David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
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.
Citations of this work BETA
No citations found.
Similar books and articles
Heinrich Wansing (2006). Logical Connectives for Constructive Modal Logic. Synthese 150 (3):459 - 482.
Dimiter Vakarelov (2006). Non-Classical Negation in the Works of Helena Rasiowa and Their Impact on the Theory of Negation. Studia Logica 84 (1):105 - 127.
Yaroslav Shramko (2005). Dual Intuitionistic Logic and a Variety of Negations: The Logic of Scientific Research. Studia Logica 80 (2-3):347 - 367.
Greg Restall (2001). Constructive Logic, Truth and Warranted Assertability. Philosophical Quarterly 51 (205):474-483.
Lloyd Humberstone (2008). Contrariety and Subcontrariety: The Anatomy of Negation (with Special Reference to an Example of J.-Y. Béziau). Theoria 71 (3):241-262.
Greg Restall (1997). Combining Possibilities and Negations. Studia Logica 59 (1):121-141.
Kosta Došen (1992). The First Axiomatization of Relevant Logic. Journal of Philosophical Logic 21 (4):339 - 356.
Dimiter Vakarelov (2005). Nelson's Negation on the Base of Weaker Versions of Intuitionistic Negation. Studia Logica 80 (2-3):393-430.
Added to index2009-01-28
Total downloads86 ( #45,620 of 1,789,998 )
Recent downloads (6 months)1 ( #424,764 of 1,789,998 )
How can I increase my downloads?