From Ch

From Ch. 9 of Modality and Meaning

…

I cannot think of any further difference between (B) [= “-------17,” where “-------“ is Frege’s horizontal] and normal sentences that would explain these idiosyncrasies. The moral is that if we do affirm that (B) means something, we will still be stuck with the fact that (B) is somehow defective as compared to normal sentences and formulas; and (B)’s particular sort of defectiveness, though hard to identify, feels semantic in nature. By way of simply labelling the problem, we could say that (B) is semantically mute, in that it asserts nothing, has no locutionary content, and cannot be used to make a statement.

So far this need not shock or even faintly disturb the working semanticist, since, as I conceded above, Frege’s horizontal does not figure in the analysis of any natural language. But I believe there is a similarly afflicted construction that does figure in linguistic semantics; to it I now turn.

3. SUBSTITUTIONAL QUANTIFICATION

Consider

(C) is not a misprint. "(Ex)" is a substitutionally interpreted quantifier whose substitution class contains a left-hand parenthesis. "(Ex)( ... x ... )" is true, in the canonical idiom I have in mind, if there is some lexical item t of that idiom such that the result of replacing "x" in "( ... x ... )" by t is a truth. Now "(y) Admires xy, Frege)"--"(y)" here being a standard quantifier--will be turned into a truth if (and only if) a left-hand parenthesis is substituted for "x" and the result, "(y) Admires (y, Frege)," is true; thus, (C) is true if everyone admires Frege and false otherwise.[17]

The situation is familiar. You and I have the ability to compute (C)’s truth-value in any possible world. And yet (C) seems to me to be gibberish; though perhaps meaningful or "meaningful," it seemingly cannot be used to make a statement--(C) is "mute." The same range of replies that we ran through as regards (B) is available here, but our rejoinders to the replies will be the same.

Notice that (C)’s persisting anomalousness explains a pedagogical phenomenon with which most of us are familiar: Upon being introduced to the substitution interpretation of the quantifiers, students typically respond, "Oh, I see; substitutionally quantified sentences are metalinguistic," meaning that substitutionally quantified sentences assert things about some bits of the object-language in which they occur. To this one responds that, no, they do not assert things about bits of language, any more than "Frege attacked psychologism and Moore attacked idealism" asserts things about bits of language just because the base clause of our truth definition which concerns "and" alludes to the truth-values of that sentence’s conjuncts.[18] But the students go away vaguely dissatisfied; they see the point of that response, but still feel that for some reason they have not grasped the purport of the substitutional quantifier. What I am suggesting is that there is a good reason for the students’ puzzlement: The students want to know, given that the substitutionally quantified sentence does not say anything about bits of language, what it does say, and the reason their puzzlement persists is that the sentence does not say anything.

Perhaps the case of (C) is not quite so clear as that of (B); perhaps we should not be so quick to conclude that (C) is at best semantically mute. For, once the quantifier is understood as I have explained it, there is some temptation to say that (C) contains a determinate assertion, namely, the assertion that everyone admires Frege. (One might be similarly tempted to say that "Ugh umph veeblefetzer and everyone admires Frege" contains that assertion.) Perhaps (C) does say at least that everyone admires Frege; let us keep this in mind as a third possibility.

Now, as we all know, no semanticist has ever used a substitutional quantifier as powerful as the one I have introduced; no sentence of any natural language would have (C) assigned to it as its logical form. This is because the substitutional quantifiers that semanticists do make use of are intended to capture the roles of quantificational expressions of English or other natural languages, and such expressions (at least superficially) appear to bind pronouns, just as do those quantificational constructions which semanticists construe objectually. Accordingly, semanticists who introduce substitutional quantifiers restrict the substitution classes of those quantifiers to singular terms or (in the case of higher-order quantification) to predicates or whole sentences and exclude silly and structurally unimportant lexical items like left-hand parentheses. Therefore, working semanticists, whose substitutional quantifiers are restricted in this entirely natural and reasonable way, will be as undisturbed by the anomalousness of (C) (which will be uninterpretable in their canonical idiom) as they are by the anomalousness of (B).

