is expressible in intuitionistic first-order logic, and so it appears to have the status of a logical principle. The result of appending this principle to a complete intuitionistic axiom system for first-order predicate logic constitutes a new logic, which could well be called ‘Markov’s logic’, and which should be regarded as the true logical system underlying Russian constructivism.

The Logic of Constructivism

Disputatio

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"The Logic of Constructivism"}

In this paper I dispute the current view that intuitionistic logic is the common basis for the three main trends of constructivism in the philosophy of...

The Logic of Constructivism

Published Online: Dec 31, 2018

Page range: 37 - 42

DOI: https://doi.org/10.2478/disp-2002-0003

© 2019 Gustavo Fernández Díez, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.