Azzouni, J. on 'on What There is

8/13/2019 Azzouni, J. on 'on What There is'

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Abstract: All sides in the recent debates over the Quine-PutnamIndispensability thesis presuppose Quines criterion for determining whata discourse is ontologically committed to. I subject the criterion to scrutiny,especially in regard to the available competitor-criteria, asking what meansof evaluation there are for comparing alternative criteria against eachother. Finding none, the paper concludes that ontological questions, in acertain sense, are philosophically indeterminate.

( What i s C. t ryi ng to pull?)

marginalia on Quines copy of a letter from Carnap

1.

A lot of philosophy of mathematics is motivated by considerations arisingfrom what has come to be called the Quine-Putnam indispensabilitythesis;1 the claim, roughly, that if ones best scientific (physical) theory

requires existential quantification over certain entities, then one is onto-logically committed to such entities.2 Many books in this area, such asChihara (1990), Field (1980), Hellman (1989), and Maddy (1990), drawtheir philosophical raison dtrefrom the view that scientific theories commitus to the existence of mathematical objects this way. The indispensabilitythesis, it seems, drives philosophers to hard choices: rewrite ones science,rewrite ones mathematics, or regretfully embrace extravagant ontologies.

Its quite unsurprising, therefore, that such a seminal claim has once

again come under intense scrutiny; and equally unsurprising, I guess, tofind philosophers on both sides of the philosophical fence. Maddy strongly

1

ON ON WHAT THERE

IS*

BY

JODY AZZOUNI

Pacific Phil osophical Quarter ly79 (1998) 118 00315621/98/01000000 1998 University of Southern California and Blackwell Publishers Ltd. Published by

Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK and350 Main Street, Malden, MA 02148, USA.


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relied on it in her 1990; but as her articles in 1992 and 1994 make clear,she has, of late, become distrustful. Sober (1993) also offers objections;while Resnik (1995) is supportive.3

Rather than plump down on one side or the other in this debate, Iwant, instead, to explore the possibility that the status of the Quine-

Putnam indispensability thesis is philosophically irresolvable. For thethesis requires the antecedent application of a criterion for evaluating theontological commitments of a discourse, and I claim there is no principledway to choose among competing criteria. Since my claim is a negativeexistential, I wont be able to conclusively show it. Rather, I ll be satisfiedif I make clear why its unlikelytools are available to decide on such acriterion.

After making this case, I ll close the paper by indicating how certain

other important philosophical issues about the differences betweenvarious sorts of posits emerge when we dismiss worries about onto-logical commitment the way I urge us to; and these issues, I suggest, aremore tractable once they crawl out from under the long shadow cast byontology (at least in the form of the subject bequeathed to us by Quine).

2.

We start with a distinction between a criterion for what exists (CWE)and a criterion for recognizing what a discourse commits us to (CRD).Philosophers have long argued over alternative CWEs. A nominalist, forexample, claims that only concrete objects (of one sort or another) exist;platonists, notoriously, think otherwise. Other philosophers may alsoclaim that anything that exists is causally efficacious, or perhaps, thatanything that exists is susceptible to observation (e.g., via the senses, orwith the aid of acceptable instrumental interventions), or is in space and

time, or, and so on.4These are all variant CWEs.Quine (1948), however, is quite clearly notoffering a CWE, but only a

CRD.5The distinction matters: those committed to one or another CWEcommonly debate about what properties everything has, whereas Quinescriterion addresses the logicians tamer concern with merely knowing howto tell what ontological commitments a discourse has, and this regardlessof the properties of those commitments.

Now, althoughQuinedoesnt do so, one may combine any of the above

CWEs with Quines CRD.6 If, for example, one thinks that anything thatexists must be causally efficacious, then one will make a point of onlyuttering discourses which can be regimented so that they have existentialcommitments solely to causally efficacious items. So too, the nominalistwill utter discourses which can be regimented so that they have existentialcommitments solely to concreta. And so on.7

2 PACIFIC PHILOSOPHICAL QUARTERLY

1998 University of Southern California and Blackwell Publishers Ltd.


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But our present interest is not in alternative CWEs; its in alternativeCRDs. What do some of theselook like? Well, even if one accepts theidea that scientific theories must be regimented in first-order languages,nothing requires the first-order existential quantifier (despite its logicalrole in such languages) to carry the burden of ontologicalcommitment:

one can, that is, regiment a scientific language just the way Quine likes,and simply look elsewhere in the regimented theory for the ontologicalcommitments. For example, one can provide a special predicate, suscep-tible to observation say, or causally efficacious, or, and so on, andrecognize the ontological commitments of a discourse to be solely thoseobjects falling under the extension of thatpredicate, to treat only thoseobjects as existing (or real). Indeed, any of the alternative candidate CWEsmentioned above can be impounded as the intended interpretation for

such an existence predicate.Three points. First, Im not wedded to using existence predicates here

(the example is illustrative); one might be inclined to use more than onekind of quantifier (quantifiers with subscripts, say, only one of which istaken to carry ontological import), or any of the other sorts of devicesthat logicians have dreamed up. The point is that we have great latitudein which idioms of a given formal discourse we choose to invest with onticsignificance. Nevertheless, in what follows, I will focus on the existence

predicate option for concreteness.Second, the import of provide a predicate should not be misunderstood.The idea is that the unregimented discourse of sciencealr eady hasone ormore phrases which are taken to carry the burden of ontological commit-ment, be it causally efficacious, observational, or whatever. Whenregimenting, therefore, one mints a predicate that, more or less, replicatesthis role.

