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Trystan King
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Kirk Ludwig

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Kirk Ludwig
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Date Created: 09/18/15
Spring 2009 PHP 5785 Camap and Quine on Ontology K Ludwig 1 Camap s Empiricism Semantics and Ontology 2 On What You Think There Is This is a quick overview of Camap s and Quine s views on ontology late 1940s and early 1950s starting with the exchange between Camap and Quine over Empiricism Semantics and Ontology Here we see both continuities and evolutions in Camap s thinking and we begin to see the ways in which Quine s thinking though heavily in uenced by the Vienna Circle takes its own distinctive course 1 Camap s Empiricism Semantics and Ontology In Empiricism Semantics and Ontology Camap distinguishes between internal and external questions by reference to what he calls linguistic frameworks A linguistic framework is a vocabulary together with a set of rules for using it where the vocabulary is used to talk about a kind of thing expressed by some most general predicate of the kind eg number physical object introduced together with a distinctive style of variable entities of the kind Internal questions are questions about a particular kind of entity asked about them after one has adopted a linguistic framework for talking about such things Camap apparently thinks that in introducing a linguistic framework one introduces rules sufficient to determine in principle the answer to any question asked about entities which can be talked about in the vocabulary of the framework1 This is a legacy of his veri cationism Given this any internal question admits of an answer For example in the framework for talking about numbers if we ask whether there are any prime numbers between 10 and 20 we can readily give an answer by following the rules introduced with the framework there are four prime numbers between 10 and 20 namely ll l3 l7 and 19 so there are prime numbers between 10 and 20 It follows from this that there are numbers and so the internal questioni Are there any numbers ilikewise admits of an affirmative answer 1 This comes out in the following remark about the need to treat certain questions as external questions I feel compelled to regard the external question whether there are numbers as a pseudoquestion until both parties to the controversy offer a common interpretation of the question as a cognitive question this would involve an indicate of possible evidence regarded as relevant by both sides New Essays in Philosophical Analysis ed by Feigl Sellars and Lehrer p 594 2 Camap makes similar remarks about the thing language but I don t believe in that case that he is committed to saying that it is analytic that there are physical objects as it is analytic that there are numbers We don t have a system of special referring terms for physical obj ects that are treated as a matter of linguistic convention as referring it s not clear this is so in the case of numerals either but put that asideiwe don t have anything comparable even so in the case of the thing language Carnap does think that we can find the answer in principle to any internal 1 Spring 2009 An external question is a question asked by a philosopher Are there really any numbers though the wilely philosopher asks And we are at a loss to know how to respond for it is apparent that he will not take as an answer something like Yes because eg ve is a number For he will say But that just begs my question for it is precisely whether five refers or refers to a number which is what I am asking But now it is clear that none of the normal procedures for answering these questions will satisfy him Camap suggests in effect a diagnosis for this kind of dialogue The philosopher has a genuine sort of concern but he has misunderstood its source Of course ve is a number for as soon as we understand the number framework we understand that for Five is a number is analytic So the philosopher must be asking a question which does not presuppose the adoption of the rules of the number framework But if he has not done this yet he cannot be really asking an object level question at all What he must be concerned with is whether we should adopt the number framework Thus his question is not about numbers but about the number framework and his concerns are to be answered not be showing that numbers exist for that is something which comes up only after we have adopted the number framework but by showing that adopting the number framework is useful So the question the philosopher is concerned with turns out to be a practical question which he has confused with a theoretical question He asks a question intended to be prior to the adoption of the appropriate framework but while using the vocabulary of that framework no wonder it appears that we cannot respond adequately to his doubts Or so the story goes Perhaps the skeptical philosopher does have a response to Camap He can say Well according to the particular framework for numbers that you have adopted it is trivial that there are numbers But I actually have my own linguistic framework for talking about numbers and according to the rules of that framework it is quite doubtful that there are any numbers Therefore you cannot tell me that I am confused and that my question can simply be dismissed This does seem to be a response the skeptical philosopher could make But would