🚀 go-pugleaf

In article <GUTTMAN.92Nov19120734@circe.mitre.org> guttman@circe.mitre.org (Joshua D. Guttman) writes:
>In article <1992Nov16.091653.1@woods.ulowell.edu> 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.
>
>For instance, to explain why we use classical first order logic (for many
>important purposes), logical theorems such as soundness and completeness are
>very relevant.  So are fancier theorems such as the non-enumerability of
>consequence in 2nd order logic, or Lindstrom's theorem.  
>
>Of course it depends what the argument is intended to accomplish.  A truly
>illogical person (perhaps a child) must be trained, not convinced.  A logical
>person who wants to gain insight into what he's doing and why can learn a lot
>from mathematical logic.  

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."

To me the chief characteristic of logic is its emphasis on sorting out
situations into *two* cases, whether always successfully (Boolean
logic) or sometimes not (intuitionistic logic).  See my message of Nov.
16 arguing this viewpoint in considerable detail.
-- 
Vaughan Pratt	  		A fallacy is worth a thousand steps.