Third, I need to stress that the existence predicate move doesntrequire avoidance of objectual quantifiers: ourregimented languages

can employ good old fashioned Tarskian semantics. Of course, thequantifiers arising in the metalanguage where Tarskian semantics livesare no more to be understood as having ontic force than the quantifiersin the object language are; ontic force will be carried in the metalanguageby a predicate similar to the one carrying ontic force in the objectlanguage.8

Admittedly the move contemplated here is weird-sounding in just theway Quine has described as ruining the good old word exist (1948, p.

3): we can find ourselves saying, that is, in the vernacular, that there arethings which nevertheless dontexist (or dont reallyexist). For example,if our existence predicate is susceptible to observation, well find ourselvesasserting that there are numbers, but they dont exist (because theyre notsusceptible to observation, say). And I wont deny that in the rightcircumstances (i.e., among philosophers) this may raise eyebrows. But

ON ON WHAT THERE IS 3



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linguistic intuitions about what sounds weird are not reliable indicationsof incoherence.9

For, frankly, intuitions can be mustered to support either Quinesapproach or the alternative existence-is-a-predicate treatment. On Quinesside, and provided we treat the first-order (objectual) existential quantifier

as a translation of the ordinary-language phrase there is, one can urgethat if our best theories force us to say, There arenumbers, there arefunctions, thats enough to ontologically commit us to the existence ofnumbers and functions. But the intuitive force for such a position, I muststress, largely arises from the antecedent impression that the ordinarylanguage there is alreadycarries ontological weight.10

And so, on the other hand, a good case can be made that physicists,and other scientists too, usually regard theiremployment of mathematics

to be ontologically neutral. Despite the (indispensable) use of quantifi-cation over mathematical entities to formulate scientific theories, and tomake empirical inferences, mathematical talk is taken to be trueeventhough, simultaneously, it isnt taken to be about anything real. Thisgives powerful intuitive evidence that someuses of the ordinary languagethere is (e.g., in the context of applied mathematics) do notcarryontological weight.11

3.

If the foregoing is right, untutored (or even tutored) intuition cantadjudicate a choice among candidate CRDs (ones intuitions are tooobviously tainted by ones career choice). So heres a stab at an argument:Granting the claim that our best scientific theory isjust ifiedadditionallysuggests that one should take allthe existential commitments of thattheory to have been justified similarly. Lets call this the global

justification strategy.Its important to note, at the outset, that justification of the truth of a

body of doctrine can come apart from the justification of the existentialcommitments of that doctrine; and this simply because our taking a bodyof doctrine to be truedoes notrequire that Quines criterion be appliedto it to determine what ontological commitments it has.

Indeed, as Ill illustrate briefly, the recent debate over the Quine-Putnamindispensability thesis has focused more on the empirical justifi-

cation of mathematical t ruththan on the justification of the ontologicalcommitments that mathematical truth (given Quines criterion) bringswith it. The move, as I suggested above, has been to undercut ontologicalcommitment to mathematical entities by undercutting the claim that thestatements codifying those existential statements (among others) are true.

One version of this approach grants the indispensability of mathematics




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to empirical science while denying that such indispensability providesjustification: Sober (1993) claims that scientific practice clearly shows thatmathematical statements are justificationally separable from empiricalones because, although scientific tests are designed to decide betweencompeting hypotheses, this is hardly ever in such a way as to place

mathematical claims at risk.Maddy (1992) argues that scientists routinely distinguish between

scientific doctrine they take to be true, and doctrine they take to be merelyinstrumentally valuable for prediction, even though the latter can be justas indispensable for the purposes that scientific doctrine is put to as theformer. Given this, the indispensability of mathematical doctrine forempirical application no longer seems to require its truth.12

Resniks (1995) countermove is to give a version of the Quine-Putnam

indispensability thesis immune to the above objections, to claim, that is,that applied mathematics is not justified (in any sense) by itsindispensability; rather, the truth of mathematical doctrine is presupposedwhen it arises in application. He gives the following argument which Ihave condensed slightly (Resnik, 1995, pp. 17071):

1) In stating its laws and conducting its derivations science assumes theexistence of many mathematical objects and the truth of much

mathematics.2) These assumptions are indispensable to the pursuit of science;moreover, many of the important conclusions drawn from and withinscience could not be drawn without taking mathematics to be true.

3) So we are justified in drawing conclusions from and within scienceonly if we are justified in taking the mathematics used in science tobe true.

4) We are justified in doing science.5) The only way we know of doing science involves drawing conclusions

from and within it.6) So we are justified in taking that mathematics to be true.7) So mathematics is true.

