Jason Turner

Jason Turner (Rutgers University), “On How Things Are,” with commentary by David Manley (University of Southern California).  Both the paper and commentary can be found here.

Comments

[Terrance Tomkow]

On the old Bob Newhart show, Larry would introduce his two brothers as  " Daryl and my other brother Daryl".  The joke was that baptizing two of your kids 'Daryl' opened the way to much confusion.

But it is not generally known that Larry had adopted a notation which allowed him to avoid  confusion when writing his familiy history and did so moreover  without betraying his parents’  wishes that the Daryls not be given different names.  When he wanted to say that at least one of his brothers was happy, Larry would write:

    (E Daryl) (Daryl is happy).

If he wanted to say that both of his brothers were happy, he would write:

     (A Daryl) (Daryl is happy).

Here the (E) and the (A) prefix clauses served as disambiguating devices, indicating whether he was committing himself to the truth of the sentence for every, or only some, referent of  ‘Daryl'.  Of course, more complicated devices were sometimes required. For example, when Larry wanted to say that one of his brothers was happy and the other not, he would write:

    (E Daryl-x) (E Daryl-y) {Daryl-x is happy and Not (Daryl-y is happy)}

'Daryl-x' and 'Daryl-y', Larry was quick to point out, weren't different names for different brothers; rather the subscripts only served to connect (or "bind" as he put it) a  'Daryl'  with the intended disambiguating prefix.

Sometimes Larry would get lazy and just leave out the 'Daryl' , resulting in a notation eerily similar to the predicate calculus.

The moral of this fable is this: Variables are merely universally ambiguous names and quantifiers are disambiguating devices. At a great baptismal ceremony the founders of the predicate calculus declared "I hererby name each and every thing 'x'; and 'y' “ and so on.  In consequence we can be utterly sure that each and everything there is, is named 'x' and 'y'.

I think this way of understanding quantifiers is TQ though arguably it predates him. (Recall  Kaplan's observation that variables in the calculus behave exactly like Russellean logically proper names).  In any case this seems to embody a way of thinking about quantification  not considered by Turner.

Turner wonders how to account for the ontological commitment of both names and variables. What, he asks, do naming and "variablity" have in common?  His answer that they both occur in "subject postion". This seems backwards: Variables are names. They occur in "subject position" because that's where names go.

This way of understanding variables answers a question Manley's objection seems to beg. Turner asks why take an assertion of  “God is great" as committing the speaker to saying that something is great. Manely says it’s because the sentence entails "(Ex)(x is great)". Turner is entitled to ask *why* that is so.   The answer is because 'x' is another name for God (among other things).

When we baptized everything "x" we included everything without exception. If there are properties and relations then our lower-case variables name  them too.  On the other hand, if we want to discourse particularly about these putative things there is nothing to prevent us from introducing a new set of names for them.  We could do the job simply by saying "I hereby baptize all the properties 'X'; and 'Y’ “ and so on.  Having done so, we would have to introduce appropriate disambiguators (quantifiers) for them and stipulate careful rules for their interpretation on pain of leaving ambiguities unresolved.

But, pace Manley, Quine’s objection to these devices was not that stipulating such conventions was impossible or that the upshot might sometimes be unparaphrasable into colloquial English.  Quine rejected second order quantification because he saw quantification as *always* ontologically committing, whether the variables were second-order or Daryl-order.  And Quine did not think there were such things as properties or relations.

[David Manley]

Thanks for your comments, Terrance. A couple of points: (1) I think things have to exist to be baptized, but I can say, 'If none of the things that exist had existed, there might have been some other things'. (2) I agree with Jason that his account tying the commitment of first-order variables (when bound by existential quantifiers) to that of names is a more satisfactory account than the entailment account I mention. I'm no TQer; but that's the response I expect a TQer to give in answer to his demand for a unified account.

[Jason Turner]

Terrance,

Thanks from me, too. I should say I'm sympathetic (well, at least not un-sympathetic) with your suggestion on how to understand quantification. (I make a similar, less-well developed suggestion in passing in my comments on Amie Thomasson's paper elsewhere in this conference.)

Notice that, while this account explains why *first-order* variables have ontological significance, it doesn't really explain why variables of *any* order have ontological significance. The way I'm thinking of "Textbook Quineanism", the view is that quantification into *any* position creates ontological committment to values for the new variable. On your suggestion, variables are like vague names (on a supervaluationist-esque construal of vagueness) --- names so vague that they precisifiy no other names --- and the universal quantifier "A" is like the operator "Definitely", except that it says the embedded sentence is true on all precisifications of the variable it binds, rather than on all precisifications of all terms whatsoever.

