David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Synthese 148 (3):701 - 717 (2006)
We put together several observations on constructive negation. First, Russell anticipated intuitionistic logic by clearly distinguishing propositional principles implying the law of the excluded middle from remaining valid principles. He stated what was later called Peirce’s law. This is important in connection with the method used later by Heyting for developing his axiomatization of intuitionistic logic. Second, a work by Dragalin and his students provides easy embeddings of classical arithmetic and analysis into intuitionistic negationless systems. In the last section, we present in some detail a stepwise construction of negation which essentially concluded the formation of the logical base of the Russian constructivist school. Markov’s own proof of Markov’s principle (different from later proofs by Friedman and Dragalin) is described.
|Keywords||Philosophy Philosophy Epistemology Logic Metaphysics Philosophy of Language|
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References found in this work BETA
Bertrand Russell (1903). Principles of Mathematics. Cambridge University Press.
A. S. Troelstra (1988). Constructivism in Mathematics: An Introduction. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
David Nelson (1966). Non-Null Implication. Journal of Symbolic Logic 31 (4):562-572.
A. A. Markov, B. van Rootselaar & J. F. Staal (1975). An Approach to Constructive Mathematical Logic. Journal of Symbolic Logic 40 (1):85-85.
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