[FOM] Negation as a non-primitive logical constant

Irving ianellis at iupui.edu
Thu Apr 15 13:35:33 EDT 2010

On Thu, 8 Apr 2010, Joao Marcos wrote:

>> I was wondering which are the earliest references to be found in the
>> literature to the "intuitionistic" definition of negation of A in
>> terms of A implying bottom

I am not entirely certain that I completely understand what the 
question may be. If what is at issue is the answer to the historical 
question of the first identifiable definition of negation in 
intuitionistic logic by an intuitionist logician, then it would be 
worth starting by examining Brouwer's paper "De onbetrouwbaarheid der 
logische principes" (Tijdschrift voor Wijsbegeerte 2 (1908), 152-158), 
in which he explicitly presents the new -- intuitionistic -- meaning of 
negation for the first time in his new interpretation of the law of 
excluded middle.

There is an historical aacount in Miriam Franchella, "Brouwer and Griss 
on Intuitionistic Negation", Modern Logic Volume 4, Number 3 (1994), 
256-265. For an exposition, looking at Heyting's formalization of 
Brouwer's intuitionism for starters, one might begin by examining W. 
Russell Belding, "Intuitionistic Negation", Notre Dame Journal Formal 
Logic Volume 12, Number 2 (1971), 183-187.

Irving H. Anellis
Visiting Research Associate
Peirce Edition, Institute for American Thought
902 W. New York St.
Indiana University-Purdue University at Indianapolis
Indianapolis, IN 46202-5159
URL: http://www.irvinganellis.info

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