From: jamie@cs.sfu.ca (Jamie Andrews)
Subject: Re: Why Logic?
Organization: CSS, Simon Fraser University, Burnaby, B.C., Canada
Date: Mon, 23 Nov 1992 20:46:42 GMT

My $0.02...

     When we're engaged in arguments, it is natural for one side
to question the other side's assumptions, modes of reasoning,
and anything else we can think of.  In my opinion, the purpose
of logic (formal or rhetorical) is to make this questioning more
reasonable, by reducing some aspects of the argument to
assumptions and modes of reasoning we can all agree on.
In particular, in formal logic we reduce the deductive process
to the "formula game" of manipulating symbols following certain
rules.

     There are some problems with this, of course.

1.)  Who says we can all agree on the assumptions and modes of
reasoning?  The extreme example is the Tortoise, in Lewis
Carroll's dialogue with Achilles, who questions even whether A
and A -> B entails B.  Less extreme examples include the Axiom
of Choice, which still causes ructions in mathematical logic.

     However, most principles of logic (such as that A and
B entail A&B) are non-controversial.  In fact, considering the
turmoil surrounding the development of formal logic, it's
amazing *how many* principles current logicians agree on.

2.)  Translating informal arguments into formal logic and then
"formally proving them" can lend a spurious legitimacy to the
informal argument, if the translation is faulty.  We have all
heard examples of "formal proofs" of such contentious
propositions as the existence of God.

     This is a real problem (related to the problem of "trusting
the computer too much").  Moreover, in some cases, in order to
prove the translation faulty, we have to dig into the axioms and
rules and involve them in the philosophical debate anyway.

     However, in many cases, the translation will be non-
controversial.  The formal or otherwise agreed-upon logic serves
a useful purpose as a common language with which one can reason,
*if* the translation of the argument into logic is agreed to be
valid.  Most debates are then reduced to debates about the
translation.

3.)  Any translation of a real-world problem into logic is
inevitably going to omit some details. This is because
everything in the real world is connected to everything else,
and until we solve the AI problem, we won't be able to represent
all that formally.  Even encoding family-tree information in
logic (the mother of X is the female parent of X, etc.) is
likely to omit details concerning adoptions, illegitimate
children, homosexual marriages, sex-change operations, and so on.

     However, in the real world we often omit details for the
sake of simplicity, and the logic is not intended -- or should
not be intended -- to capture everything.  Many of the arguments
against "logic-based AI" are just arguments against clumsy
translations which omit important details.

     All of which is just putting in a different way what
Charles Martin said in an earlier article:

In article <MARTINC.92Nov22152326@hatteras.cs.unc.edu> martinc@hatteras.cs.unc.edu (Charles R. Martin) writes:
>More pragmatically, there appear to be only two forms of reaching
>agreement available: either we appeal to an idea of "valid argument"
>under which, by a dialectic or discursive process, we arrive at a
>conclusion acceptable to all parties; or we deny that such a process can
>exist, in which case we are reduced to the more direct method of hitting
>one another over the head with large rocks until one side or the other
>gives in.

     Good point!

--Jamie.
  jamie@cs.sfu.ca
"The Tao's net encompasses the whole universe."  - tao te ching
Newsgroups: sci.logic,sci.math