his skeptical conclusion perhaps that there are no numbers really then show that there was anything wrong with Camap claiming that ve is a number and therefore there are numbers Consider a case in some ways parallel allegedly due to Camap Let us call a on this page n object Now consider How many objects are there in this diagram Clearly there are four Or are there Consider a different conceptual scheme or framework We count in this new framework any and any pair of distinct s as objects as well Now how many objects are there in this diagram Clearly there are ten objects What should we say a We might say well one of these view must be wrong for four is not ten and if there are only four objects there then there are not as many as ten b We might say but that can t be right since we have just seen given the shift in question in the thing language even the categorical internal question are there any physical obj ects But we must do so by empirical means e g by pointing out that this is a hand or a cup and that hands and cups are physical obj ects so that there are physical objects Spring 2009 framework that there isn t after all any incompatibility So what we have really discovered is the relativity of ontology and hence of truth to a conceptual scheme Whether there are four or ten objects there depends on one s conceptual scheme Or we could say c Both a and b are wrong for they both equivocate on the word objec What the two different linguistic frameworks give are two different definitions of object so they do not con ict contrary to a but nor can we say that we ve discovered the relativity of ontology to a conceptual scheme in the sense that the number of objects of a given kind there are depends on one s conceptual scheme or linguistic framework for here we are not talking about a single kind of object but two different kinds Is not the skeptical philosopher s alternative framework for talking about numbers in the same boat It might be said that Camap is committed to a kind of idealism about numbers and objects This is a charge that Barry Stroud makes in The Signi cance of Philosophical Skepticism in chapter V on Camap The charge is that if Camap is right then whether there are e g mountains in Africa or whether there are not for that matter depends on whether or not we adopt the thing framework If we do adopt it then we follow empirical procedures and conclude that there are mountains in Africa If we do not then it does not even make sense to say it That is why the philosopher s question asked external to the appropriate framework doesn t make sense Is Camap committed to idealism That hinges on the answer to questions like on the assumption of Camap s view Do physical objects exist independently of our adoption of the thing framework If the answer is yes Camap is not committed to idealism if the answer is no he is There are three responses one could make to the question whether Camap is committed to idealism 1 Yes for the reasons given above ie surely whether it even makes sense to say there are mountains in Africa depends on our adopting the thing framework so the answer to is no 2 No because it might be said that whether the question whether there are mountains in Africa has an affirmative or negative answer is determined independently of our adopting the thing framework since the rules for the framework determine that and those are independent of our adopting them so the answer to is yes 3 Neither yes or no because doesn t even make sense One might champion the third response on the grounds that what exists means depends on what linguistic framework one is talking in and yet here we are attempting to use exists to apply to physical objects and frameworks independently of relativizing it to either framework in particular There is perhaps a ground for this response in what Camap says about the introduction of a linguistic framework for he says that we introduce a special style of variable to range over the kind of entities that fall in the extension of the category term introduced with the framework That means that when we formulate an existential sentence in the new framework we use a special style of variable say script letters to indicate something about what values the variables can take If we carry through this procedure for all our different basic kinds of things frameworks roman letters and numbers script letters for example then we will nd ourselves saying things like Spring 2009 Elxx is a number Elxx is a framework But here the existential quanti ers receive different interpretations since the different styles of variables represent a restriction on the range of the variables and so constitute a different interpretation of the quantif1ers So the charge would go when we attempt to say what does we equivocate on exists in much the same way that b did in our earlier discussion of objects Query is this right Now consider the following suggestion that Camap s view makes expanding our ontology too easy If pragmatic considerations guide the choice of a linguistic framework then perhaps a framework could be judged a good one to adopt because it made us e g happier than we would be otherwise For example acceptance of the framework in which the following sentences are treated as analytic might be thought by many to lead to happier lives FS Angels are supernatural beings God is a supernatural being God is omniscient omnipotent and supremely benevolent There are angels Supernatural beings are not located in space