I shall now argue that there is a theoretical reason why the semanticist ought to worry about (C) nevertheless. The argument will be a bit roundabout, but I believe it has some force and calls for a response from any semanticist who continues to appeal to substitutionally interpreted quantifiers as underlying (some) quantificational construction in English.

Let us begin with an uninterpreted formal language. Any such language may be considered and then interpreted in any way one likes, so long as the interpretation yields a truth definition for the language that assigns determinate truth-conditions to each well-formed formula of the language; subject to this last requirement, the interpretation of formal languages is otherwise arbitrary. Now consider an uninterpreted language containing operators which look like quantifiers and which, according to the (syntactic) formation rules for the language, are called "quantifiers." We may propose two distinct interpretations for this language, each of which treats the "quantifiers" substitutionally. The two interpretations are exactly alike, except that one applies only to variables in singular-term positions and accordingly restricts the quantifiers’ substitution class to singular terms, while the other is syntactically general and assigns an appropriate substitution class to each of the other syntactic categories as well. Now consider

(D) (Ex)(y) Admires (y,x)

I shall argue two points:

(1) that (D) on the second of our two substitutional interpretations of the quantifier has exactly the same semantical status (whatever it may be) as (C) has;

and

(2) that (D) on the first of our two interpetations (that involving the syntactically restricted substitution class) has exactly the same semantical status as (D) on the second interpretation has.

In support of (1), I would point out that, so far as formal semantics is concerned, the fact of the "quantifier"’s "binding" a "variable" that appears in singular-term position is totally accidental; our semantics gives singular-term positions no pride of place within our system of syntactic categories. For this reason, though the interpretation itself is entirely clear from a model-theoretic point of view, the "quantifier" is no more intuitively a quantifier of any sort than is its cognate in (C). In particular, (D)’s "quantifier" on our second interpretation has nothing whatever to do with existence, even existence very colloquially and fancifully construed. To see this more clearly, note that there is no uniform informal way of paraphrasing the "quantifier" into any even faintly quantificational expression of any better-understood formal or natural language that makes clear sense of (C) as any sort of existential assertion (objectual or otherwise).

It is important not to be misled by the fact that in (D) the "bound variable" happens to replace a singular term, by the orthographic similarity of the "quantifier" to an objectual quantifier, or by (D)’s similarity to sentences of more familiar idioms that we would translate into existential sentences of English; that these similarities are specious is just what is shown by the underlying semantical parity (identity) of (D)’s "quantifier" with (C)’s. It is also important not to be misled by the fact (already acknowledged) that the singling out of the syntactic category of singular terms is not at all arbitrary or "accidental" for serious philosophical and technical purposes such as that of analyzing natural languages. For now I am considering (C) and (D) solely as formulas of a logical idiom to which we are assigning formal semantical interpretations, regardless of what uses these formulas thus interpreted may or may not turn out to have. And the moral of the foregoing argument is that, from this abstract point of view, there is no reason at all to think that (C) and (D) on our second interpretation differ in their semantical status or that their "quantifiers" differ in any semantically relevant way.

In support of (2), I would return to the point that I believe Quine (1969a, p. 106) had in mind in reminding us of the kind of construction exemplified in (C). Again: From the purely formal truth-theoretic point of view, the restriction of substitutional quantifiers’ substitution classes to singular terms is entirely arbitrary--not just in that any truth-theoretic interpretation of any logical functor is arbitrary, and not just in that the choice of singular terms from among all the language’s syntactic categories is arbitrary, but also in that the idea of making any such choice at all is arbitrary. (The urge to restrict the use of our "quantifier" to singular-term positions is not a mathematical urge; it comes only from philosophers’ or linguists’ desires to model or parody natural languages.) And it seems therefore that the same sorts of considerations that assimilate (D)’s "quantifier" on our second interpretation to (C)’s "quantifier" also suffice to assimilate (D)’s "quantifier" on our first interpretation to (C)’s. The fact of that interpretation’s having restricted the application of (D)’s "quantifier" to singular-term positions is accidental in just the same way as is the fact that (D)’s "variable" on the second interpretation occurs in singular-term position. And, as before, (D)’s "quantifier" even on our first interpretation is no more intuitively a quantifier of any sort than is (C)’s; it has nothing to do with existence in any sense or with any quantificational expression of any more familiar formal or natural language, and so on. Here again, we must resist being misled by the "quantifier"’s superficial similarity to a quantifier etc., or by the nonarbitrariness for purposes of linguistics of singling out singular-term positions, for the same reasons as before. There is equally no reason to think that (D)’s semantical status on our first interpretation differs from (D)’s semantical status on our second, or from (C)’s, and there is no reason to think that their "quantifiers" differ in any semantically relevant way.

