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Abstract
Formal semantics and Natural Semantic Metalanguage are widely held to be radically incompatible as ways to study meaning in naural language. Here I will show that they can to some extent be reconciled. In particular, for linguists working with NSM, formal semantics can be viewed as providing mathematical accounts of some of the same phenomena that NSM studies, such as entailment, and for the formal semanticist, NSM offers a small target in the form of mini-languages that exhibit the essential logico-semantic features of full natural languages, such as extensionality, intensionality and hyperintensionality, and algebraic principles such as transitivity, symmetry etc. or various of the primes. Therefore, although these two approaches are likely to remain distinct enterprises for the foreseeable future, some intercommunication is possible and indeed desirable.
Notes
* I would like to acknowledge many extremely useful comments from three anonymous (Australian Journal of Linguistics) reviewers, in addition to comments on earlier versions from Maïa Ponsonnet, Zhengdao Ye and Andras Kornai, and also especially Barbara Partee for many discussions over the years, and comments on what might be regarded as preliminaries to this paper. But they are not responsible for my errors.
1 Katz himself had little to say about entailment as such, focusing on ‘analyticity’, without saying anything that people appear to have managed to understand as to how this was supposed to be different from entailment.
2 Explicit acknowledgements seem to be rare, absent for example from Chierchia and McConnell-Ginet (Citation2000: ch. 1), although many of the same MBPRs are discussed in a similar way.
3 As presented for example in http://nlp.stanford.edu/projects/natlog.shtml (accessed 6 June 2015).
4 There is a subject of ‘paraconsistent logic’ where one does this on purpose, but that is not a topic for beginners (the goal is to construct logics which can tolerate contradictions, for use in situations such as database management where they will inevitably arise in the data, and one doesn't want the entire system to become useless as a result).
5 Link (Citation1998) contains many examples; Landman (Citation1991) provides a textbook-style presentation.
6 This is my interpretation of a p.c. from Barbara Partee of a remark made to her by Johann van Benthem.
7 At an average growth rate of one every year or so, there would appear to at least a century's worth of headroom before the size of the inventory gets uncomfortably close to 200, which seems to me to be a plausible approximate maximum size for the inventory. And of course this is a proposed worst case; the prime set will not necessarily continue to grow at this rate.
8 The programming language Prolog provides an example of predicates that can be defined but not eliminated from the places where they are used.
9 ‘Because of this, after this’ is a recurrent formula in NSM explications of verbs describing actions.
10 As pointed out by an anonymous reviewer.
11 NSM publications in particular make considerably use of cooccurrence data from texts, but based on my observations of seminars and workshops, these appear to play more of a supporting role than to be the primary techniques of discovery. That this is in fact the case is indicated by the fact that neither of the words ‘corpus’ or ‘cooccurrence’ appears in the indices of Wierzbicka (Citation2006) or Goddard (Citation2011), although observations of natural use abound. Formal semantics can of course use corpus data in the same way that NSM does, as an additional check on hypotheses, to compensate for some of the problems with intuitions about possible use rather than observations about actual use.
12 NSM researchers tend to believe that they have no meaning in any sense whatsoever, but that is not an issue I want to contest here.
13 And therefore that intuitionistic logic, useful as it is, does not provide an accurate representation of ordinary language meaning.
14 With respect to which I note that it would be very interesting to see how many of the complex and problematic scenarios discussed by Bennett work out in the same way for the standardly recognized conditional constructions of other languages, especially non-European ones without significant cultural heritage from Ancient Greece.
15 There is a terminological subtlety here: the term ‘set’ in mathematics implies commitment to some propositions such as that two sets are identical if they have the same members, and there is a set with no members (and therefore only one such), and also that sets can be members of other sets. In typical situations of use, these commitments don't create problems. But it is not clear that we really need them for natural language semantics, and we perhaps could avoid them by talking of ‘collections’ instead, as often happens in introductions to category theory. How to explain this and other aspects of mathematical discourse in NSM is an interesting topic, but not one that I will attempt to pursue here.
16 There is terminological variation here; I am following Pollard (Citation2008).
17 See Wierzbicka (Citation2006: 277) for a proposed explication, which does not however seem to me to capture the ‘plausibility’ constraint that I suggested at the beginning of the section. This explication appears in an extended discussion of many related works, such as likely, presumably, etc.
18 Note the subtlety that least as tall as is not antisymmetric; two people can be at least as tall as each other but still be different people. Their heights however will be the same.
19 Amongst the issues here is the nature of the difference between part of X (e.g. a car) and a part of X.
20 The issue of the Reflexivity of like arises with sentences such as ‘John isn't like John, he IS John’; there is an intuition that this is odd, but that can be plausibly explained by the Gricean Maxim of Quantity (based on a p.c. from Andy Egan).