Whats striking about Resniks argument is that, although both thetruth of mathematical doctrine andour undertaking the burden of onto-logical commitment to mathematical entities are explicitly acknowledgedin the first premise, ontological commitment plays no further role in the

argument. And, actually, this should be no surprise: drawing conclusionsis a matter of a relationship between sentences, not a matter of whatentities those sentences commit us to. And so its open to one to acceptResniks presuppositional ploy, to claim that indeed, the indispensabilitythesis commits us to the truthof mathematics without conceding that itcommits us to the existence of mathematical objects as well.13




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Two points should now be clear. First, as suggested earlier, despitethefact that the letter of the indispensability thesis is couched in terms ofontic commitment, and becauseof the (usually implicit) acceptance of theQuinean CRD, debate over the thesis takes place at the sentential level:arguments for or against it are posed in terms of the truth of mathematical

doctrine; and this despite the fact that the major underlying motive forattacking the thesis in the first place is the various epistemic and acausalpeculiarities that mathematical objectsare taken to have. Ontologicalcommitment to mathematical objects on the basis of existential commit-ment is presupposed by all parties to the debate, but itself plays nosignificant role in arguments either for or against the indispensability thesis.

Second, once one refusesto take Quines criterion for granted, andprovided one can show that some significant difference exists between

kinds of posits in a scientific theory, one can deny that the existentialcommitments of a scientific theory are equally justified ontologicallydespite our presupposing the truth of allthe sentences in such a theory.

Its worth adding that Quineans, or at least those who subscribe to hisepistemology of theory-adoption, use broad considerations about theoreticalvalue (simplicity, scope, fecundity, etc.), which gives the impression thatepistemic factors routinely brought to bear by scientific practitioners toevaluate theories are ones indifferently applying to all the ontological

posits of said theories. But detailed examination of the epistemology hereshows that quite significant and systematic epistemic differences betweenthese sorts of posits exist. The much celebrated epistemic and acausalpeculiarities of mathematical posits are actually not metaphysicalproperties of such objects, but a methodological indication of howdifferent our epistemic access to mathematical posits is from our epistemicaccess to non-mathematical posits. In addition, there are good reasons tothink that mathematical posits are introduced into a theory because oftheir structural role in making theoretical manipulation easier. Ive

discussed these matters at length elsewhere.14

4.

The flow of argument in section 3 went like this. We started by examiningwhat we took to be an argument in favor of Quines CRD, namely theglobal justification strategy of showing that all posits of a scientific theory

are justified in the same way. Thus our attention naturally turned to therecent debate about the Quine-Putnam indispensability thesis, where thisparticular claim seems to be in contention, and in particular, to Resniksargument for the thesis, whereupon Quines criterion (or something likeit) popped out as an explicit assumption.

Resnik, of course, was nottrying to provide an argument for Quines




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criterion; and indeed, it now looks like the global justification strategy(or anything like it) as a support for Quines criterion would beg thequestionagainst opponent CRDs. For a theory may be justified by anexperiment, say, but this only justifies the existence of those items thatour already-in-place CRDallows us in pr incipleto admit the theory as

committed to in the first place. Notice that no story of justification,however powerful, allows us to recognize a commitment to neutrinos,numbers, and whatever the connective & refers to, unless weve alreadygranted & a potential ontological-committing role.

One might try to enlist grammatical similarity to protect one or anotherversion of the global justification strategy against the charge of beggingthe question.A llpredicates into which the existential quantifier quantifiesare the same, ontologically speaking; for all such predicates are regimented

translations of grammatically-similar ordinary-language locutions.15 But,frankly, there is no good argument for this. In Quines version of first-order logic, the existential quantifier plays two quite distinguishable roles:an implicational role vis--visconstants, and an ontological role. Weveknown for some time that these roles can be separated;16 and as I said atthe end of section 2, the attitude of scientists towards the use of mathe-matics in scientific languages perhaps shows that the unregimented useof there is already exemplifies such a separation of roles. Furthermore,

as already mentioned, otherwise identical predicates (identical, that is,grammatically, and in how the ordinary-language quantifiers operate withrespect to them) can still be distinguished by whether their extensions fallunder what is taken to be the existence predicate. Consequently,similarity of grammatical role does notrequire similarity of ontologicalrole (accepting thisis alreadyto rule out alternative CRDs, under theguise that one is simply respecting grammatically-natural kinds).17

Its worth stressing that a philosophicaldebate about ontology, about,say, whether mathematical objects exist or not, should not be a debate

about whether certain criteria have been correctly applied or not; it shouldbe a debate about which criteria are appropriate. Once these are decidedon, philosophical debate (in this arena, anyway) is over; there is now onlythe formidable problem of regimenting a discourse, and then reading offontological commitments according to the CRD; there may also be, inlight of the CWE, one or another programof reworking the regimentationof one or another scientific theory (to avoid undesirable ontologicalcommitments otherwise imposed by the choice of the CRD).18

5.

We have been focusing on alternative CRDs which, in a clear sense, arenarrowerthan the Quinean one; and indeed, this is natural, since the brunt




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of the Quine-Putnam thesis has been to force ontological commitment tomathematical objects (on the basis of scientific doctrine) that abstracta-adverse philosophers are otherwise loath to take on. But the criterion isused, by Quine in particular, in other ways: to rule outcommitment toobjects that the use of his CRD does not commit us to. Perhaps we can

find examples of genuine justification for Quines CRD in his polemicsagainst the ontologically profligate.

