🚀 go-pugleaf

pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
   guttman@circe.mitre.org (Joshua D. Guttman) writes:
   >cotera@woods.ulowell.edu writes:
   >
   >   Can anyone explain why we use logic? Unfortunately, any logical arguments to
   >   support logic, are unfortunately, invalid.
   >   --Ray Cote
   >
   >On the contrary, logical arguments may be not only valid, but also informative.
   >(etc.)

   This seems to fall far short of addressing the basic question of why we
   use logic.  Why not do all our thinking with just the equations of
   arithmetic?  Or the equations of binary relations under composition and
   converse as suggested by Tarski and Givant in "A Formalization of Set
   Theory without Variables."

Are you asking why we use a syntax of variables and predicates (or rather a
natural language grammar in which these can be discerned)?  Or are you asking
why a particular logic, quantified predicate logic, is more beneficial than
another, say purely equational logic?  

As for why we do not do all our thinking with equations of arithmetic, I'd
answer, because numbers are not the only things we want to think about, and
quantifier-free formulas are not the only ones we want to assert.  I have not
looked at Tarski/Givant.

As to why we use any sort of deductive reasoning, I'd answer, because we have
beliefs and we examine assumptions and we want to know what their consequences
are.  Indeed, it would hard to imagine that we could attribute beliefs to a
creature that did not trouble itself about their consequences.

	Josh