Page 389 - Encyclopedia of Philosophy of Language

truth of A gives radical falsity of BA and thus of A A BA). A sentence like:
Nob's dog has died and he is sad about it. (32) should thus presuppose that Nob's dog has died,
1
which is not what the operational criteria tell us. T oe fares better for this type of conjunction, since here, if vn(A) = 2, vn(BA) = 3, and therefore, vn(A A BA) = 2.
2
Both TGC' and roc
disjunctions (and hence conditionals). In both systems, the following theorem holds:
(~AvBjA(-B/lvCJ»A (33) Thus, a sentence like:
If Nob's dog has died Nob knows it, and if he (34) knows it he is sad about it.
is said to presuppose that Nob's dog has died. And a sentence like:
hand.' The notion of 'non-language' is defined in terms of'sequential discourse incrementation.'
The 'sequential incrementation' of a (monologue) discourse D is a process restricting D to specified valuation spaces. Intuitively,it locates the situation to be described in a progressively narrower section of U. Incrementation involves the assignment of the value T or '2' to sentences of the language L. The result of the sequential incrementation of A, or i(A), is a (fur- ther) restriction of the D under construction to the intersection of/D/ and /A/. D + A is thus equivalent to D A A: D can be considered the conjunction of all its sentences. The initial valuation space is U.
The 'sequentially criterion' requires that:
(a) if B » A then i(A) must precede i(B),
(b) i(A A B) consists of i(A) followed by i(B),
(c) foranyD,/D/=/D+A/,
(d) noi(A)mayresultintheemptyvaluationspace.
Condition (a) requires that if A has not already been incremented prior to i(BA) it is quietly 'slipped in.' This process is called 'accommodation' or 'post hoc suppletion.' A text requiring accommodation is not fully sequential. Condition (b) splits up a conjunction into separate subsequent incrementations of its con- juncts. Condition (c) is the 'informativeness condition.' It requires that every subsequent incrementation restricts the valuable space of D, thus specifying further the situation to be described. Con- dition (d) prevents logical inconsistency in any D. Again, the sequentiality criterion does not imply that a discourse or text not satisfying it is unacceptable in some sense. It only sets out the prototypical conditions of a possibly unexciting but well-ordered discourse.
If A is valued '2,' then BA is excluded from D since now both BA and ~BA are valued '3,' which is not allowed in D: neither B nor ~ B can be processed in D. Thus, at each stage Q in the development of D there is a set of sentences of L that are excluded from the further development of D, and also a set of sen-
If Nob's dog has died Nob knows it or he doesn't know it,
and if he knows it he is drunk,
and if he doesn't know it he is sober
(35)
make incorrect predictions for
presupposes that Nob's dog has died in TGC',whileit is 2
entailed in TGC . Both are thus seen to make incorrect predictions if and is made to translate A, and 'if A then B' stands for (~ A vB).
3. The Discourse Approach
The problems raised by a purely logical definition of presupposition are compounded by the fact that a logicaldefinition ofpresupposition,suchas(31),inevi- tably entails that any arbitrary sentence will pre- suppose any necessary truth, which would take away all empirical content from the notion of presup- position. Attempts have therefore been made (for example, Gazdar 1979; Heim 1982; Seuren 1985) at viewing a presupposition A of a sentence BA as restricting the interpretable use of B to contexts that admit of, or already contain, the information carried by A. If one sticks to trivalence, (31) may beweakened from a definition to a mere logical property:
tences that can still be processed. The former is the Q
IfB»AthenBt=Aand ~BNAand ~A(=^B and =sANc*B
(36)
tains no negation of any of the presuppositions of the Q
One advantage of this approach is that it leaves room for an account of the discourse-correcting 'echo' function of radical NOT. Horn (1985; 1989) says, no doubt correctly (though his generalization to other metalinguistic uses of negation is less certain), that
NOTis'metalinguistic,'inthatitsayssomethingabout 21 the sentence in its scope. Neither TGC nor TGC
accounts for this metalinguistic property. What NOT- ('BA') says about the sentence 'BA' is that it suffers from presupposition failure, and thus cannot be coherently used in a discourse where A has been denied truth. NOT is interpreted as the complex predi- cate 'belongs to the non-language for the discourse at
sentences of PL(D) .
For example, let D consist of the sentences a, ba,
and ~CA, in that order (ba has no presuppositions c
beyond a, and analogously for CA). Now */ceNL(D) , since c is valued '2.' The sentence NOT('rf') is now true, as it says precisely this. In this interpretation, NOT('rf') is incremented the way sentences normally are: /D/ will contain states of affairs involving sentences, which are objects like other objects. But the logical relation of NOT(W) with respect to ~</and d cannot be expre- ssed due to the metalevel shift. NOT(W) is now under- stood as 'the truth-commitments entered into so far
'nonlanguage' of D at Q, or NL(D) ; the latter is the Q
'presuppositional language' of D at Q, or PL(D) .
PL(D)
Q
is thus defined by the constraint that D con-
are satisfied and d suffers from presupposition failure; C
it therefore belongs to NL(D) .' Both i(d) and i(~d) 367
Presupposition