In this case, though, second-order variables won't be ontologically committing by Quinean lights. Second-order variables will be vague predicates --- predicates so vague that they precisify no other predicates at all (and, conversely, every other predicate is either a precisification of them or is another variable). But predicates don't, by Quinean lights, commit us to semantic values for them, and this won't change just because a predicate is vague. So second-order variables ought to count as innocent, and the *general* principle of TQ, that quantification (of any order) is ontologically significant, will fall.

[Terrance Tomkow]

Can it just be the three of us? Where are all those readers who will, tomorrow, go placidly off to teach predicate logic to their undergraduates? Can it really be they have no opinion on this? That is, can it really be that, at bottom, they have no real clue how it is supposed to work?

Whoever among us is right, I think that it is very interesting that Jason's paper has exposed these fundamental differences about how to understand quantification. That is because Jason has had the nerve to pose fundamental questions and I congratulate him on that.

I'm not sure whether David's point (1) is intended against the picture of quantification I sketched or against my claim that it is Quinean but I would defend it on both counts. It is puzzling how we can talk about things that don't exist, but, Quine thought, the existence of possibilia is precisely what we are committed to by quantified modal logic. And wasn't he right about this?

I don't recognize my (or Quine’s) understanding of quantifiers in Jason's retelling. An advocate of *substitutional* quantification might hold that the semantic role of a variable was to stand in place of more precise names. But a believer in *referential* quantifcation thinks that variables stand for the things names *stand* for, viz. things. Likewise, second order variables will not ambiguously/vaguely stand for *predicates*, they will stand for the things that predicates stand for whatever they may be.

Agreed, Quine did not think that using predicates commits us to saying that there are things that predicates stand for. We can specifiy the satisfaction conditions of "x is red" by saying that the predicate is satisfied by something x iff x is red. There is, Quine argued, no need here to treat "x is red" as expressing a relation ( instantiation?) between something x and something named by "red"-- presumably, Redness-- in order to make systematic sense of the predicate's semantic contribution to sentences in which it occurs. On the other hand, Quine thought that as soon as you quantify into the verb position you *are* treating "Red" as a name-- because in referential quantification variables are names. Names contribute to determining truth conditions of sentences in which they occur by standing for things. Which is why, Quine thought, second order quantification was inherently ontologically committing.

[Jason Turner]

Thanks, Terrence, for both your continued interest in the topic, and for supporting my bucking of the establishment. O' course, this particular establishment has been bucked by more established figures than I (Yablo and Williamson, and to a slightly lesser extent, Boolos), so I'm not so sure the limb I'm on is all that thin. The encouragement is appreciated none the less for that, though.

I meant for my retelling of what I took to be your suggestion (that variables (first-order) are "indeterminate" names) to be purely referentialist. My point was supposed to be different: if first-order variables can be indeterminate *names*, and the quantifiers (kind of like) disambiguating devices, why can't 2nd-order variables be indeterminate *predicates*, with the quantifiers still as disambiguating devices? This would be an understanding of 2nd-order quantification which would be neither referentialist nor substitutionalist.

I think my "vagueness" suggestion above might have been overly cryptic, so I'll try to go through it a touch more carefully. In the first-order case, the vagueness suggestion is pretty much a notational variant of the Tarskian semantics (provided there are no prenumbral connections between variables and other terms). Make truth of a sentence relative to a precisification, and say that Ex(p) is true relative to a precisification P iff there is a precisification P' that precisifies every term the same way P does except perhaps "x" on which p is true. Note that a precisification of a name, on this account, is a member of the domain --- not another word. We may say that a name n precisifies another name m when the acceptable precisifications (a subset of the domain) for n is a subset of those for m.

So this is a referentialist semantics for first-order quantification with parallells to supervaluationist accounts of vagueness. Now let's see how it would go for the 2nd-order case: 2nd-order variables wouldn't be vague *names* (the way 1st-order ones are), but vague *predicates*. Why? Because they are syntatically predicates, not syntactically names. They go in predicate, not name, position. So we could let second order variables be vague predicates, and let EXp be true according to a precisification P iff there is a precisification P' that precisifies every word the same way P does except perhaps for how it precisifies "X". But since "X" here is a predicate, precisifications *aren't* objects from the domain. They aren't objects at all, because predicates don't have "semantic values" on the Quinean conception.

