🚀 go-pugleaf

In article <1992Aug28.150002.14160@klaava.Helsinki.FI>, amnell@klaava.Helsinki.FI (Marko Amnell) writes:

|> But I didn't mean _theory_.  The point I was making was just that
|> Analytical philosophers all employ formal logic, and first order
|> predicate logic is used in many contexts by the vast majority.  Set
|> theory can be expressed in this logic as well.  So I still say it's
|> a question of objectivity too.  The philosophers accept a common idiom
|> and agree to respect its grammar, conventions, etc.  This allows them
|> to work together better and not fight over interpretation as much
|> as other schools.

So I guess your claim is that the use of a certain *notation* lends
some kind of objectivity to the writings of the philosophers who share
that notation.  Okay, but this certainly is a very weak sense of
'objectivity'.  I would argue further that the use of the notation of
set theory and first-order logic contributes nothing to this objectivity
beyond what is present in the careful use of natural language.

Keep in mind that the notation must be *explained* -- that its sense
or semantics must be accounted for.  Thus you cannot really say in a
reasonable way "I don't mean _theory_".  *My* point (a bit implicit,
perhaps), was that the membership sign has a different *meaning* in the
different set theories (as is evident by their differing sets of
theorems).  Now you might say, "Well, we don't need to think of an
axiomatic set theory here.  We just use the notation in the sense of
naive set theory."  But then, if the notation can be said to have any
sense at all (an intuitive sense, perhaps) you are confronted with the
various well known paradoxes -- and if you want inconsistency and
confusion there are a lot simpler ways to achieve these than using
set theoretic notation.

I find your view that the philosophers who use this notation "work
together better and do not fight over interpreattions as much as
other schools" to be without any foundation or evidence.  It smells
at least slightly of some ideology of formalism.  In fact, on reflection,
it smells a lot like _The_Logical_Syntax_of_Language_ before Carnap
figured out what semantics really was and what formal theory construction
might do for you.

When you say that "Analytical philosophers all employ formal logic,"
I think you might get some argument on this (Peter Cash?  You still
there?).  Also, the sense of "employ" is far from clear.  I know
how *I* used it -- to build formal systems (complete with proof theory
and semantics) that were used to model, represent, or exhibit certain
concepts or collections of concepts (while keeping in mind the limits
of the technique and the degree of approximation one might achieve).
In fact, I believe I have a rather well thought out view of the proper
use of formal approaches in philosophy and even published on that
topic.  Not everyone employs "logic" in this way.  Notice that if
you *do* use this approach, the formal system becomes an *object*
of study (as does its purported relation to the concepts of interest)
and is not the basis of some *shared* understanding.

Perhaps you mean to point out that "analytical" philosophers have a
tendency to sprinkle their publications with formulae.  To some
degree this is true, but often the sprinkling is purely gratuitous.
In fact, I usually tried to avoid such sprinkling since it breaks
up the flow of the text and is harder to set.  When the extra precision
was required, well that's another matter.  Even then, you *can* be
precise in natural language.  The formalism typically takes up less
space -- provided its meaning is clear.



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SAS Institute Inc. / SAS Campus Dr. / Cary, NC  27513 / (919) 677-8000
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