On some proposals for the semantics of mass nouns

entities. What are we to say of such sentences as ‘gold is yellow’? We cannot attribute yellowness to an abstract entity we must instead construe this as an assertion about quantities of Gold. Generally, what seem to be direct attributions to a thing (viz., the thing denoted by a mass name) turn out to be indirect attributions to quantities of that thing. Moravcsik says that, intuitively, the substance Red Ink should be a part of the substance Ink; but since these substances are abstract entities in Parsons’ system, this cannot be so. The relation in question will have to be put: all quantities of one are quantities of the other. This is different from the case where we have two predicates: in that case it is permissible to look to the physical objects and show that all things that satisfy the one predicate also satisfy the other (e.g., ‘white man’ and ‘man’). But here we do not have properties we have things, and the relation should be that one is a part of the other. If Red Ink is not part of Ink, it is hard to see why ‘Red ink is ink’ is analytic. That is, I grant that ‘All quantities of red ink are ink’ is symbolized by Parsons in such a way as to be analytic; still the intuitive understanding of the semantics does not make Red Ink a part of Ink. Hence, the semantics gives us no reason to believe that ‘Red Ink is Ink’ is necessarily true; so it seems improper for it to be symbolized in such a way as to be analytic. I.e., it would seem that ‘Red Ink is Ink’ cannot be adequately characterized as ‘All quantities of red ink are ink’. (This argument is adapted from Aristotle’s criticism of Plato’s theory of forms, Meta. B6). We could put this objection: in sentences like ‘Red ink is ink’ we are not talking about quantities, and so Parsons’ symbolism involves a violation of our condition 4, the “aboutness” condition. Parsons himself points out that in sentences like ‘Most gold is unmined’ we are not talking about quantities (pp. 371373). It’s not clear that ‘Most quantities of gold are unmined’ even makes sense, given an indefinite number of ways of counting quantities. And if we do agree on a way, ‘Most gold is unmined’ can be true while ‘Most quantities of gold’ is false as if all the unmined gold is in one big nugget. Parsons avoids the problem here by (a) claiming that he is not interested in ‘most’ quantifiers, only ‘all’ and ‘some’, and (b) with ‘all and ‘some’ the 102 FRANCIS JEFFRY PELLETIER truth-values are the same, and (c) he is only interested in the “truth-value” condition, not the “aboutness” condition. It seems to me, though, that the “aboutness” condition is an important one, both in its own right and in its implications for the “analyticity” condition (see above). An artificial language just cannot be adequate if it talks about one group of things while the natural language talks about a different group. Finally, whatever advantages Parsons’ language has, it is not the basic explanation of the denotation of mass terms. In his informal explanation of ‘Q’ (quoted above) he had said: “If it is true to say of an object.. . that ‘it is gold’, then the matter making it up will be a quantify of gold”. For all the world, it looks as if we here have a notion more basic than ‘xQg’ namely, that ‘x is gold’ is true. But if this is so, then there is a more straightforward explanation of mass terms than the one given by ‘Q’. This one will be studied in the next section. V. MASS NOUNS AS PREDICATES When confronted with a sentence like ‘Water is wet’, the first impulse of a student who has completed an elementary course in logic is to translate it as (x) (Water x 3 Wet X) i.e., to translate ‘water’ as a predicate. Presumably, this impulse stems from the instructor’s recommendation to translate ‘Men are mortal as (x) (Man) XX Mortal x). It is, however, easy to dissuade the student. First one points to the dissimilarities in the two cases. ‘Men’ is obviously plural and takes the plural ‘are’, while ‘water’ seems non-plural since it takes the singular ‘is’. We can give a clear sense to the phrase ‘For all X, if x is a man.. .‘, because we have an understanding of what it is to be one man (or a distinct man, or the same man, etc.); but in the case of water we do not have an analogous understanding. In ‘For all x, if x is water . . .’ it is difficult to give a clear meaning to what ‘x’ is. And if we do attempt to give a clear meaning to such locutions, it seems to involve a change in sense. For example, we might try to restate the quantifier phrase as ‘For all x, if x is a water.. .