Ryszard Zuber Towards a Semantic Description of Logical Connectives Series A: General & Theoretical Papers ISSN 1435-6473 Essen: LAUD 1976 (2nd ed. with divergent page numbering 2013) Paper No. 41 Universität Duisburg-Essen Ryszard Zuber Towards a Semantic Description of Logical Connectives Copyright by the author Reproduced by LAUD 1976 (2nd ed. with divergent page numbering 2013) Linguistic Agency Series A University of Duisburg-Essen General and Theoretical FB Geisteswissenschaften Paper No. 41 Universitätsstr. 12 D- 45117 Essen Order LAUD-papers online: http://www.linse.uni-due.de/laud.html Or contact: [email protected] ii Ryszard Zuber Towards a Semantic Description of Logical Connectives In spite of the importance that the notion of presupposition plays in the discussions on the logic and semantics of natural languages, little has been said about the presuppositional properties of the logical connectives of natural language. Prior to Karttunen 1973 no interesting results concerning presuppositions of complex non-embedded sentences were reported. Karttunen's work on logical connectives and presuppositons can by no means be considered as definitve in this domain and it is very likely not to be viewed as such by Karttunen himself (see for instance his more recent work on presuppositions and context). In this paper I would like to concentrate on the socalled phenomenon of cancellation of presuppositions, the phenomenon which is the basis of the filtering conditions Karttunen proposed for logical connectives. This phenomenon was already discussed before Karttunen (Lakoff 1970, Horn 1972) but Karttunen's paper is the first to give a clear statement of the problem to which the data give rise and to make an attempt towards solving it, the problem namely, of exactly what it takes to cancel a presupposition. To solve this problem he proposes a special filtering device. I will try to show, however, (1) that this filtering device has some strange consequences and that, strictly speaking, the phenomenon of filtration as conceived by Karttunen does not exist, and (2) that Karttunen's filtering device should be replaced by the principle of neutralisation explained below ((19) - (21) and following comment). In this connection some remarks concerning the symmetry (or asymmetry) of logical connectives (predicates) will be made. The discussion of these two problems will lead to certain modifications in the description of presuppositional properties of complex sentences. It will follow from this modified description that some aspects of the meaning of logical connectives which have been considered as pragmatic in nature should be analysed as semantic. I will use the following semantic notion of presupposition: Sentence S presupposes sentence T if S semantically implies T and ¬S semantically implies T (Where ‚¬S’ is the strong (internal) negation of S, and "S semantically implies T" means that T is true whenever S is true.) When S semantically implies T, we will also say that S entails T or that T is a (semantic) consequence of S. 1 It is clear that when S presupposes T then S semantically implies T. Some other consequences of the semantic definition of presupposition, as those examplified in Keenan 1973 for instance, will be assumed. Let me begin by discussing some problems from Karttunen 1973. He proposes a general treatment of complex sentenses that allows for widespread lose of preeuppositions in certain specified circumstances. This lose of presuppositions is done by a special filtering mechanism designed to deal only with the logical connectives of natural languages and, or, and if ... then. Filters, following Karttunen, are predicates which, under certain conditions cancel (filter out) some of the presuppositions of a component sentence. For instance in (1) where filtering conditions are satisfied, the known presupposition of the consequent clause is cancelled: (1) If the king of France exists he is bald. It is precisely the cancellation of (some) presuppositions which is a very strange phenomenon. For it takes place only under some conditions which depend on the semantic relations between the component sentences. This means that we cannot tell from the general logical description of a connective whether it is a filter or not; logical connectives are filters only sometimes, when some semantic conditions between arguments of these connectives are satisfied. Consequently the semantic content of logical connectives of English depends on the semantic content of the arguments of these connectives. Furthermore, following the filtering conditions Karttunen gave, some presuppositions of a component sentence may become presuppositions of the whole sentence, but logical consequences of these presuppositions may be cancelled. For it is possible that a presupposition of the consequent of the conditional, for instance, is not entailed by