Two points: first, we have to describe how the first-order variables are vague across the whole domain. We have to say something like "everything in the domain is an acceptable precisification of 'x'." Notice that we have to *use* 1st-order quantification to say this. Likewise, in order to say the same thing for the 2nd-order case, we have to use 2nd-order quantification; we have to say something like "However(X) a thing may be, there is a precisification of a 2nd-order variable v such that some things satisfy v iff it's like that(X), too." (It'll get way more complicated if we want our second-order variables to make intensional or hyperintensional distinctions, but I don't want to get into that here.)

Second point: this isn't substitutional quantification, because a term can be vague across a range without there being precise terms that pick out every point in that range.
"Pink" can be vague across different shades without our having more precise predicates for each (or any, for that matter) of those shades. In 2nd-order substitutional quantification, if "...X..." is true, then there must be a predicate P for which "...P..." is true also. On the other hand, if "V" is a vague predicate, "...V..." can be true even if there is no more precise predicate P for which "...P..." is true. Thus helping ourselves to precisification-talk in the metalanguage helps us out here.

OK, all that being said: agreed, Quine thought that variables were always name-like (i.e., referential) and so to quantify into predicate position was to engender ontological committment. I'm trying to suggest that this is a mistake: it's generalizing the *wrong lessons* from our study of 1st-order variables. Our first-order variables are referential not because they're *variables* but because they're *names* (or name-like). But why think variables of *every* order must be names (or name-like) just because first-order ones are? First-order variables are names because they're *first-order*, not because they're *variable*.

[Antti Kauppinen]

A very nice paper as usual, Jason! I do see a way out for Quine, though. That involves denying the following: "Whether alleged names are covert quantifiers is a matter for linguistics,
not ontology, and a criterion of ontological commitment ought not presuppose one
answer over another." (p.5) The relationship between linguistic deep structure and logical deep structure doesn't seem as simple and obvious to me as you presuppose here. Are linguists really in the business of articulating logical structure? Wasn't Russell postulating the quantificational structure he did precisely because of ontological concerns? If articulating logical structure and making claims about ontological commitment are part of the same process, then the Quinean is surely entitled to assume a particular treatment of the semantic contribution of names when doing ontology. Moreover, that view allows her to answer a question you leave hanging, namely the question of when names involve ontological commitment and when they don't. This allows her to handle the problem of negative existentials.

The objections on the part of Janus to this are not very convincing. Surely his insistence that he's not a descriptivist is beside the point, given that logical structure isn't transparent on anyone's view. Nor does inventing a new language help - as long as the terms in it have the same function as those in ours, we can expect it to share logical structure as well.

This isn't to say that there isn't a great deal of intuitive plausibility to the idea that use in the subject position is relevant to ontological commitment, and it does seem to me a neat way to handle second-order quantification. But what's wrong with a hybrid view that would combine a quantificational view of ontological commitment and a quantificational treatment of names with the condition that the committing term must occur in a subject position? Wouldn't this avoid all the problems of the unrestricted quantificational view and the view that all uses of names commit?

(I didn't read the commentary yet; apologies if these points have already been made.)

[David Manley]

Hi again Terence. I do not believe that quantified modal logic commits us to the existence of mere possibilia. But the contrast I wanted to mark can be illustrated using more mundane operators, like negation. For Kripkean reasons, I believe that if 'Bill' does not refer, then both 'Bill is F' as well as 'It is not the case that Bill is F' fail to have truth value. But 'Some Fs are G' is false if there are no Fs, and 'It is not the case that some Fs are G' is true if there are no Fs. Even if you buck contemporary linguistic theory and take the quantifiers here to be completely unrestricted, so that the sentence contains a covert conjunction, it seems clear to me that the second sentence does not commit one to the existence of anything at all. (Neither, one would hope, does 'nothing exists'). In contrast, I believe that for any sentence involving a proper name to express a truth-evaluable propositions, there must a referent for the name. The point that non-denoting quantified expressions, unlike non-denoting logically proper names, can be used as building-blocks for true and false claims goes back at least to Russell.

[David Manley]

Terrance: Sorry for mangling your name in the last post!

[Jason Turner]

Antti,

I didn't mean to be suggesting, with my line on p. 5, that ontology doesn't inform semantics. Let's grant that Russell made his "On Denoting" suggestions thanks to ontological considerations. (I'm not sure this is historically accurate, but it's a favored reading, and I don't want to get into it here.) And, to a certain extent, articulating a semantics -- I take it this is what you mean by "logical structure" (as opposed to "linguistic structure", which I'm guessing refers to LFs and the like) -- is saying something about "ontological committment."