‘. But under the most normal understanding, PROPOSALS FOR THE SEMANTICS OF MASS NOUNS 103 “a water” is a certain kind of water; and then the sentence would be equivalent to ‘All kinds of water are wet’. And surely this should not be so. Once that student is in doubt about the adequacy of his translation, the teacher can give some arguments to show that the general attempt to force mass nouns into the mold of predicates is mistaken.6 (1) If we treat mass nouns as predicates, then it is not clear what these predicates should be true of (there may be many answers: ‘My ring is gold’ suggests physical objects, ‘The element with atomic number 79 is gold’ suggests elements in the chemists’ sense, and ‘The particular bit of matter which makes up my ring is gold’ suggests matter). (2) Demonstrating the deducibility of arguments like ‘X is made of gold, Gold is the element with atomic number 79, ergo X is made of the element with atomic number 79’ depends on ‘gold’ being a name in the canonical notation, not a predicate. By now the bright student is puzzled. If ‘water’ is not a predicate but rather a name, what sense are we to make of the phrase ‘all water’? Further, if ‘water’ is a name what is ‘dirty water’? If it is a name does it have internal structure? The various attempts to construe mass terms as names (of mereological entities, of sets, or of abstract entities) have all met with serious difficulties. It seems that the only option left is that the student is right: mass nouns are predicates. Hence, I shall attempt to answer the difficulties raised by this identification. Let’s start by adopting the notion of property given by Kripke (1963). It is a function on possible worlds to classes: the property indicated by the predicate 4 is the function from possible worlds to the set of 4’s in each world.6 In the non-mass case this is fairly clear: ‘pig’ indicates a function from each possible world to the set of pigs in that world. But things are not so clear in the mass case. ‘Water’ does not pick out the class consisting of water in each possible world, unless we give it a special sense. For, as it is, it seems to suggest “water as opposed to milk, honey etc.” Consider sentences like ‘Pigs are pink’. In such sentences we can always paraphrase the (implicit) quantification as ‘Anything that is a pig...‘. The analogue of this in the mass case as in ‘Water is wet’ is ‘Anything that is sm water.. .‘, where we have a use of ‘sm’, the indefinite article appropriate to mass nouns. In any case when we wish to speak 104 FRANCIS JEFFRY PELLETIER of some physical object (say this puddle) of which the predicate ‘water’ is true, we can paraphrase it as ‘This puddle is sm water’. Generally, when we are speaking of the extension of the mass term ‘M’, we can paraphrase it ‘sm M’. Recall now the fist argument against treating mass terms as predicates that we cannot specify what it is that (say) ‘is sm water’ if true of, other than simply to say that it is true of whatever is sm water. However, when put this way, the objection loses whatever force it once had. Compare it with: we cannot specify that (say) ‘is a man’ is true of other than simply to say it is true of whatever is a man. And surely this objection is off base perhaps it is an interesting philosophical mater to find out what being a man amount to, but it is absolutely clear that the philosopher of language need not decide such a matter before he says ‘is a man’ is true of whatever is a man. And is merely this last that we need do in giving a semantics for a language. This is perhaps a critical mark of predicates as opposed to names with a name it is essential for the semantics to assign it a denotation. With a predicate, however, we need merely indicate what things it is true of. It was in the inadequacies of satisfactorily explaining what mass nouns allegedly named, that enabled us to show the deficiencies in the previously-discussed proposals. “But still,” our detractor might continue, “‘is sm gold’ is true of so many different sorts of things nuggets, flakes, veins, watches, rings, etc. that it must be the case that we need some further information”. The tist answer to this is to point out that watches and rings are made of gold; nuggets, veins, etc., are not. Secondly, an analogous objection could be made in the non-mass case: ‘is an animal’ is true of many different things species (“The camel is an animal”), breeds, individuals that we must need further information. But surely it is pointless to make this objection here: ‘animal’ individuates its reference into individuals; the fact that other things can also be called ‘animal’ is irrelevant. ‘Gold individuates in its own way (picks out a certain stuff), and the fact that other things (nuggets, veins) can be called ‘gold’ is irrelevant. There are other advantages in interpreting certain terms as predicates rather than as