[FOM] Why inclusive disjunction?

Stephen Pollard spollard at truman.edu
Thu Jan 11 12:04:41 EST 2007

Exclusive 'or' is the more distinctively classical of the two  
classical disjunctions. In particular, if your logic features

1. a binary connective that behaves like exclusive 'or'
2. a binary connective that behaves like the intuitionist conditional
3. a unary connective that behaves like intuitionist negation

then your conditional will satisfy Peirce's Law and your negation  
will satisfy double negation elimination. Inclusive 'or' lacks this  
property. The deductive behavior of exclusive 'or' is incompatible  
with intuitionism; that of inclusive 'or' is not.

Stephen Pollard
Professor of Philosophy
Division of Social Science
Truman State University
spollard at truman.edu

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