Meaning postulates

Meaning postulates were developed by the philosopher Rudolf Carnap (1891–1970) as a way of integrating into logical systems the entailment information that comes from word meanings. A short account of this should help you appreciate some of the wider significance of semantic description. First, we need to distinguish between inferences that depend solely on structure and inferences that depend also upon the meanings of particular words.

The inference at the end of (2.13) – after the word Therefore – depends entirely on the structure of that three-line discourse. The reasoning is valid simply because it fits a particular pattern that always yields true conclusions if the premises (initial statements) are true. The pattern is set out in (2.14).

When both of the premises – in the first two lines – are true, then the conclusion must be true. To emphasize that it is the structure of the discourse that ensures validity here, rather than the individual words or the particular ideas being spoken about, (2.15) is another instance of the same pattern.

By contrast with (2.14) and (2.15), (2.16) is an inference that depends crucially upon the meanings of particular words.

Leaving out the material in brackets gives an argument which is accepted as valid by people who know English: The A380 is bigger than a B747, therefore a B747 is smaller than the A380 (even if they do not realize that the reference here is to two kinds of aircraft). However, it is an argument that does not follow from the structure of the discourse. The discourse has the structure ‘p therefore q’ and that is certainly not a generally valid line of reasoning. If the formula ‘p therefore q’ was generally valid, then it should yield satisfactory arguments no matter what we substitute for p and q, but in fact this pattern can yield nonsense, as suggested by (2.17).

A meaning postulate is needed between p and ‘therefore q’ before the reasoning in (2.16) can be seen to be valid. The particular meaning postulate required for (2.16) has to represent a linguistic fact about English: that ‘when any thing, x, is bigger than some other thing, y, then y is necessarily smaller than x; and vice versa’. This is, in effect, the information summarized in the sense relation of converseness. In formal systems of logic there are ways of representing this and the other sense relations that have been discussed above. See Cann (1993: 218–24) for an account that explicitly accommodates sense relations (but without some study of symbolic logic, you are likely to find the details hard to grasp).