names. Aristotle long ago pointed out that if we interpreted such terms as ‘man’ and ‘animal’ as naming objects (Forms) which are distinct and not part of one another, then the most that can be said of the relation between the two is that anything which “partakes of” the one PROPOSALS FOR THE SEMANTICS OF MASS NOUNS 105 also “partakes of” the other. There is nothing we can add which will make ‘All men are animals’ be necessarily true. This is because when we talk of two objects, X and Y, we have to have the relation be part of in order for ‘AI1 X is Y’ to be necessarily true. Aristotle points out that such is not the case with predicates here one looks to other criteria, such as whether the extension of ‘X’ must be included in the extension of ‘Y’. And the same seems to be the case with mass nouns: we want to avoid treating them as names so that ‘All red ink is ink’ can straightforwardly be shown analytic by appeal to the extensions of ‘ink’ and ‘red ink’. We want to give a rough-and-ready method of distinguishing extensional from non-extensional uses of mass terms. If ‘M is a mass term and is used extensionally when not in subject position or when after an explicit quantifier (but then grammatical considerations may force a change in the form of the quantifier: ‘all’ to ‘any’, etc.), then ‘M’ can usually be paraphrased by ‘(is) 8m 44’. Thus ‘This puddle is water’ becomes ‘This puddle is sm water’, ‘John is eating cake’ becomes ‘John is eating sm cake’ which in turn becomes ‘There is something which John is eating and that is sm cake’, ‘All water is liquid’ becomes ‘Anything which is sm water is liquid’ (there are other ways to paraphrase this). When ‘M’ occurs without a quantifier in subject position, it most often is paraphrased by ‘Anything which is sm M’, as when ‘Water is wet’ becomes ‘Anything which is sm water is wet’. There are cases though, where an unquantified mass term in subject position is existential in its meaning: ‘Water is leaking through the crack’ becomes ‘Something which is sm water is leaking through the crack’ or when ‘Water is found on Mars’ becomes ‘Something which is sm water is found on Mars’ (note the interplay at the quantifier ‘some’ with the article ‘s&).7 When these attempted paraphrases are not correct, we are not talking extensionally. The second argument given above against identifying mass nouns with predicates contains such a use. In ‘The element with atomic number 79 is gold’, we cannot correctly paraphrase it as ‘The element with atomic number 79 is sm gold’, for the former is true but the latter false (or meaningless). Rather what is being asserted is that in the actual world, two properties are true of the same entities. A paraphrase might be ‘Anything which is (entirely) made of the element with atomic number 79 is sm gold’. Thus we could demonstrate the deducibility 106 FRANCIS JBFFRY PELLETIER of ‘Xis made of gold, The element with atomic number 79 is gold, ergo x is made of the element with atomic number 79’ without requiring mass nouns to be names. However, this paraphrase has the disadvantage that it does not imply ‘Gold is the element with atomic number 79’ as the original did. Perhaps we would want to handle this as a case of predicate identity, but only identity in this possible world. Even if this line is taken, it is not the same as introducing abstract objects in Parsons’ sense; rather it is resorting to second order logic. Complex mass terms can be handled in the same way: ‘Dirty water is bad to drink’ can be paraphrased ‘Anything which is sm dirty water is bad to drink’. Now consider sentences such as ‘Water is a liquid’: this is clearly a case of predicating the second-level predicate ‘is a liquid’ of an ordinary predicate ‘water’. (This is justified by noting the anomaly of ‘Anything which is sm water is a liquid’. Of course one must distinguish ‘is a liquid’ from ‘is liquid’). We can also form such sentences as ‘Dirty water is a liquid’, which again is a case of second-level predication. The proposal put forth by Montague (1973), which is in many ways similar to the one advocated here, differs on this point. As Montague notes, his theory implies that complex mass phrases in subject positions must be taken extensionally; i.e., it is always the case that we are talking about the (physical) things of which (say) ‘dirty water’ is true. Or, as we can put it, it is alwars permitted to put ‘is sm dirty water’ in its place. But this makes such sentences as ‘Dirty water is a liquid’, ‘Salt water is a liquid’, etc., ill-formed. Surely this is false: in English such sentences are true; to preserve our “truth-value sameness” condition their translations must also be true, not meaningless, in any adequate artificial language.