Quine (1948) seems to utilize two sorts of arguments against the haplesssciolists McX and Wyman. One, employed both against attributes (non-extensional properties) and possibilia, has to do with sloppy individuationconditions for purported entities.19 I propose to leave this well-plowedarea aside, and simply grant that if ones individuation conditions for apurported type of entity are much sloppier than the individuation conditions

for the things we ordinarily take ourselves to be committed to (houses,roses, sunsets), that may be a reason to repudiate ones commitment tothe entities in question. But this doesnt bear on the question of competingcriteria (sloppy individuation conditions can arise, or fail to arise, regardlessof ones CRD).

The other sort of argument Quine regularly employs (and in this respecthes been quiteinfluential) is Occams razor, the dictum that one shouldnot multiply entities unnecessarily. This characterization of the dictum is

open to more than one interpretation, but the primary way it has beenapplied by Quine, and those who have followed him, is to formulatescientific theories in a way that involves existential quantification over thesmallest number of kinds of entities possible. This translates into arequirement that, all other things being equal (such as simplicity), oneformulates ones theories so that there are as small a number of logicallyinequivalent instantiated predicates as possible. This is how wellunderstand Occams razor in what follows.

The first point to make is that, surely, the razor, however construed, isnot a uncontestable principle of first philosophy: it needs justification.

Justification, perhaps, is not far to seek (given ourinterpretation of therazor, anyway). I f one theory T requires fewer instantiated logicallyinequivalent predicates than another, T*, where the two theories areotherwise the same, thenT , in some sense, is easier to manipulate than T*.One, after all, needs to draw implications of the theory with regard to (andon the basis of) a smaller number of independent predicates: in certaincases, the number of primitives of the language (axiomatically) is smaller.20

But its hard to see why this sort of principle (with this sort of justifi-cation) can be used againstmore generous criteria than Quines. Considerthe scorned McXs position that there are attributes. Quine has him say:

There are red houses, red roses, red sunsets; this much is prephilosophical common sense

in which we must all agree. These houses, roses, and sunsets, then, have something in




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common; and this which they have in common is all I mean by the attribute of redness.

(Quine 1948, pp. 910)

Well, on one view of McXs suggestion, a different criterion thanQuines is notbeing offered. Instead, were being given an inference rule

which licenses us to infer, from a claim that a predicate is instantiated,that something elseexists too, namely that property (attribute, whatever)that the items (the predicate holds of) have.21 Now perhaps we can objectto a language with an inference rule of this sort by means of Occamsrazor as we understand it here. For one needs to know what all these newexistential commitments are doingfor us; and were within our rights, onemight think, to rewritethe theory eliminating such an inference rule, ifthe result is as good.22

But there is anotherway to understand McX, and this is as offering adifferent CRD: one is committed to attributes and properties even ifonecant explicitly assertones commitment via the existential quantifier. Oneis committed solely by virtue of possessing meaningful predicates, andone can seethat one is so committed even if one cant quite sayit.

Ive deliberately alluded to Wittgensteins (1961) notorious say/showdistinction to describe the possibility in question. Of course, its alwayswithin ones right to make explicit ones tacit commitments by augmentingthe language (if one can); although as soon as thatsdone, one is opento an attack by Occams razor. So, interestingly, Occams razor, as wehave interpreted it, actually supplies motivation for suppressing explicitacknowledgments of ones ontological commitments when the result ofdoing so is a theory with a larger number of instantiated materiallyinequivalent predicates.

There is another way of understanding the alternative criterion beingexplored here, however: one isexpressing ontological commitments to theattributeREDwhen one says houses are red; one just isnt doing it thesame waythat one does by saying there is redness. And if it is suggestedthat ontological commitment should always be recognized by the sameidiomatic means (in a regimented theory), a goodresponse is this: thisrequirement can saddle us with what are (given Occams razor) otherwiseless acceptable theories.23

Alternative CRDs are proving peculiarly evasive with respect to philosoph-ically respectable arguments that can decide among them: if one alreadyunderstands the ontological commitments of a theory a certain way, one can

claim that ontological commitments have been justified when a theory isjustified; so too, once we have been told what CRD is in place, we can justifya version of Occams razor (via one or another version of the comparativesimplicity of theories). But its hard to see how any form of Occams razorcan be used to adjudicate amongCRDs, because its hard to see how such aversion of Occams razor could be philosophicallyjust ified.24




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The attempt to use Occams razor to adjudicate among alternative CRDsis simply confused: the razor instructs us to choose that theory with theleast number of kinds of entities (all other things being equal). But onecant use anything like thatto adjudicate among different CRDs; one hasto apply one or another criterion first, and only thenOccams razor.

I suggested at the outset that the debate over the Quine-Putnamindispensability thesis is philosophically indeterminate, and from theforegoing discussion, it looks clear why: a CRD is so fundamental thattheres no hope of slipping a rationale underit. In a way similar to howany argument supporting the use of logical principles would need (onewould think) to employ those very same logical principles it was providing

justification for, so too, arguments supporting one or another CRD seemto either beg the question against the opponent, or be intelligible to begin

with only if that CRD is already in place. The natural conclusion is thatthere is no bedrock belowones CRD, no place to get a foothold to applypressure against an opponent.

But the analogy with logic only goes this far and no further. Animportant difference is that choosing an alternative logic almost alwayshas real and profound effects when it comes to applications (consider thechoice between intuitionistic and classical logic, for example, and theimpact of the choices on ones mathematics); this can provide principled

means for choosing among such alternatives. Unfortunately, choosing analternative CRD has no significant effects whatsover (and this makes achoice of such a criterion insignificant in a way that a choice among logicalsystems never is). The reason is that one can mix and match CRDs withCWEs.

