[FOM] Why inclusive disjunction?

Timothy Y. Chow tchow at alum.mit.edu
Fri Jan 12 09:47:42 EST 2007

Arguments about natural language, and about the choice of OR vs. XOR *in 
isolation*, are kind of fun but are doomed to be inconclusive, and I don't 
think they address the right question anyway.  A better question is, given 
that we're interested in the AND operation, should we pair it with OR or 
with XOR?

The answer is, we pair AND with OR if we're interested in the duality 
between them---de Morgan's laws; series vs. parallel circuits; the analogy 
with intersection/union, meet/join, for all/there exists, etc.; the fact 
that each is distributive over the other; and so on.  We pair AND with XOR 
if we're interested in arithmetic/algebra/geometry over F_2, where AND is 
multiplication and XOR is addition.


More information about the FOM mailing list