Is The English Connective ‘or’ Best Modelled By Inclusive Or Exclusive Disjunction? Essay, Research Paper

We know from our everyday experiences that natural language is plagued by ambiguities and a lack of clarity. Often these can be a source of humour – c.f. the age old gag, ‘My dog used to chase an old man on a bicycle. How did you stop him? I took his bike away.’ and many would argue that our languages are enriched by the presence of such idiosyncrasies. However, to linguists attempting to implement a model of language and lay down concrete laws, such anomalies present sizeable problems. Consider attempting to model the English language connectives ‘and’ and ‘or’ with their logical operator counterparts and we see just such a situation arising. As we shall see in this essay with the examination of one such connective, the English disjunction ‘or’, it is perhaps sometimes the case that a rigorous definition in logic is not as simple as might first be thought and that we must look beyond such pragmatic definitions and into the world of semantics, c.f. Cohen’s (1971) argument that the English connectives and their logical counterparts are irreconcilably different and a pragmatics approach similar to that of Grice (1967) cannot cope with these differences and thus require some semantic information. A strict interpretation of the word ‘or’ into its logical operative form would imply that, reminding ourselves that the truth-table for OR is as follows: A B A or B 0 0 0 0 1 1 1 0 1 1 1 1 ‘A or B’ should be read as meaning that either or both of the clauses being true leads to the disjunction being true. This is known as inclusive disjunction. In natural language we could easily imagine a situation in which this type of disjunction would be the implied meaning for the word ‘or’. For example, consider the following sentence: ‘In a course requiring an overall mark of 50% to pass and consisting of 50% coursework and 50% examination, it is possible for a student to pass by gaining 100% for the coursework or by obtaining 100% in the exam.’ Clearly we do not suppose that a student who scores 100% in both sections will fail, and therefore the implication here is for inclusive disjunction. However, we could just as easily set up a situation in English in which we use the word ‘or’ to mean either of the two clauses, but not both. Consider, for example, a traveller coming to a fork in a road. He now has to decide whether he will take the left path or the right path, a situation in which it is quite clearly impossible for him to take both paths simultaneously. Here then, the implication is for exclusive disjunction, in which either of the clauses being true makes the disjunction true, but not both. The truth table for this type of disjunction is as follows: A B A xor B 0 0 0 0 1 1 1 0 1 1 1 0 It can be seen from the examples given above then, that the word ‘or’ when used in English can assume various meanings dependent on the context in which it is used. But is it possible to ascribe one of the above disjunctions to ‘or’ more than the other, or indeed to rule out one altogether by arguing that the metalinguistic and pragmatic interpretations are not equivalent, i.e. that it is possible to produce an unambiguous linguistic construct for any English sentence using just one of the disjunctions? Gazdar (1977) has claimed that ‘or’ is unambiguous in English. He refute’s Hurford’s (1974) claim that English has two ‘or’s (which he argues for on the strength of sentences such as those which were given earlier) by arguing that these apparent different disjunctives are in fact a result of the logical properties of permission giving sentences, i.e. if it is the case that both clauses together are not allowed, this does not mean that we have an exclusive disjunction. Using the sentence ‘John isn’t either patriotic or quixotic’, he argues that the ‘ambiguity thesis’ (the idea that ‘or’ is both inclusive and exclusive) predicts a reading of the above sentence which he fails to find acceptable, namely that John is both patriotic and quixotic. He forms this from the logical operators thus: ~(P v Q) = (P . Q) (not exlusive or) = (and) Investigation of the truth tables for these two functions does indeed suggest that one such reading is: ‘John is both patriotic and quixotic’, and also the opposite reading ‘John is neither patriotic nor quixotic’. Gazdar says he is unable to find the former interpretation of this sentence and hence ‘or’ is unambiguously inclusive, apparent instances of exclusive disjunction being incidental of the fact that (P v Q) entails (P v Q). Burton-Roberts (1984) argues against Gazdar in this issue, suggesting that the exclusive reading can be found by interpreting the sentence as ‘John isn’t either … he’s both’. This translation suggests that emphasising the negation of ‘either’ is the key to finding the exclusive interpretation. However, Horn (1985) argues for