the antecedent, but that some logical consequence of thie presupposition is entailed by the antecedent and as such is filtered out. In other words a consequence of a necessary condition (for having truth-valuee) may not itself be such a necessary condition. For instance, following Karttunen's filtering conditions and usual description of the verbs regret and state, one should consider that (2) presupposes (3) and (4) but does not presuppose (5) and (6) (filtered out because they are consequences of the antecedent): (2) If Sue comes, then Steve will regret that she did not hesitate to come, (3) Steve will know that Sue did not hesitate to come. (4) Sue will not have hesitated to come. (5) Sue will have come. (6) Somebody will have come. This consequence of filtering conditions is not only incompatible with the semantic notion of presupposition but even with our intuition concerning the notion of semantic content in general. For it means that some semantic content can disappear as a whole while logical 2 consequences of it, and thus proper parts of it in come sense, may not appear. This fact makes the notion of cancellation still more obscure. Thus my first step will be to present in another light the phenomenon of cancellation. To do this I will apply the idea put torward in Zuber 197: that some presuppositions of one component may combine with the non-presuppositional part of another component of the sentence to give a "new" presupposition of the whole complex sentence. And it may, happen that by such a combination the new presupposition thus obtained expresses a trivial truth (is an analytic sentence). Let me illustrate this point. Usually it is assumed that sentence (7) presupposes (8), (9) and (10): (7) Steve is a bachelor. (8) Steve is a human being. (9) Steve is an adult. (10) Steve is a male. Now, let us substitute the subject NP Steve by another NP which is not a proper noun and which has some semantic feature common with the noun bachelor. We have then (11) for instance, which should presuppose (12), (13) and (14): (11) This king is a bachelor. (12) This king is a human being. (13) This king is male. (14) This king is an adult. Clearly we do not want to eay that the two preeuppositione (presupposed features), those corresponding to human and male, are lost or cancelled; only that they are combined with the features of the noun king to form tautologies with trivial semantic information as in (12) and(13). Similarly with (15): we cannot say that all presuppositions obtained through the supposed features of the NP bachelor were filtered out. Sentence (15) still presupposes (16), (17) and (18), but these presuppositions are not felt because they express analytic truths: (15) This man is a bachelor. (16) This man is a human being. (17) This man is male. (18) This man is an adult. Now having in mind the analogy between the subject of a simple subject-predicate sentence and the antecedent of a conditional on the one hand, and between the predicate and the consequent clause of the conditional on the other hand, we can posit the following: presuppositional analysis of the conditional sentence: the sentence of the form (19) presupposes (20) and (21): (19) If S, then T 3 (20) Pres (S) (21) S implies Pres (T) (where Pres (S) is a conjunction of all presuppositions of S and implies has the meaning of the 'horseshoe' taking into the account the third value. 'A implies B' is non-true only in case when A is true and B nontrue. 'Non-true' means either false or 'neither true nor false'). This description holds independently of what the semantic relations between the component sentences S and T may be. Thus supposing that presuppositions express truth-preconditions for the truth and falsity of a given sentence, the clause (21) says that for a conditional (of the form (19)) to be considered as (or even to be) true or false, it is necessary that the antecedent of the conditional entails the presupposition of the antecedent clause. For instance (22) (22) If it rains only Steve will come. presupposes that in every possible world in which it is true that it rains, it is also true that Steve will come. Let us now look at the case in which, due to the particular semantic relation taking place between the antecedent and consequent clauses of the conditional, there is a supposed filtering out (or cancellation) of some presuppositions of the consequent. Suppose first that T presupposes S (this is a particular case ot Karttunen is filtering conditions for conditionals). Then following the above description, (19) presupposes (23): (23) S implies S Clearly (23) is a tautology. A more general case of the semantic relation between S and T in which a presupposition of T is supposed to be filtered out is the following: sentence which is a presupposition of T is filtered out, according to Karttunen, if and only if it is entailed by the antecedent S.