Heres an illustration. Suppose I think a suitable CWE is to linkexistence to causal efficacy. Under such circumstances, it really wont doto adopt QuinesCRD, as that puts me at a distinct disadvantage (nowI have to rewrite my regimented discourse, or perhaps treat some of it as

false). The right move here is to square my CWE with my CRD, to simplydeny, that is, that recognizing the existential commitments of a discoursesuffices for recognizing the ontological commitments. Perhaps I shouldadopt a predicate view of the ontological commitments of a discourse,say, treat only those terms falling under a certain predicate asontologically committing.

But its precisely at this point that the apparent tools philosophers havefor adjudicating debates in this area evaporate; for now theories with

exactly the same syntactic and semantic properties can be usedto draw rather different conclusions about what one isjust ifiedin takingto exist. In other words, all the competing pairs of matching CWEs andCRDs are entirely on a par with regard to the pertinent evidence (namely,the scientific theories we accept). As long as one chooses a CWE whichdoesntsquare with ones chosen CRD, one can think something substantial




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is afoot: regimentation of scientific discourse becomes frought with philo-sophical complexity. But once one sees how such complexity is due to aCWE operating at cross purposes with a CRD, such an impression vanishes.

6.

So it looks like we must conclude that not only is it philosophicallyindeterminate what CRD is suitable, but that the question of what thereis, understood in its philosophically broadest sense, is equally philosophicallyindeterminate.

I hasten to add that, by this last phrase, I dont mean that what thereisis philosophically indeterminate; for I glibly talk about what there is,

based on my knowledge of science and the world around me (pretty muchthe way you do). I say, there are chairs, there are neutrinos, thereare prime numbers, just like you. Its only when someone asks me, butdo numbers reallyexist? that Im taken aback (and for good reason):thatsthe question which is indeterminate.

One possible way out is to open a pathway to evaluating CWEsindependently of CRDs. This can be done either by settling on a CRDindependently of the question of what CRE one should adopt, a project

we have been vainly attempting throughout this paper. Or vice versa(something we havent tried yet).Quine, as I have suggested, settles on a CRD, and lets science do the

rest. When pressed, as noted in note 10, he invokes the triviality of hischoice of CRD. Indeed (although its a bit desperate), one might claimfurther that his CRD is trivial because its based on a purely technicalmove that makes sense only within certain sorts of regimented languages,and that it draws none of its philosophical significance from how weinterpret (ontologically-speaking) idioms in the ordinary vernacular. But

claims of triviality cant handle competitors: as we have seen, there arealternative CRDs, and because of the way these interlock with alternativeCWEs, Quines choice turns out to be philosophically tendentious.25

The other route may seem more promising, especially to those whowant a greater role for philosophical argument in metaphysics than theQuinean picture offers. One can argue that the forgoing discussion hasshown only that the logicians gambit of first settling on a CRD, and onlythen, if at all, turning to the issue of what CWEs are appropriate for staking

out what exists, is misguided (if only because it is so metaphysicallytendentious). Instead, we must first provide an appropriate CWE, andonly then determine what a suitable CRD will look like.

Indeed, perhaps a case can be made for the priority of settling on CWEsfirst, since after all, what motivates so much work in philosophy ofmathematics is precisely that the Quinean CRD fits so badly with




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conflicting CWEs that other philosophers explicitly and implicitly arecommitted to.

One should not overlook how radical this suggestion really is, however:one is not just rejecting the logicians request to go first, one is also denyingthat scientific discourseis the sole determinate ofwhat there is. Something

else, metaphysical principles of some sort perhaps, are going to be neededto provide a choice among the competing CWEs.

Reasons of space prevent me from saying very much about this suggestionnow, but I think its prospects are notgood. Ill briefly and sketchilyindicate why I think this and leave details for later work. I claim thereare only two places one can look for ways of adjudicating amongcompeting CWEs. The first is, broadly speaking, showing how ontologicalcommitment is linked to explanationso that one must take a certain sort

of object to exist in order to keep the cogency of the sorts of explanationswe take seriously. This route (I claim) is blocked by the fact thatexplanation operates at the sentential level, and is indifferent to how wetease out the ontological commitments of the sentences which provide theexplanations we take seriously.

The other route operates by a kind of canvassing of ontologicalintuitions of various sorts. Unfortunately, such intuitions in practice seemto be little more than intellectual prejudices. They are not universally

shared (not even among similarly-trained philosophers); and given thatsuch intuitions are used as a basis for argument, rather than themselvesbeing open to justification, it seems unlikely they compel assent to aparticular CWE. How are we to use intuitions to adjudicate between thephysicist convinced that mathematical objects are just the non-existentreifications of a mathematical formalism, and the mathematician who isconvinced of the existence of these things? The disagreement, after all, isbased, to begin with, on conflicting intuitions.

7.

The philosophical indeterminacy weve been exploring here, with respectto CRDs and CWEs isnotas horrible as it may sound. As Ive mentioned,it isnt as if, after all, we cant wonder whether there are even primes otherthan 2, or more than two genetically distinct kinds of porcupine, and soon. Thosequestions all make sense.

