Parameters and values in language
You may never have thought about it, but sentences like Five days is too long are acrtually quite strange and quite intriguing. One would expect a plural verb after the plural subject, but Five days are too long is a very odd sentence. And Seventy people is excessive means something totally different from Seventy people are excessive. When I was seventeen or eighteen, a charming Italian movie appeared in the cinemas, called Domani è troppo tardi (‘Tomorrow is too late’). Having just learned good Italian, I baulked, since I had learned that the use of a future adverbial required a future verb form, so I expected sarà (‘will be’) instead of è (‘is’). But when I went to see the movie, I understood. It was about the sexual education of school-age adolescents and what the title said was that delaying it till tomorrow was delaying it till it would be too late. What is going on here?
Let me start on a different tack. There is a long tradition in philosophy of discussions around the notion of identity (you may remember my fourth blog posting on sameness). The American philosopher Willard Van Orman Quine (1908–2000) wrote a lot about identity and the ‘identification of indiscernibles’. Yet this whole tradition, Quine included, made a basic mistake: they mistook the assignment of a value to a parameter for identity, and they still do (see my Language in Cognition, OUP 2009, pp. 191–194). Thus, when I say My name is Pieter, they analyze that as ‘my name = Pieter’, using the same identity sign as in cases where one object has two different names, as in The Morning Star is the Evening Star, properly analyzed as ‘the Morning Star = the Evening Star’, or Mark Twain is Samuel Langhorn Clemens, properly analyzed as ‘Mark Twain = Samuel Langhorn Clemens’. Even in mathematics, value assignment is usually confused with identity. But not in computer science, I am told, where proper identity is often rendered by ‘==‘ and value assignment by ‘=‘ or ‘<—’. Thus, My name is Pieter would come out as ‘my name <— Pieter’. Further examples of value assignments are The temperature is 25 degrees, He is seventy years old, The captain of the ship is Walter Smith, My phone number is 715563. In the value-assignment cases mentioned above, the parameters are ‘my name’, ‘the temperature’, ‘his age’, ‘the captain of the ship’, and ‘my phone number’. The values assigned are, respectively, ‘Pieter’, ‘25 degrees’, ‘70 years’, ‘Walter Smith’, and ‘715563’.
Typically, value assignments allow for the verb change to occur: The temperature/His age/My phone number/His name/The colour of the box has changed. This is not possible for true identity statements: The Morning Star has changed is a good sentence, but it does not mean that it has changed identity, or has become a different value on a parameter.
What does all this have to do with sentences like Five days is too long? The answer is not too difficult. In interpreting Five days is too long, one needs a parameter for the value ‘five days’. This parameter is not explicitly mentioned in this sentence, but it could be. We could say, for example, Five days is too long for our planned conference on animal rights, where ‘the duration of our planned conference on animal rights’ is the parameter. Likewise, instead of saying simply The temperature is 25 degrees, I could, depending on the context, specify the parameter and say, for example, The outside temperature at ground level is 25 degrees. But it is also possible to leave the parameter implicit in sentences of this nature so that it has to be retrieved from the preceding discourse.
Something similar is going on in WH-questions and pseudo-clefts. When I ask What did John buy? and you answer A magnifying glass, then your answer provides a value on the parameter ‘what John bought’. Likewise in so-called pseudo-clefts, as in What John bought was a magnifying glass. My friend and colleague Dany Jaspers drew my attention to an excellent dissertation on pseudo-clefts written by Francis Roger Higgins back in the seventies and published as The Pseudo-Cleft Construction in English (Garland, New York, 1979). Higgins does not use the terms parameter and value (these terms were not yet en vogue at that time), but his semantic analysis is the same.
To my delight, he takes on W. V. O. Quine, mentioned above, regarding Quine’s analysis of modals as predicates introducing what are known as intensional contexts. The question of intensional contexts goes back to the German mathematician-cum-philosopher of language Gottlob Frege (1848–1925), who discovered that the classic Principle of Substitution Salva Veritate of Co-referential Terms (known as the SSV Principle) does not hold in intensional contexts. I must explain.
Gottfried Wilhelm Leibniz (1646–1716), who formulated the SSV Principle explicitly, saw that the old Aristotelian notion of truth as correspondence between what is said and what is the case in the world entails that in cases where two different terms, A and B, refer to the same entity E, it does not matter whether you, as a speaker, use A or B, as long as the term chosen refers to E, because what matters is what you say about E, regardless of what term you use to refer to E. Thus, whether you say The Morning Star is inhabited or The Evening Star is inhabited, when the one is true (or false), so will be the other, because you are speaking about one and the same entity, known under both names (we now prefer to speak of the planet Venus). This is not too complicated.
