Re: Logical formalisms

[David Byron <david.byron@aya.yale.edu>]

At 04:40 AM 7/29/99 , James Anderson wrote:
 >On 28 Jul 99, at 22:13, David Byron wrote:
 >
 >> In classical logic, presuppositions are trivial and wimpy.
 >
 >I'm sure I ought to know this by now, but -- why is this so?

Consider the following:

	A presupposes B if and only if
		[a] B is true whenever A is true
	and
		[b] B is true whenever A is false

According to this definition, B must be true for A to have any
truthvalue at all.  An instance of this relationship might go
this way: The proposition A{"Euclid stopped beating his wife a
month ago"} cannot be valuated as true unless Euclid had a wife
and had been beating her.  But it also cannot be valuated as
false unless Euclid had a wife and had been beating her (and
had not yet stopped!).  So, the possibility of truthvaluating
A{"Euclid stopped beating his wife a month ago"} depends on the
truth of the proposition B:"Euclid had a wife and had been
beating her".  If B is false, then A is neither true nor false;
the question of its truthvalue doesn't arise.  All of this seems
to agree with our intuitions and our usage in natural language;
for which reason we tend to reply to loaded questions such as
"Has Euclid stopped beating his wife yet?" not with a simple
"yes" or "no" but with a *corrective* "Euclid has no wife," or
"Euclid has never beat his wife".

Now, the problem with this definition of logical presupposition
is that if A "presupposes" B in the manner described, and if (by
the principle of bivalence) A is either true or false in *every*
possible world, then it follows that B is "true in every possible
world".  This means by definition that B is a logical truth.  But
in a bivalent system, when *any* other proposition is either true
or false, then a truth of logic is true.  Consequently, in a
bivalent system, the relationship of "presupposition" described
above holds between any proposition and any logically true
proposition, but never otherwise.

Cheers,

David Byron
david.byron@aya.yale.edu


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