and time Suppose we adopt FS Then we ask are there any supernatural beings Well God is a supernatural being so there are supernatural beings Does God exist Well God is a supernatural being so clearly God exists Is there an omniscient omnipotent and supremely benevolent being Well if God exists he is omniscient omnipotent and supremely benevolent God exists Therefore there is such a being Suppose someone is skeptical however Suppose someone says I know that you have this linguistic framework and that in it you take as definitional that God is omniscient etc but that s all about words What I want to know though is whether God really exists Are there really any angels Ifwe adopt Carnap s view are we then to regard this as a pseudoquestion and provide the skeptic with philosophical therapy until he comes to see that the question he really wants to ask is a practical one properly posed in the formal mode of speech And then does the skeptic s complaint come down to the charge that FS is not useful But there are certainly some ways in which it is useful or at least has been argued to be so For example it is often cited as a nonepistemic virtue of religious belief that it makes people more charitable than they would otherwise be and that it makes them more content with their lives because it holds out some hope of their surviving the destruction of their bodies the inevitable prospect of which it is said would otherwise rob their lives of all meaning or significance And by the way what of the Absolute which is both perfect and lazy To end let me turn brie y to Quine s criticism of Camap Quine charges that Camap s distinction between internal and external questions rests on the distinction between category and subclass questions It begins to appear then that Camap s dichotomy of questions of existence is a dichotomy between questions of the form Are there soandsos where the soandsos 4 Spring 2009 purport to exhaust the range of a particular style of bound variables and questions of the form Are there soandsos where the soandsos do not purport to exhaust the range of a particular style of bound variables Let me call the former questions category questions and the latter ones subclass questions I need this new terminology because Camap s terms external and internal draw a somewhat different distinction which is derivative from the distinction between category questions and subclass questions The external questions are the category questions conceived as propounded before the adoption of a given language and they are Camap holds properly to be construed as questions of the desirability of a given language form The internal questions comprise the subclass questions and in addition the category questions when these are construed as treated within an adopted language as questions having trivially analytic or contradictory answers p 599 Quine s criticism of the distinction rests on a criticism of the signi cance of the categorysubclass distinction upon which he argues it rests Since that distinction is made in terms of whether there is a distinctive style of variable introduced for the soandsos we are asking about the distinction can be signi cant only if we can attach some signi cance to the introduction of a special style of variable for a kind of entity However introducing a special style of variable appears to be a purely notational convenience which is in principle dispensable For example if we introduce as above script variables to range over numbers then we can write there is a prime number between 10 and 20 as follows Elx10 lt x lt 20 amp x is prime where the use of the script variable restricts the range of quanti cation However we can equally well say the same thing without the use of a special style of variable Suppose we use roman letters as variables that range over everything Then we can equally say Elxx is a number amp 10 lt x lt 20 amp x is prime Elx x is a number10 lt x lt 20 amp x is prime Similarly we could translate a universally quanti ed statement such as Vxx has a successor into Vxx is a number 3 x has a successor Vx x is a numberx has a successor The use of a special style of variable achieves some economy of expression but does not give us new expressive resources If the categorysubclass distinction can be eliminated by a shift to a language which eliminates a special style of variable but which does not restrict what we can Spring 2009 say then it cannot be of any philosophical significance3 Does this criticism undermine Camap s distinction The passage that Quine focuses on in Camap s article is the following one describing the procedure for introducing a new linguistic framework as consisting of two steps I quote it here together with a sentence that appears earlier in the same paragraph with italics added for emphasis The acceptance of a new kind of entities is represented in the language by the introduction of a framework of new forms of expressions to be used according to a new set of rules The two essential steps are the following First the introduction of a general term a predicate of higher level for the new kind of entities permitting us to say of any particular entity that it belongs to this kind e g Red is a property Five is a number 9 Second the introduction of variables of the new type The new entities are values of these variables the constants and the closed compound expressions if any are substitutable for the variables With the help of the variables general sentences concerning the new