But, and this is what Frege discovered (well, it had already been discovered by the ancient Greek philosopher Eubulides, who used it to attack his enemy Aristotle, but this historical detail had been forgotten in Frege’s day and was rediscovered during the 20th century), SSV fails to apply in cases like John believes that the Morning Star is inhabited. Why? Because if it is true that John believes that the Morning Star is inhabited, it is not necessarily also true that he believes that the Evening Star is inhabited: John may, after all, also believe that the two names denote two distinct objects, that is, that the Morning Star is not identical with the Evening Star. This was a direct threat to Aristotle’s classic definition of truth and Frege wished to defend Aristotle and the whole tradition following him by means of an analysis that would save the classic theory of truth. This question has become one of the most central problems in the philosophy of language of the 20th century. Frege provided a solution involving mental representations, but later philosophers, especially Richard Montague (1930–1970), who suffered from neopositivist tendencies, did not like that and sought relief in ‘possible worlds’. It is generally admitted, however, that this latter solution does not work. In any case, the problem of the non-substitutability salva veritate of co-referential terms in intensional contexts is still wide open and constitutes a real threat to the whole framework of possible-world semantics. Its solution, moreover, has become a necessary condition for the viability of any serious semantic theory of natural language.
There is no doubt that verbs of cognition, like believe, think, know, be convinced, remember, introduce intensional contexts, that is, contexts in which SSV does not hold. But Quine wanted to add the epistemic modal predicates of necessity and possibility (must, may or necessary, possible) to this class. And he was quite successful in worldly (though less in intellectual) terms: since he proposed this, it has been slavishly believed all over the world of philosophy of language and formal semantics, with widely ramifying and far-reaching consequences. So successful was he that in the standard textbook on Montague’s possible-world semantics by David Dowty, Robert Wall and Stanley Peters Introduction to Montague Semantics (Reidel, Dordrecht, 1981), on p. 142, the authors attribute Quine’s misguided attempt to add the epistemic modals to the class of intensional-context-creating predicates to Frege (“Frege noticed the problem with modal operators”), whereas good old Frege wouldn’t touch modals with a barge pole. The classic source for this mistaken idea is Quine’s article ‘Reference and modality’ in his book From a Logical Point of View (Harvard University Press, 1953, pp. 139–159). These twenty pages have caused untold harm in the philosophy of language. I must now explain why.
Quine’s two crucial example sentences are (1) 9 is necessarily greater than 7, and (ii) Necessarily, if there is life on the Evening Star, then there is life on the Evening Star. Both sentences are true (the second trivially so). Now Quine takes sentence (iii) The number of planets is 9, to be an identity statement, paraphrasing it as The number of planets = 9. Yet sentence (iv) The number of planets is necessarily greater than 7, with 9 replaced with the number of planets, is false, as is, according to Quine, the sentence (v) Necessarily, if there is life on the Evening Star, then there is life on the Morning Star. There are two errors here. The first, pointed out with great clarity by Higgins on pp. 215–218 of his book, and again (though I leave the degree of clarity for you to judge) in my Language in Cognition (OUP 2009) on pp. 192–194, is that sentence (iii) is NOT an identity statement but, in my terms, a value assignment to the parameter ‘the number of planets’. This annuls the argument of the number-of-planets sentences (i), (iii) and (iv).
But the argument consisting of the Morning Star–Evening Star sentences (ii) and (v) is likewise invalid, because of Quine’s second error, which is that he assumes the wrong semantics for epistemic necessity and possibility. For Quine (p. 143), “necessarily p” (where p is any proposition) means ‘p is` analytic’, and “possibly p” means ‘not-p is not analytic’. This in itself is curious, as in his paper ‘Two dogmas of empiricism’, in the very same book, Quine argues that the Kantian notion of analyticity is invalid. But apart from that, this semantic description of necessary and possible in no way corresponds with what these words, in their epistemic use, mean in natural language. Quine’s semantic definitions are a philosophical construct, and a rather strange one at that. Using them in an argument pertaining to natural language is simply a consequence of a philosophical tunnel vision carried to absurdity. In natural language, sentence (v) is true, not false, because, in language, “necessarily p” means ‘p is entailed by available knowledge and the available knowledge is correct’ (see my The Logic of Language, OUP, 2010, pp. 203–205). In the case at hand, available correct knowledge tells us that the Morning Star and the Evening Star are the same identical object, namely the planet Venus. This knowledge entails that necessarily, if there is life on the one, there is life on the other. In other words, the epistemic modals do not create intensional contexts. Quine and the long cortège of those who blindly followed him, were all wrong. (Pity Quine died in 2000: I would have loved to see his reply!)