And, along more broadly philosophical lines, it isnt as if we cant askwhat sorts of considerations go into legitimizing existentialcommitmentsto abstracta, and whether they are different from the considerations thatlegitimate empirical commitments.

Indeed, we can even note, and avoid, certain kinds of explanatoryblunders by making the sorts of distinctions between existential




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commitments that I suggest. For example, if someone says that a goodexplanation for why he realized that 2 + 2 = 4 is that, in fact, the numbersin question havethat relation and he intuitedit, we can complain that thisexplanation is not acceptable, notbecause mathematical objects dontreally exist (whatever thatwould mean), but only because abstracta, and

truths about them, are not discovered in anything like a quasi-perceptualway (i.e., talk of intuition is a bad explanation because it covers upprecisely what needs to be explained, and in just the ways that talk ofperception in the empirical context does not).

So too, if one inaugurates a nominalist-style program on the epistemicgrounds that there are genuine problems explaining how our knowledgeof mathematical objects can be made to fit with general constraints onepistemic stories: that such stories require, say, a reliabilist connection

between abstractaand those who know about such abstracta, we can,again, tease apart the various kinds of existential commitments inquestion, and show that the epistemic practices of scientists towards thevarious kinds of commitments are significantly different. We can explain,that is, the epistemic datum that would-be nominalists are concerned with;and indeed, explaining that datum is, I think, the philosophers job, anda job that can be done perfectly well without getting embroiled in broadly-construed questions about what exists.

In other words, the important question, the important philosophicalquestion, about mathematical objects is notwhether (in contrast withrobuster empirical objects) they exist or not, but what kind of epistemicstory we should tell about what mathematicians know, how they knowwhat they know, and what story we should tell about the role mathematicsplays in our conceptual scheme doing so will simultaneously reveal whatsort of roleexistentialcommitments to mathematical objectsplay (relative,of course, to one or another regimentation of scientific discourse); but indoing this, there is no need (and no way) to evaluate whether such objects

really exist or not.

8.

In the days of yore, our forefather Carnap (1950) distinguished betweenmeaningful questions and meaningless ones. Ontological questions, inparticular, divided into external ones and internal ones. External questions

are apparently asked about what exists and what doesnt independentlyof any linguistic framework. Such questions, if sensible, are not to beinterpreted ontologically, but rather are pragmatic questions aboutwhich framework (conceptual scheme, formal language) one should choosefor one or another purpose. Internal questions are asked within one oranother framework; these questions, although sensible, do not carry the




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philosophical weight that ontological questions, in the broad sense, aresupposed to. If one persists in asking, Are there prime numbers? outsideof any such framework, the question suffers from lack of a context tomake it meaningful. But ask the same question within such a framework,and an answer is philosophically trivialin the sense that its answer isstipuated once a linguistic framework is chosen (although, despite thestipulative nature of the answer, it might take work to establish its truthvalue). Carnaps criterion for ontological commitment, being wedded toa conceptual scheme chosen on the basis of convenience, really is aphilosophically trivial one; for, presumably, the specific criterion one usesto evaluate commitments (when carried out in an internal way) comesautomatically with the framework itself.26

Im sympathetic to the changes Quine wrought in this picture: do theregimentation of all of science, and mathematics applied to that science,within one formal scheme, and use one topic-neutral logic across it; thisbetter captures what goes on in science than the Carnapian vision ofpiecemeal formalized systems tailored for particular purposes. A lthoughthere are reasons to doubt this Quinean modification suits our entireintellectual heritage,27 it works quite nicely when it comes to the interestingamalgam of science and applied mathematics that our empirical science

operates with, and that Quine is primarily concerned with.But Quine went further: he repudiated Carnaps assimilation of thebroad philosophical concern with ontology (metaphysics) with themeaningless sort of question. Ontological questions, to the extent theyare reformulatable withinour conceptual scheme, are meaningful. Whatprevented this fromsimplybeing a terminological decision to call Carnapsinternal questions ontological (with the added caveat that there is onlyoneon-board in-progress conceptual scheme to pose these questions in)

was Quines wedding such ontological issues to the existential quantifiervia his criterion: in doing so, he achieved a technically crisp criterion (but,as I have tried to show, at the expense of its Carnapian triviality).

Carnap raised worries with Quines importing the traditional philo-sophical term, ontology to describe the role he gave the existentialquantifier in evaluating what a discourse is committed to (Carnap 1950,p. 215, n. 5). Quine, in turn, believed that Carnaps separation of externaland internal ontological questions relied on a bogus analytic/synthetic

distinction.28

Quine is widely taken to have won the battle on this; butCarnaps impression that there is something trivial about ontologicalcommitment was deeper than the tools he used to support that claim.