entities can be formulated Clearly Quine has focused on only the second step As he notes the introduction of a special style of variable cannot of itself provide the means to make a signi cant distinction between internal and external questions But there is more to Camap s picture than this and the other part seems to be more important After all the introduction of a special style of variable depends upon the introduction of a new general term in terms of which the special style of variable is introduced The category subclass distinction can be drawn in terms of the general term that is introduced A question that purports to exhaust the extension of the new general term is a category question and one that does not is a subclass question This can hardly be called a matter of notation since it is not a matter of notation whether one has introduced a new general term together with a new set of rules This leaves Camap with an important question namely which general terms should be treated as category terms presumably is prime wouldn t count But despite there being open questions it seems clear that Quine s attack here is unsuccessful In the end Quine says that the real dispute he has with Camap is over whether there is a tenable analyticsynthetic distinction Ifthere is Quine seems to suggest then Camap can talk about semantic rules for the use of expressions that enable us to settle unequivocally in principle the truth of sentences about a certain kind of entity If there is not then we cannot make sense of a linguistic framework of the kind Camap has in mind whose rules are stipulative and fix the meanings of the expressions in the new framework Then any decision about the acceptance of a kind of entity becomes connected with its contribution to the success however conceived of what must be conceived as one overarching empirical theory of the world I 3 Quine says that one would have to adopt type theory to avoid this criticism This would be to hold that it is nonsense to predicate some things of some types of object eg the number 2 is yellow on this view would be nonsense rather than false Quine thinks the main motivation for type theory comes from the aim to avoid paradox in mathematics and he thinks there are better ways to do that than to adopt type theory so he rejects this as an adequate response He also argues however that even the adoption of type theory for the purposes for which it is introduced is not necessary for one can do the same work using the guiding idea to eliminate from the language formulas which type theory regards as meaningless but then formulate the language without any distinctions among types of variables This is the basic idea of Quine s New Foundations for Mathematical Logic 6 Spring 2009 confess that while the analyticsynthetic distinction is necessary for the tenability of Carnap s view I do not see that it to him gives a license for introducing terms as referring to a new type of entity by stipulation4 The trouble as I see it is that we really do have a general conception of what it is for something to be which is connected with our understanding of what it is for a term to refer For a term to refer there must be in the general sense a thing for it to refer to But that there is is not something to be settled by stipulation though it may be settled by stipulation once we have identified something that a certain name is to refer to it 2 On What You Think There Is In On What There Is Quine advances his famous criterion for ontological commitment a To be assumed as an entity is purely and simply to be reckoned as the value of a variable In terms of the categories of traditional grammar this amounts roughly to saying that to be is to be in the range of reference of a pronoun Pronouns are the basic media of reference nouns might better have been named propronouns The variables of quantification something nothing everything range over our whole ontology whatever it may be and we are convicted of a particular ontological presupposition if and only if the alleged presuppositum has to be reckoned among the entities over which our variables range in order to render one of our affirmations true New Essays in Philosophical Analysis ed by Feigl Sellars and Lehrer p 551 b a theory is committed to those and only those entities to which the bound variables of the theory must be capable of referring in order that the affirmations made in the theory be true p 551 In another essay Logic and the Reification of Universals 5 he puts it as follows c In general entities of a given sort are assumed by a theory if anal only if some of them must be counted among the values of the variables in order that the statements af rmed in the theory be true From a Logical Point of View p 102 We will return to how these passages are to be understood in a moment Perhaps they are not quite so transparent or innocent as they seem But first what is the problem the criterion is a response to 4 That this is the basic issue between Camap and Quine does not mean however as Quine urges that Camap s talk of frameworks is pointless that there is no work for the talk about frameworks to do since it provides Camap with a tool for the diagnosis of traditional philosophical puzzles about ontology 5pp 102129 in From a Logical Point ofView Spring 2009 The problem is guring out what we actually are committed when we set out to decide what our ontology includes Enter McX and Wyman henchmen of the nonexistent companions in philosophical crime