🚀 go-pugleaf

In article <1992Nov21.115346.17656@husc3.harvard.edu> zeleny@husc10.harvard.edu (Michael Zeleny) writes:
>
>Just because the correctness of your definition of synonymy is not
>amenable to confirmation by (narrowly construed) empirical means, does
>not imply that there is no matter of fact about it.  In particular, one
>failing of the possible-worlds approach consists in its identification
>of proof-theoretically equivalent propositions.  This is unproblematic
>in situations which call for the study of such deductively closed
>domains as doxastic commitment; however even in such cases, full
>generality will be sacrificed to the implicit assumption that the
>underlying Boolean algebra of propositions must be atomic.

I may be an outsider to this discussion, but it's quite clear to me that
a whole lot of smileys have been omitted here.  As near as I can
determine, this paragraph is some sort of self-parody.  I like the way it
sucks me in, starting with statements which almost seem to have some
meaning -- at first, the absurdity of confirming the correctness of a
definition by empirical means doesn't really hit one -- and it almost seems
that I vaguely perceive what it is you're saying.  

And the you build up to the grand finale statement that 
>full generality

[of what? in what sense? Of course the joke is on the poor reader who
believes that there actually is some referrent for the word "generality"
but that he is to dense to find it.] 

>     will be sacrificed to the implicit assumption 

[Another put on:  You see, reader, the reason you didn't see this
assumption  [assumed by whom?]  is that it's implicit, and you just weren't
smart enough to notice it!] 

>that the underlying Boolean algebra of propositions must be atomic.  

[Aha!  You see, dear reader, this is very deep stuff, having to do with
highly abstuse concepts such as Boolean algebras, and that's why you
can't understand it.]  

In fact, I can't imagine any context except highly contrived ones in
which the boolean algebra of propositions would ever be atomic.  


I can only guess that the point you want to make is that attempts to
develop a theory of meaning by invoking model theory and the model-theoretic
concepts of syntactic truth and semantic truth ... are only useful as venues
to display one's erudition and engage in one-upmanship.  

(Incidentally, in model theory a sentence is said to be syntactically true 
if it can be proved from the axioms.  A sentence is semantically true if
it is true in every model, i.e. in every "interpretation."  This
definition was paraphrased in this discussion by saying that the
statement is true "in all possible worlds."  A mathematical theory is
called "complete" is every semantically true statement is syntactically
true, i.e. "every true statement is provable.")  

(Sorry if I'm spoiling everyone's fun by explaining what the words
actually mean.)

You did remind me of an interesting question is mathematical thinking,
though.  It is commonplace for mathematicians to say that two particular
theorems are equivalent to each other.  This is definitely a statement
about syntactic equivalence, i.e. that either of the two can be proved by
using the other.  On the other hand, by basic logic any two
syntactically true theorems are in fact syntactically equivalent.  So is
it possible to assign any somewhat precise meaning to the statement that
two theorems are equivalent, or is this just an impossible vague
assertion, comparable to the assertion that certain things are
"interesting"?   (What this has to do with cognitive science is more than
I can figure out.)  

--
It is a poor sort of skepticism which merely delights in challenging
those claims which conflict with one's own belief system.  
                                                          --Bogus quote 
lady@uhunix.uhcc.hawaii.edu         lady@uhunix.bitnet