We concluded above that (C) is semantically mute. Thus, given (l) and (2), we should draw the further conclusion that (D) on either of our substitutional interpretations is semantically mute also, and that any inclination to deny this arises only from (D)’s mendacious orthographic familiarity. (We did consider allowing that (C) asserts that everyone admires Frege, but no analogous option is available here, since (D) does not "contain" any closed sentence.)

Even now we have said nothing to trouble the working semanticist. I have talked only about the logical particles of a couple of nonstandard and useless formal systems. The trouble begins, however, as soon as we turn at last to the analysis of natural languages and try to explain some of their surface constructions in terms of underlying substitutional quantifiers, relating relevant surface expressions to the underlying quantifiers via fairly simple lexicalizing transformations. For example, as we saw in Chapter 1, Marcus (1975-1976) supposes that an expression of English such as "There are things that" in

(E) There are things that don’t exist

reflects a substitutionally interpreted quantifier, since it is a plainly quantificational expression but cannot comfortably be regarded as straightforwardly mirroring an objectual quantifier, at least not in the absence of an elaborate Actualist or Concretist metaphysics of possibility. Besides, in a way we do talk as if (E) were made true by the truth of certain substitution-instances of (E)’s matrix: when one tokens (E) in a philosophical discussion one feels an inclination to add, "...Pegasus doesn’t exist; Santa Claus doesn’t exist; and so on." But if substitutionally quantified formulas of formal languages are, as I have argued, semantically mute in the sense that they (can be used to) assert nothing, and if whatever transformations derive English sentences from the interpreted formulas of underlying formal languages preserve meaning and all meaning-related properties (as is widely insisted), then on the hypothesis that "There are things that" in (E) reflects a substitutional quantifier, (E) itself is semantically mute. Congenial as that consequence would be to a ferocious antiMeinongian, as a contention about ordinary English it is pretty obviously false. I have already argued in Chapter 1 that Marcus’ substitutional proposal will not do, but here is a new difficulty.

The point generalizes quickly to any theory according to which any perfectly meaningful sentence of English reflects an underlying substitutional quantifier--e.g., a sentence containing apparent higher-order quantification ("There are three things I am concerned to deny:...").

The consequence that (E) is mute, taken together with the antecedent plausibility of one or more substitutional-quantifier hypotheses, may make us suspicious of my argument for the muteness of (D). I suspect that some semanticists will simply ignore the argument for that reason. But I think that to do so would be a mistake. The argument seems to be sound; therefore, to find a flaw in it would probably teach us something interesting and perhaps important about meaningfulness or about the surrounding semantical and syntactical notions.

4. WHAT IS SEMANTICAL MUTENESS?

We have left section 2’s residual question unanswered. What is "semantical muteness"? That is, what is it about a formula such as (B) that makes us feel that that formula asserts nothing and is semantically deficient in some way? Not (B)’s untranslatability into English, as we have seen, or any more basic pragmatic property of (B) that I know of. At present I have very little to offer on this. One feature of Frege’s horizontal stands out, however, and it is one that is shared by (C)’s substitutional "quantifier": Each of these "funny functors" is syntactically ambivalent or promiscuous, in that it operates grammatically on arguments of more than one grammatical category. The horizontal applies either to a singular term or to a closed sentence; the "quantifier" applies to an "open sentence" whose "variable" may occur in any grammatical position. (And I argued that the "quantifier" in (D), though by happenstance (on our second interpretation) or by fiat (on our first) it "binds" a "variable" in singular-term position, might just as well apply in the same way to a position of any other syntactic category.) If anything can explain (B)’s and (C)’s felt emptiness, I should say, it must be this property of their contained funny functors.