For a starting puzzle suppose I wish to bring McX to book about his ontological excesses Suppose McX maintains that Pegasus exists Iwish to dispute this with him but McX cleverly turns the tables on me by producing as his argument the very thing I wish to say McX You are right We are not in disagreement at all as you will see For surely we can all agree that Pegasus does not exist and hence doesior at least is for it is evident that we cannot say that Pegasus does not exist unless it is Pegasus that we are talking about Otherwise we would have missed our mark or said nothing at all How then can any one so much as dispute with another about ontology without admitting the disputed items Somewhere in the back of the courtroom we hear someone shouting What is this nothing The judge motions to the bailiff Crossexamination You say McX that Pegasus is what we are talking about when we say there is no such thing and even you admit that there is no esh and blood horse equipped with wings let alone one captured by Bellerophon What then is this Pegasus that you insist is though it does not walk talk or act like a horse even a ying one Where is the body McX Pegasus is what we think about when we say Pegasus does not exist that is it is what um we have in mind Yes Pegasus is an idea in our minds when we assert that it does not exist Ladies and Gentlemen of the jury render your verdict Jury We hereby nd McX guilty of irremediable confusion in thinking that what if it is anything is a winged horse is an idea an idea than which there is none more absurd Wyman who slipped back into the courtroom unnoticed interrupts Why man you have made a terrible blunder McX I cannot be so convicted for I maintain that Pegasus does not exist at all either as an idea or as a esh and blood horse or in any other form When I say Pegasus does not exist I mean Pegasus does not exist Of course you were quite right to insist that Pegasus cannot be talked about if Pegasus does not refer to something Thus Pegasus refers to something only something that does not exist ie something which is not actual say rather that Pegasussubsists And here all of our puzzlement is removed Crossexamination Wyman you assert whenever we assert that something does not exist we are committed to its subsistence Then let me ask you a few questions of clari cation Take that thin man who does not exist in that doorway And take that fat man who does not exist in that doorway Pray are they the same man Or are they different How do we decide how many things there are in your overpopulated universe How many possibilia Moreover what of that famous round square cupola on Berkeley College that does and cannot exist Yes that one the one I had to refer to say that there is and could be none such It is not even a possible object yet you see to be committed to saying that it is as well Wyman I do not understand you You utter these words The round square cupola does not exist but it is only so much noise as if you had said curiosity barks intermittently in the center of silence And as for your other objection in kindness I will pass over it As Bishop Spring 2009 Butler declared everything is what it is and not another thing Member of the jury Let me interj ect Bishop Butler aside Wyman do you then assert that every contradiction is meaningless Wyman Why I suppose I do if it doesn t get me into trouble Jury Is every truth function of a meaningful sentence also a meaningful sentence Wyman Why of course Jury Then you assert that there can be no necessary truths since the negation of every necessary truth is a contradiction iIncidentally I have some dry land in southern Florida I d like to sell you Wyman No no I did not mean to say that every contradiction is meaningless only some But tell me more about that real estate Jury Then pray tell which contradictions exactly are meaningless The ones employing indefinite descriptions in which nonexistence or existence is putatively asserted of the denotation of the description Wyman Yes you ve put it exactly Jury Let C be a contradiction Consider a negative existential statement of the form the x such that x is F and C does not exist Ifthis does not make sense as you Wyman must say if you are to avoid commitment to impossibles then it must be because C does not make sense Clearly however any contradiction may be substituted for C So you have once again committed yourself to saying that all contradictions are meaningless Consequently as Quine observes you are committed to denying that reductio ad absurdum is a legitimate form of inference a challenge in which I sense a reductio ad absurdum of the doctrine itself At this point raging Wyman is led from the courtroom by the bailiff for later arraignment I don t understand There is nothing to your argument Nothing Once again nothing has foiled me Nothing has defeated me Nothing will ever be the same gtltgtlt So much for McX and Wyman s unlovely overpopulated ontological slum But what is the deliverance from the apparent commitments of negative existential statements With defmite descriptions the solution is Russell s theory of descriptions The round square copula on Berkeley College does not exist becomes It is not the case that there is an x such that x is round and x is square and x is a copula and x is on Berkeley College or there is an x and there is a y such that x i y and x is round etc and y is round etc In the latter clearly there is no term that must refer to a round square copula The work of