From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Why Logic?
Organization: Computer Science Department,  Stanford University.
Date: Mon, 16 Nov 1992 21:24:10 GMT

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.

For the same reason that courts accept only two pleas: guilty or not
guilty.  It is quite hard enough to get a jury to agree on that one bit
without asking them also to agree on details of the witnesses'
stories.

Once the high order bit is settled, the lower order bits (severity of
sentence and such) can be decided more casually according to the
position of that bit and with the aid of information left over from the
determinations of the higher order bits.

Voting tends to be organized along similar lines, with questions
preferably framed to have yes/no answers in order to simplify
discussion and to maximize the representativeness of the winning
outcome.

Pretrial hearings and primaries serve to sharpen the question, not to
refine the answer.

This is the principle of the most significant bit, MSB.  Over the
millennia we have acquired an intuitive appreciation of the MSB
principle, not just in the courtroom and the legislature but
everywhere, and we have evolved and refined tools for dealing with that
bit.  These tools constitute logic.

Our modern view of these tools recognizes a library of predicates, each
producing a bit that for certain applications is the appropriate high
order bit.

In addition there is the collection of all n-ary operations on a
2-valued set, better known as the Boolean operations, giving a complete
library of operations for manipulating bits.

But this modern view in terms of predicates and Boolean connectives is
as much a stereotype of natural logic as the Pentagon is pentagonal,
and any simple modern account can bear only a superficial resemblance
to the full gamut of tools of natural logic.  In particular there has
been no convincing demonstration that the weighty matters contemplated
in courts and the legislature are judged exclusively, or even
primarily, according to the rules of the first order predicate
calculus.  The logic of the court would appear to center more on
catching smugglers of argumentum ad hominem and other logical
contraband, while that of Congress is the same with the additional
requirement of alienating the fewest number weighted by alliance.  In
such settings the MSB principle plays a critical role in conferring the
benefit of logical rigor on a situation whose natural state is logical
chaos.

Formal logic presumably did not appear until well after natural logic
had evolved and been adopted for everyday use.  The first two millennia
of formal logic to make it into today's historical record focused on
the correct application of an abstract view of the extant tools,
without raising questions of their soundness or completeness.  Peirce
in the 1870's was the first to explicitly incorporate the two-valued
nature of truth into the methodology of formal logic, though Boole had
earlier come very close when he tied truth to sets.

Today formal logic continues to focus on correctness of argument, with
two-valued truth playing a central though by no means solo role as the
importance of the first bit comes to be seen, if only subconsciously,
in its proper light: a very good but by no means essential heuristic.

As nonlogical principles are assimilated along with logical rules of
inference into single decision methods and conditional rules of
calculation, the boundary of logic and nonlogic blurs, leaving us with
formal reasoning systems containing a blend of rules whose origins in
their respective logical and nonlogical calculi grow less discernible
with every passing decade.
-- 
Vaughan Pratt	  		A fallacy is worth a thousand steps.