Department of PhilosophyTufts University




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NOTES

* This paper is dedicated to the memory of George Boolos. He started me in this directionwhen he wrote me (back in 1992) that: There are a number of writers, myself included,who believe that there is no version of platonism that is either obviously true or obviouslyfalse. That is, there is no interesting doctrine deserving the name of platonism to be defended

or refuted. This claim strikes me as both true and in need of explanation. M y thanks toArnold Koslow, Nathan May, and Michael Resnik for their comments on an earlier versionof this, and also to the audience at the Graduate Center on 16 October 1996, especially

Jerrold J . Katz, for the same reason.1 Quine (1948) and Putnam (1971) are classicus loci.2 Putting the doctrine this way allows wriggle-room. Scientific theories, couched as they

are in an enriched vernacular, do not (grammatically-speaking) transparently reflect theirexistential implications. In Quinean hands, these existential implications are read off of first-order regimented translationsof scientific theories; and in such a context (relativeto aparticular translation) the doctrine, and its implications, are technically crisp: the ontological

commitments of a theory Tare directly read off of sentences of the form (x)Sdeducedfrom T. See the discussion of Quines criterion in Gottlieb (1980), chapter 2. But whenregimentation is allowed other resources (e.g., higher-order logic, modalization,substitutional quantification), the impact of Quines criterion is murky at best. My approachto the indispensability thesis is designed to avoid this particular thicket.

A word about terminology. Existential commitment, as we have seen, is syntacticallycharacterized. Ontological commitment, by contrast, only arises relative to a criterionforsuch commitment: something is taken to exist on the basis of a criterion employed to detectsuch commitment in a discourse.

3 I too have contributed to the subject. See my 1997a and 1997b. But I ve been deliberatelycoy in those papers about whether I favored the thesis or not; this paper explains why.

4 Van Fraassen (1980) seems to takesusceptibil it y to observat ionto be a CWE. Hacking(1983) is tempted by causally efficacious, but eventually settles on something even narrower:used by us to intervene in phenomena. Presence in space and timeis another commonsuggestion; and its also one Quine (1948) explicitly argues against.

Its sometimes difficult to distinguish when a philosopher is supplying an ontologicalcriterion, as opposed to merely airing epistemic scruples; but I believe the cases Ivementioned are clear examples of ontologicalstrictures, although motivated (in some cases)by explicit epistemic views.

5

He calls it a more explicit standard (1948, p. 13) which we now have.6 I suspect Quine would deny its the philosophers or logicians role to dictate CWEs.Thatrole belongs to the scientist. Or better yet, the scientist simply determines whats true,and the Quinean logician then reads off what exists from a regimented version of whatstrue. So, actually, its nobodysjob to dictate CWEs.

7 Although the above is a strategy attempted by some, its proven to be really hard: nowonder that Quine, despite his nominalistic lusts, has never actually embracednominalism.

But another strategy has become quite popular of late: treat sentences with criterion-violating existential commitments as false, and then tell a story why these otherwise falsesentences are instrumentally valuable for finding truths. This move is relatively explicit in

Hacking (1983), van Fraassen (1980), Cartwright (1983), and Maddy (1994). Im scepticalit can work for mathematical posits because I doubt that, in physics for example, one canisolate the offending sentences from the rest of physics in such a way that leaves anythingto be true. Notice, however, that one powerful motivation for the approach is an implicitacceptance of something like Quines CRD.

8Tarski (1944) noted that his approach is neutral in regard to the various notions oftruth available. Its ontically neutral as well.




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9 Philosophical tradition allows more leeway with this kind of talk if we switch to real.There are numbers, but they arent real, sounds better, and has antecedent philosophicalresonances. Notice, in any case, that the problem doesntarise in the regimentation properunless one insists on subvocalizing appearances of the existential quantifier with the ordinarylanguage phrase, There is.

10 Its this which allows Quine (1981, p. 175) to take his criterion as trivial, and write:The solemnity of my terms ontological commitment and ontological criterion has ledmy readers to suppose that there is more afoot than meets the eye, despite my protests.Recall that he has also written (1970, p. 89): What there are, according to a given theoryin standard form, are all and only the objects that the variables of quantification are meantin that theory to take as values. This is scarely contestable, since (x) and (x) are explainedby the words each object xis such that and there is an object xsuch that. Some languagesmay have no clear equivalent of our existential phrase there is, nor of our quantifiers; butsurely there is no putting the two asunder.

11 See my 1997a for a fuller explication of this point.12

Both these strategies require that one somehow isolate the mathematical doctrine thatone wants to treat as false from physical doctrine that one otherwise takes to be true. I vealready expressed doubts about the possibility of doing this.

13 Resnik (1995, p. 170) knows this. He writes: ... the claim in (1) that scientists presupposemathematical objects depends upon taking the mathematical parts of their scientific writingsat face value and applying something like Quines criterion of ontic commitment.

14This topic is the burden of most of Part I of my 1994, as well as of my 1997a and1997b.

15 For whether such a locution sustains ontological weight or not turns on its semantics,and that, in turn, requires us to honor whatever results the science of linguistics brings to

bear on the topic. But how could linguistics legislate a semantic difference betweengrammatically-indistinguishable locutions? One sees a version of this argument in Benacerraf(1973, p. 408).

16 Indeed, this insight is behind debates over substitutional quantification between Quine,Barcan-M arcus, and others.

17 Its surprising, perhaps, that the Benacerrafian requirement that identical grammaticalroles require identical semantical roles (and therefore (!) identical ontological status) hasturned out to be a disguised version of the old Humean/Kantian claim that existence isnot a predicate.

18This is how to understand work such as Field (1980), or Hellman (1989): they have

already decided whatontologicalcriteria they want to use, and they are already presupposingsomething lik eQuines CRD. This, perhaps, makes their programs unappealing to those ofus who dont find the choice of criteria convincing.