reference is done by the variable which functions something like an ambiguous name no value of x satisfies the open sentence following such that and hence the sentence is true This solves the problem for definite descriptions but what about names For notice if Wyman had only been a Russellian he would have dispensed with the trouble about the round square while still retaining Pegasus and his ilk Quine takes the line that every proper name can be replaced by a definite description In the case of Pegasus perhaps the winged horse captured by Bellerophon which but for the use of another proper name might seem to do well enough And if we are short of appropriate 9 Spring 2009 de nite descriptions we can employ the expedient Quine says of introducing a predicate to correspond to the name in the case of Pegasus the verb is to pegasize Thus Pegasus does not exist gets transformed into The x such that x pegasizes does not exist to which we apply Russell s theory of descriptions One objection to this apparently convenient maneuver is that it fails what we might call Kripke s test see Naming and Necessity No de nite description is equivalent to a proper name unless it picks out the same object in every possible world as the proper name proper names in Kripke s terminology are rigid designators they designate the same thing in every possible world in which they designate anything so unless a de nite description which is a rigid designator can be found no de nite description will play the same semantic role as any proper name Or to put it metalinguistically no de nite description is equivalent to a proper name unless it is intersubstitutable for it in all contexts salva veritate without change of truth value including modal contexts Now clearly I Necessarily Pegasus is identical with Pegasus is true But suppose we substitute using our supposed equivalence to reach 2 Necessarily the winged horse captured by Bellerophon is identical with Pegasus It is a bit dif cult to know what to say might have been true with respect to ctional characters But let us suppose that this is not so and that Pegasus is supposed falsely to apply to some actual being and Bellerophon as well In that case would 2 be true Well it does not seem so for surely Bellerophon might not have captured Pegasus Bellerophon might have been a bit slower eg or died when he was ve years old But perhaps a simpler suggestion will do the trick Suppose we said this is a suggestion originally made by Russell that the de nite description that gives the sense of a proper name N is always of the form The thing named N Then we would have 3 Necessarily the thing named Pegasus is identical with Pegasus Is this true No For surely Pegasus might have been called something else Or midway through life dogged by notoriety Pegasus might decide to change his name to Charles to avoid press hounds and curiosity seekers If Pegasus were necessarily the thing called Pegasus then a name change would be suicide Well then suppose we avail ourselves of Quine s device This gives us 4 Necessarily the x such that x pegasizes is identical with Pegasus A difficulty with evaluating this is that unless we know what it is to pegasize we are hardly in a position to understand what is being said in 4 Let us suppose that it is a very complex property however perhaps a very precise description of the dimensions history color etc of the supposed wingedhorse Is 4 true then Worse and worse surely for it seems easy to 10 Spring 2009 imagine that Pegasus might have e g weighed a little bit less or had a slightly different history or had his tail bobbed Well then we might avail ourselves of the suggestion that pegasizes means is identical with Pegasus This gives us 5 Necessarily the x such that x is identical with Pegasus is identical with Pegasus And no doubt 5 is true But now we see that we haven t eliminated Pegasus after all but only hidden him in unfamiliar linguistic garb Clearly if we cannot paraphrase away proper names then we will not have met the challenge of negative existentials such as Pegasus does not exist Would Quine be worried Probably not for several reasons First Quine notoriously rejects talk of possibility and necessity as unintelligible and in reference to footnote 4 likewise talk of propositional attitudes which he has said are creatures of darkness Not admitting the intelligibility of the sentences in which the divergence between proper names and descriptions is exhibited he would not admit this as an objection to his paraphrase Second though it is not clear that Quine is committed to saying that a paraphrase is a translation of the original expression What he really needs to maintain to get us out of having unwanted ontological commitments through the use of a certain discourse is that all the purposes for which we employ that discourse can be met by the paraphrases Then we can treat the original forms of discourse as a facon de paler and not take its overt ontological commitments seriously Well so much for this rst argument for ontological commitment What of the claim that ordinary forms of speech commit us to the existence of universals Here is one hand here is another well then both must have something in common namely the property of being a hand Quine objects that what we want to say can be said without appeal to properties this and this are both hands Well maybe meanings will do as a poor cousin to universals for surely we are committed to what we say being meaningful and our words