But *what* is it saying about ontological committment? It's saying exactly what things we are committed to. If I give a semantics for a language L on which every predicate is taken to denote an abstract object, then (insofar as I insist my semantics is to be taken literally), I've said something that committs me to abstracta. So, in a sense, I've said something about ontological committment. If I give a (more TQ-ish, I take it) semantics on which bound variables range over a domain of things but predicates are not taken to denote or otherwise linguistically express any *thing* at all, then I've avoided a certain kind of committment.

But this presupposes we've already got a formula for figuring out ontological committments in our pocket and are using it to decide which semantic hypotheses result in which committments. My point was that deciding *what this formula is* is independent of which semantics is the correct one. The picture I've got is, in essence, that a "criterion" (as it is often called) of ontological committment will take in different semantic hypotheses and spit out corresponding ontological committments. But if different semantic hypotheses carried with them not just different ontological committments, but different standards as to what counts as an ontological committment, then game would be pointless.

Granted, given the Quinean criterion, on the semantic hypotheses that names are in fact quantifiers, a Quinean can answer a lot of questions I can't. But the question I'm asking is what that criterion should say when it encounters a direct-referentialist-esque hypothesis about names. Janus is a foil to help us think about what that criterion should say. That's why it matters that Janus could, at least in principle, speak his piece in a language where names aren't quantifiers -- because we can see that even if he did, his use of "God" would still have ontic significance.

As I see it, the Quinean can say one of two things: (1) such languages are impossible, or (2) committments can't be evaluated for such languages. Since Quine already limits the scope of the "criterion" to first-order languages (as David nicely points out), I suspect if he had to make the choice, he'd plump for (2) -- and maybe for the reasons you say. (What should we say about negative existentials?) I don't have any direct argument against this. But it does put additional pressure on TQ. As just pointed out, we can all tell that Janus, if speaking a language where names aren't quantifiers, would commit himself with (at least certain uses of) names. This shouldn't, I think, be controversial. If TQ is forced to say that this uncontroversial thing we can all see is in fact *false* -- because committments aren't well-defined for such languages -- so much the worse, then, for TQ.

But (1) just doesn't seem any good at all. Surely the direct referentialist semantic hypothesis is out there, and our criterion of ontological committment -- unless it is limited in the way (2) suggests -- should tell us what we'd be committed to on such a hypothesis. Unless there were some reason the hypothesis were internally incoherent, there'd be no reason to think that it couldn't be plugged into our criterion to find out what its corresponding committments are. And we can't charge it with incoherence on the basis of its having bad committments (the way Russell might have when he complained about the generic man), for that presupposes we in fact *do* have a way to evaluate the hypothesis's committments and they come out looking shabby.

[Terrance Tomkow]

Return to my first comment. Neither of Larry's brothers were fat, so none were fat and gay. As he would put it:

(1) Not (E Daryl) (Daryl is Fat & Daryl is Gay)

Now, *of course*, in so saying, under the stipulated conventions, Larry is not committed to the existence of a Fat brother ("an F") . Indeed asserting *this* sentence does not commit Larry to the existence of anything. On the other hand, if we are going to understand Larry's language-- if were are going to say what he's talking about and decide whether this sentence is true or false-- we have to say what domain he is quantifying over and specify the satisfaction conditions of his predicates on this domain. This sentence is true because no object in the domain is fat and gay. We know that because I've told you who "Daryl" refers to and I've told you that none of those guys are fat.

Suppose one day Larry had said:

(2) (A Daryl) (Daryl does not Exist)

I agree that, in so saying, Larry would not have asserted the existence of anything. On the other hand, in the story as told, Larry would be saying something false if he said (2) *because* there *is* a "value of the variable" ( = a guy 'Daryl' names) who does exist. In fact, every value of this variable in the domain of discourse--- i.e. every brother-- exists. As far as Larry's brothers are concerned, to be is to be the value of a bound 'daryl'.

Notice how this way of understanding variables and quantifiers keeps yielding Quinean results. What, one wonders, does Manley think Quine was trying to say when he said things like "to be is to be the value of a bound variable"?

Let me put the same points more conventionally. On a standard semantics for referential quantification, one explains the truth conditions of a predicative expression (and recall that Russell's "denoting phrases" are just predicates) by:

(a) stipulating the conditions under which some object in the domain of discourse satisfies the predicate.

(b) demarcating the domain of discourse.

