Philosophical claptrap in semantics
Formal semanticists are universally agreed that standard modern logic as devised by scholars like Frege, Peirce and Russell, is the one and only possible basis of natural language semantics. They take it as an objective and unassailable fact that the universal quantifier all, as in All flags are green, yields truth when the class quantified over (the class of flags) is empty, or that the disjunctive propositional operator or, as in ‘p or q’, yields truth when both p and q are true. The fact that these interpretations are not backed up by natural intuitions is explained away with the help of a pragmatic principle, proposed first by Grice, then by Horn and Levinson, which says that the hearer expects the speaker to commit him/herself to neither more nor less than what (s)he can vouch for. So if I say Some flags are green, the hearer will take it that I cannot vouch for the stronger statement that all flags are green, so my utterance will be interpreted as ‘some but not all flags are green’. Likewise, if I say John or Harry was late, my interlocutor will take this to signal that I cannot vouch for the stronger ‘John and Harry were late’, so I will be understood as having meant ‘either John or Harry was late, but not both’.
Apart from the fact that there is an essential difference between what a speaker can vouch for on the one hand and either (objective) truth or (somewhat less objective) truthfulness on the other, there is the fact that this pragmatic principle fails to account for other, similar clashes between official logic and natural intuitions. Thus, one will agree that a sentence like She doesn’t like planes or trains is immediately felt to be equivalent with ‘she doesn’t like planes and she doesn’t like trains’, but the converse is not true: She doesn’t like planes and trains is clearly not immediately felt to be equivalent with ‘she doesn’t like planes or she doesn’t like trains’. Yet both are instances of the well-known De Morgan’s Laws, which say that ‘not-p and not-q’ is equivalent with ‘not(p or q)’, and ‘not-p or not-q’ is equivalent with ‘not(p and q)’. Here, pragmatics has nothing to contribute.
The strange thing about this all is that while intuitions of wellformedness are generally considered to be a valid empirical basis for a theory of syntax, intuitions of meaning are not generally considered to be a valid empirical basis for a theory of meaning. And why should this be so? The question is never asked and the answer is never given explicitly, but, when challenged, I think formal semanticists will say that the only solid foundation for the semantics of logical words such as all, some, and, or, not, lies in standard modern logic, and to hell with intuitions, which are to be accounted for by soft theories about linguistic interaction, where human beings are taken to be logically incompetent.
But this is mere philosophical claptrap. Semantics, like all science, is an empirical enterprise and thus needs data and a theory explaining them. And the data show that standard modern logic does not provide a suitable basis for a theory of natural language meaning, neither in general nor, in particular, for the logical words occurring in language. So why not take the bull by the horns and see if we cannot devise a sound logical system that does indeed do justice to the relevant intuitions and assume that system to be somehow present in the human mind as an emergent property of the meanings of the logical words concerned? This obvious question is, however, never broached and the reason for this oversight lies in an irrational awe for the unassailable standard modern logic that holds everyone, including professional logicians, in thrall. What I am saying sounds like blasphemy in church, but so what? It remains a sensible question.
There is an interesting parallel with phonology. At first, it was thought that the physical, phonetic qualities of speech sounds were sufficient to define the sound units in terms of which speech is interpreted, that is, the phonemes. Then it was found that physical qualities are not enough to define phonemes and that phonemes, as systematic units in language and speech, are mental or cognitive units in a mental phonological system and that phoneme recognition is a matter of projection of these mental units onto actual speech sounds, whereby the physical, phonetic properties of the speech sounds are nothing more than clues for a holistic interpretation process. Unravelling that system is what phonology amounts to. Difficult but interesting.
In like manner, we find that standard modern logic, though objectively applicable, in the form of an adequate formal logical language, to all physical structures and processes, is not co-extensive with the way the human mind deals with psychologically real logical relations like contradiction, contrariety or entailment. This applies in particular to the logical operator of negation in language and cognition, which is a whole lot more complex, and more functional, than negation in standard modern logic. And this is not a matter of pragmatic principles, but of the species-specific way human cognition deals with logical relations.
The analogy with phonology lies in the active role that must be assigned to the human mind in dealing with the outside world. This role is now gradually being brought to the fore. In fact, one may say that, over the past one hundred years or so, the human sciences are broadly characterizable as an implicit but sustained effort to detect the active powers of the human mind, working from within, in the ways it deals with the outside world. There is now overwhelming evidence that the mind at birth is not a tabula rasa but a sophisticated special-purpose machine enabling the growing up individual to deal with the world in a highly functional way. It is useful to give an explicit formulation to this dominant trend in the human sciences. In linguistics, it manifested itself first in phonology, then, though in a biased and somehow perverse way, in the formal study of syntax, and now we see it cropping up in semantics. At least, that is what I have tried to make happen in my work on the natural logic of language and cognition over the past fifteen years.