Gazdar’s interpretation of the inclusive nature of ‘or’ in this sentence. Whilst disagreeing with Gazdar that the exclusive version can be found, he posits that in this case ‘or’ is inclusive, and that the ambiguity comes not from the ‘or’ but from the ‘not’. He refers to the addition of ‘he’s both’ to the sentence to give the exclusive meaning, by stressing that the ‘not’ in this case refers to the ‘either’, thus arguing that ‘either’ specifies one or the other, and thus it’s negation by ‘not’ in this reading allows the interpretation of ‘not either’ and hence ‘both’ that Gazdar rejects. However, as Browne (1986) points out, Horn provides support for Gazdar in a way in which Gazdar almost certainly would not approve of, since the crux of Horn’s argument relies upon the ambiguity of the negation operator ‘not’, and this is something against which Gazdar has vehemently fought. The argument seen above is not the only case that has been put forward for the unambiguity of ‘or’, and unlike the case above, the next example that we shall examine does not require the ambiguity of the negation operator ‘not’. Browne (1986) puts forward the sentence ‘John is either patriotic or quixotic or both’ and suggests that if ‘or’ is ambiguous then there are four interpretations of this sentence, since each of the two ‘or’s could be thought of as inclusive or exclusive. By investigation of the logical derivations of each interpretation he finds that one interpretation is equivalent to P v Q whilst the other three are equivalent to P v Q. Browne argues that if the ambiguity thesis is correct then the first derivation, i.e. (P v Q) v (P . Q) must have an interpretation equivalent to P v Q , since they are both derivations of the same ambiguous sentence. However, this first derivation is in fact a very explicit way of expressing inclusive disjunction, thus a contradiction occurs and the ambiguity thesis is proven false, ‘or’ in this case being univocal. However, having carried out this impressive analysis of the sentence and found this apparent contradiction to the ambiguity of ‘or’, Browne concedes that it doesn’t actually tell us which reading of ‘or’ is in fact the correct one, merely that in this instance the two are irreconcilable and ambiguity is not logically possible. To this end he then refers back to the original sentence which we examined here and points to an interpretation of ‘isn’t either ….or’ as inclusive, which is not entailed by the sentence ‘is both ….’. Thus, he argues, it is possible to have a reading of this sentence as inclusive ‘or’ that does not correspond to exclusive ‘or’, and consequently that if either disjunction is a correct model of the English language ‘or’ it is the inclusive one. Looking at the arguments presented here, it seems that we are still unable to unequivocally ascribe one of the logical connectives to the English language ‘or’. The fact that semantically we are able in English to construct sentences which have either meaning precludes such a rigid binding of ‘or’ to either inclusive or exclusive disjunction, though Gazdar would argue that in such cases it is the logical properties of permission giving sentences such as ‘may’ which account for the apparent exclusive interpretation. Gazdar seems to be the strongest opponent of exclusive disjunction in English, indeed he goes further to say; “there is no clear evidence that exclusive disjunction has ever been lexicalised in any language”.He dismisses as unconvincing Eid’s claims that Cairene has exclusive disjunction, and citing Karttunen’s counter-arguments to Collinson’s (1948) claim that Finnish has exclusive disjunction concludes by suggesting an important difference between ‘ambiguity’ and ‘univocality plus implicature’ to explain apparent cases of two ‘or’s in natural language. It does seem from the cases put forward by Browne et al that inclusive disjunction is a more accurate model for the metalinguistic ‘or’ than exclusive disjunction, since we have observed sentences in which the exclusive disjunction cannot be a valid interpretation, whilst no counter-examples of exclusivity without inclusivity, except when in connection with permission giving constraints have been produced. Whether such examples exist remains to be seen, though in the meantime the proponents of the inclusive model seem to have the initiative. However, whilst such arguments may imply that inclusive disjunction is a better model than exclusive disjunction, the fact of the matter is that neither definition can really be considered an accurate definition of the metalinguistic properties of the English word ‘or’, and it is thus the opinion of this author that we should not seek to preclude either interpretation in any pragmatic modelling of the English language. approx 1,500 words Bibliography Browne, A.C. (1986). Univocal OR – again Linguistic Inquiry, no.4. pp 751-754 Gazdar, G. (1979). Pragmatics Academic Press