Quine thinks that when we do (b) we reveal our ontological commitments. Apparently Manley thinks we need not do (b). Or maybe he thinks we can do (b) without actually committing ourselves to saying that anything in the domain exists?

It's not clear because Manley does not tell us how he thinks quantifiers work. He insists that you can't name things that don't exist, but seems to think you can quantify over non-existents all you like. This would be a neat trick. Manley should tell us how to pull it off.

[David Manley]

If "Daryl" is really an ambiguous name, then neither sentence (1) nor sentence (2) could be true in the absence of the existence of any referent for the name. You suggest imagining that everything was baptized 'x', but on this kripkean view of names, a failed baptism yields a term with no semantic value. In contrast there need be nothing in the domain of a quantifier expression for it to successfully contribute to a true or false sentence. Thus, on your fable according to everything was baptized "x",

I do not think we can quantify over non-existents. I simply think there needn't be anything in the domain of a quantifier for it to contribute semantically to a truth-evaluable sentence. When do quantifiers not range over anything? On standard treatments of quantifier domain restriction, the quantifier in "there's no beer" can have its domain contextually restricted to things in the fridge. If there's nothing in the fridge, the sentence is nevertheless true: beerhood is not instantiated by anything in the domain.

You ask how quantifiers work. A standard way to treat the semantic value of a determiner like 'some' is that it expresses a relation between properties; a relation that holds just in case the properties are coinstantiated by an object in the domain. But there need not be an object in the domain for the determiner to contribute this semantic value, whereas in the absence of a referent, a name cannot have a semantic value.

Think also of attitude contexts. To say "Jim believes there is a man who is 100ft tall" is not to say in some indeterminate way of all the actual things, that Jim believes one of them to be man who is 100ft tall. If there are three things, A, B, and C, it is not at all equivalent to saying: "Either Jim believes A is tall, or Jim believes B is tall, or Jim believes C is tall"; nor is it equivalent to saying "JIm believes that either A, B, or C is tall". Jim may in fact deny this of all the actual things, believing (wrongly) that there is yet a further thing. On a simple compositional account, the attitude report relates Jim to a proposition, the one expressed by "a man is 100ft tall". This proposition essentially involves (on a Russellian metaphysical picture of propositions, actually contains) the property of being a man and the property of being 100ft tall, but it does not involve any objects at all.

[David Manley]

please ignore the sentence fragment at the end of para. 1 of my previous post!

[Terrance Tomkow]

David,

If we are talking about universal quantification, there is no fear of an empty domain since, as Lewis taught us, there is (necessarily) always something. If nothing else, there are always those properties you require for your account.

Context might work to "restrict the domain" of "x is a Beer" to things in the fridge, but so would explicitly adding the conjunction "and x is in the fridge". I know of no reason to think the former kind of restriction can't be handled in the manner of the latter kind and hence see neither as an obstacle to referential quantification.

In any case, how are you permitted to talk of "domains", restricted or otherwise?

On the account you advocate, quantifiers do not express relations between properties and domains; they express properties of properties. This would indeed explain how one can talk about properties even when there are no (first order) objects around, but it notoriously leaves much unexplained. E.g. What is the the connection between these properties of properties to the properties of (first order) things? Why does "Joe is tall" entail that Tallness has the property of being instantiated? Why would the property of Tallness having the attribute of Universality have the consequence that Joe is Tall? Or, to use your example, if Jim believes that some man is 100 feet tall "isn't about objects at all" why does the truth of his belief require that some male object be 100 feet tall?

It seems to me that these are the sorts of things a theory of generality ought to explain, not take as primitive. Indeed I would argue that the modern period of logic begins precisely with Frege's realization that verbs should be treated as functional expressions-- expressions whose meaning was exhausted by pairing of arguments and values-- and not property names. But that, as they say, is a long story.

Obviously we aren't going to settle this here but I will retire from this field a happy man if I can get you to allow that the views I have been arguing for-- wrong as they may be-- are not unlike those held by the author of "On What There Is". What say?

Best

Tomkow

[David Manley]

Thanks for the exchange, Terrance. I don't think I can concede that your proposal similar in spirit to Quine's view of quantifiers. If the view of names operating in the background is a Kripkean one, then I don't think so, in part because of problems involving commitment in attitude contexts, etc. If the view of names operating in the background is Quinean, then names are understood as quantifiers, not vice versa. On the other hand, though I've read my Quine and have some familiarity with TQ, I'm not a Quine scholar and I do find him less than pellucid at times.