[FOM] A Query about Logical Content
Ken Gemes
K.Gemes at bbk.ac.uk
Tue Sep 25 04:42:39 EDT 2007
It is natural to say that a wff is partially true iff part of its
content is true.
As Alex points out (see below) if we count tautologies as part of the
content of every wff this yields the result that every wff is partially
true.
I take this to show that we should not count tautologies as part of the
content of every statement. Indeed on my account they are not part of
the content of any statement they have no relevant models. I take
tautologies to be without content.
The point behind my particular examples - which I did not make clear in
the overly succinct original posting - was to show that even if we
restrict the content of a wff to its non-tautologous consequences, as
Carnap proposed in The Logic Syntax of Language, we still get the
unpalatable consequence that every statement is partially true.
Thus were the atomic wff Fa is false and Fb is an atomic statement then
either Fa's non-tautologous consequence FavFb is true or its
non-tautologous consequence Fav~Fb is true and so Fa, and indeed all
other statements, will count as partially true given that we count a
statement as partially true if part of its content is true and we take a
statement's content to be the class of its non-tautologous consequences.
Ken Gemes
Reader in Philosophy
School of Philosophy
Birkbeck College
University of London
Malet Street
London, WC1E 7HX
Reader in Philosophy
Philosophy
School of Humanities
University of Southampton
Southampton, S017 1BJ
web page: http://www.bbk.ac.uk/phil/staff/academics/gemes/
-----Original Message-----
From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf
Of Alex Blum
Sent: 21 September 2007 11:42
To: Foundations of Mathematics
Subject: Re: [FOM] A Query about Logical Content
Ken Gemes wrote:
>...
> Note, if AvB counts as part of the logical content of A then on the
evidence of B one would have to say that part of A is true, and hence A
is partially true. There are many other reasons for not counting AvB as
part of the logical content of A.
>
>The basic idea was to say X is part of the logical content of Y iff Y
logically entails X and every relevant model of X can be extended to a
relevant model of Y.
>
>
Why would we want to say that if p implies q then having q confirmed it
follows that p is partially true. For every proposition implies a
necessary truth. We should thus be tempted to say that every proposition
is partially true,e.g.,both 'p' and '~p' .
Alex Blum
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