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(METHODO)LOGICAL PRESUPPOSITIONS IN THE WORK OF LEIBNIZ 21
“Because the main thrust in enouncing a proposition is to divide the
relevant set of possible situations – the set of presuppositions – in
two categories or to distinguish those in which the proposition is true
from those in which the proposition is false, using for this purpose a
proposition that does not manage to realize it would obviously
constitute an entirely mistaken approach” (Stalnaker, p. 452).
Consequently, to increase the informational baggage by one statement
means, according to Stalnaker, to limit the number of “possible worlds” to
those in which this statement is true. It does not make sense – considers
Sandu (1997) as well – for one to enounce a proposition S that logically
presupposes P unless P is true. In the contrary case, the dialogue gets
interrupted and the intention for communication fails.
An immediate observation is that Stalnaker’s pragmatic approach
does not exclude the Fregean logical approach; on the contrary, it
assumes it to be true. Presuppositions’ criterion of identification (the
“negation test”, in U. Eco’s words) stops being necessary in a pragmatic
context. Its place is being taken by a pragmatic criterion of adequate
accord between the “new” information and the “old” one.
The problem of projection
One of the problems at the core of the theories on logical
presuppositions, a problem whose solution has been sought by various
scholars such as G. Gazdar, L. Karttunen, R. Van der Sandt, etc., is the
so-called “problem of projection”. The problem poses the question:
What is the relationship between the set of logical presuppositions of
a complex proposition and the set of logical presuppositions of the
elementary propositions that, linked together by various logical
connectors, comprise the complex proposition?
This is not a simple question. The cumulative conjecture proposed by
Langoeden and Savin (1971) offers a solution according to which the set
of logical presuppositions of a complex proposition coincides with the set
of logical presuppositions of each elementary proposition that comprises
the complex proposition. The conjecture assumes that, if logical negation
“conserves” presuppositions, so do all the other logical operators. There
are, and have been highlighted, situations in which the cumulative
conjecture does not work.