19 Quine 1948, p. 4: How many possible men are there in that doorway?20 Nevertheless, there are contexts, such as that of pure mathematics, where Occams

razor, construed this way, isnt relevant. See my 1994.21 Actually, the implicit principle is stronger than I indicate: the property in question exists

whether the predicate is instantiated or not. We leave this particular wrinkle aside.22This isoneway to understand Quines objection to McX (1948, p. 10): That the houses

and roses and sunsets are all of them red may be taken as ultimate and irreducible, and it

may be held that McX is no better off, in point of real explanatory power, for all the occultentities which he posits under such names as redness.

23 Note: The CRD being explored at the moment is neither one which reads suchcommitments off the quantifiers, nor one that reads them off of a privileged (existence)predicate, but one which reads them off of the presence of anypredicate at all.

24 Notice the same problems with Occams razor would arise if we tried to use it againstQuines CRD, and in favor of some narrower version (say, an existence-predicate version).




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The considerations wed use to formulatetheories would remain the same: so the debatecould turn only on how we read off ontological commitments fromtheories which areotherwise semantically and syntactically identical. This leaves us without tools to debatewith. I ll expand on this point momentarily.

25 I stress again the other factors that can make the triviality thesis seem plausible: (1)the tendency to readthe existential quantifier as a direct translation of the ordinary there

is; (2) the related tendency to read Tarskian semantics as giving a straightforwardontological interpretation.

26 Alas, this is notCarnaps view. Disastrously, he accepts Quines way of readingontological commitment from the variables in a conceptual scheme (see Carnap 1950,p. 214, n. 3). I stress again: there is a strong tendency to read ontic commitments in astandard way off of what, after all, is only a formalism. (In calling it a formalism, I dontmean to understand it as uninterpreted: it is still a formalism even if it comes equippedwith Tarskian semantics.)

27 In particular, I think the Carnapian approach fits more nicely than Quines picture ourpractice in puremathematics. See my 1994 for a specific discussion on this matter.

28 Quine (1951), pp. 4546, and Quine-Carnap (1990), p. 406.

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Azzouni, J . (1994).M etaphysical myths, mathematical practice: the ontology and epistemologyof the exact sciences. New York: Cambridge University Press.

(1997a). Applied Mathematics, Existential Commitment and the Quine-PutnamIndispensability Thesis, Philosophia M athematicaVol. 5, pp. 193209.

(1997b). Thick Epistemic Access: Distinguishing the Mathematical from theEmpirical, Journal of Philosophy94, pp. 47284.Benacerraf, P. (1973). Mathematical truth, Journal of Philosophy70, pp. 66179.

Reprinted in Paul Benacerraf and Hilary Putnam (eds), Phi losophy of mathematics, 2ndedn (pp. 27294). Cambridge: Cambridge University Press.

Carnap, R. (1950). Empiricism, semantics, and ontology, Revue I ntern. de Phi l. 4, pp.2040. Reprinted in hisM eaning and Necessity. Chicago: The University of Chicago Press(1956), pp. 20521.

Cartwright, N. (1983). H ow the laws of physics li e. Oxford: Oxford University Press.Chihara, C.S. (1990).Constructibil it y and mathemati cal ex istence. Oxford: Oxford University

Press.Field, H. (1980). Science without numbers. Pr inceton, NJ .: Princeton University Press.Gottlieb, D. (1980). Ontological economy: subst it utional quantification and mathematics.

Oxford: Oxford University Press.Hacking, I . (1983). Representi ng and Intervening. New York: Cambridge University Press.Hellman, G. (1989). M athematics without numbers. Oxford: Oxford University Press.Maddy, P. (1990). Realism in mathemati cs. Oxford: Oxford University Press. (1992). Indispensability and practice, Journal of Philosophy89, pp. 27589. (1994). Taking naturalism seriously, in D. Prawitz, B. Skyrms, and D. Westersthl

(eds) L ogic, M ethodology and Phi losophy of ScienceIX, pp. 383407.

Putnam, H. (1971). The philosophy of logic, reprinted in his M athematics, matter andmethod. New York: Cambridge University Press 1975, pp. 32357.

Quine, W.V. (1948). On what there is, reprinted in his From a logical point of view.Cambridge, Mass.: Harvard University Press 1980, pp. 119.

(1951). Two dogmas of empiricism, reprinted in his From a logical point of view.Cambridge, M ass.: Harvard University Press 1980, pp. 2046.

(1970). Philosophy of L ogic. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.




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(1981). Responses, in hisTheories and things. Cambridge, Mass.: Harvard UniversityPress, pp. 173186.

Quine, W.V., and R. Carnap (1990). Dear Carnap, Dear Van: The Quine-Carnapcorr espondence and relat ed work Ed. R. Creath, Los Angeles: University of CaliforniaPress.

Resnik, M. (1995). Scientific vs. mathematical realism: the indispensability argument,Philosophia M athematica(3), 3, pp. 16674.

Sober, E. (1993). Mathematics and indispensability, Philosophical Review 102, pp. 3557.Tarski, A. (1944). The semantic conception of truth, Phi losophy and Phenomenological

ResearchIV.Van Fraassen, B. (1980). The scientific image. Oxford: Oxford University Press.Wittgenstein, L . (1961). Tractatus L ogico-Philosophicus. Trans. D.F. Pears and B.F.

McGuinness, London: Humanities Press.



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Azzouni, J. on 'on What There is