having meanings Not at all Quine says the work that meanings are meant to do can be done so far as ordinary talk goes by talking about synonymy which is a relation between words or expressions and introduces no sort of entity in addition to them 6 One final move might be to appeal to a rigidifred description such as the x such that x was actually a winged horse captured by Bellerophon etc This would secure the rigidity of Pegasus across possible worlds However such expressions do take scope in attitude reports so saying that the x such that x was actually a winged horse captured by Bellerophon was believed by Bill to be white is saying something different from Bill believed that the x such that x was actually a winged horse captured by Bellerophon was white The former might be false while the latter true since the latter doesn t require that there be a winged horse captured by Bellerophon However Pegasus does not take different scopes with attitude verbs and we always have the existential commitment I would argue when we use it even in attitude reports In any case it is clear more generally that in using a name like Pegasus we do not require people to know any particular descriptions of its referent to be competent in its use so representing it as a description mischaracterizes its linguistic role and what counts as linguistic competence in its use 11 Spring 2009 So these are bad signs of ontological commitment according to Quine which leaves us with the question what a good sign of ontological commitment might be Paraphrasing away names as basic referring devices we are left with the variable and the upshot is the above suggested criterion for ontological commitment Let us now take a closer look To be assumed as an entity is purely and simply to be reckoned as the value of a variable What is it to be reckoned as the value of a variable It is to be taken to be one Put in this way the criterion is unhelpful because we know that we committed to those things that are in our ontology and everything in our ontology we would reckon to be the value of a variable The second formulation is more helpful a theory is committed to those and only those entities to which the bound variables of the theory must be capable of referring in order that the affirmations made in the theory be true Note the use of must be to which we will return but let us ask for now exactly how this gets applied in practice Here is a sample theory Tl Vxx x Let us suppose for concreteness that we are formulating our theories in a rst order language say but in keeping with Quine s suggestion without any individual constants What does Tl commit us to In classical logic it is assumed that one s domain is nonempty Note that to assume this is to commit oneself to a particular way of understanding the quantifier expressions in one s theory as is putting various restrictions on the objects that the variables are allowed to range over So if we assert anything we are committed to saying that something exists In the case of T1 we are committed to saying that the open sentence x x is satis ed by every object in our nonempty domain and so we are also committed to asserting Exx x But what exactly does this commit us to Well we might have specified that our domain is to include say all real numbers Then in order for x x to be satis ed x would have to take on as value at least one real number Thus we could be said to be committed to the existence of entities that are real numbers Here however all the work seems to be done previously by our specifying what is in the domain and our theory is not what is doing the work Let us then suppose that we let the domain be unrestricted we say our variables will range over everything there is In this case Tl commits us to no particular ontology We would not want to say that it commits us to all the kinds of things there actually are for then no matter what its axioms every theory with an unrestricted domain would be committed to the same ontology This helps to bring home that in matters of ontology what we are concerned with is not just what particular entities we might be committed to but also what kinds those entities fall under Robust ontological commitments will come from finding that we are committed to saying that open sentences involving predicates that are satis ed only by certain kinds are satisfied by something in the unrestricted range of the variables of quanti cation Let s turn then to a somewhat more robust theory to see how this might come out T2 A1 VxL2xx Spring 2009 A2 VxVyL2xy gt Lzyx A3 VxVyVzszy amp Lzyz gt szz Let us interpret szy as x is larger in volume than y 7 Now to evaluate our ontological commitments we must discover what values our variables have to be capable of taking on in order that T2 be true and in particular what kinds of entities our variables must be capable of taking as values for T2 to be true Now is this entirely straightforward Consider a purely immaterial world of spirits Is Al true in such a world In part it seems this question hinges on whether it could be truly said that some spirit is not larger in volume than itself and this depends in turn on whether L2 can sensibly be thought of as relating an immaterial thing to itself Thus questions of ontological commitment are connected with questions about whether certain predicates and relations express functions that can take as arguments only specific types of entities the assumption of type theory Ifwe suppose that the truth of T2 can be evaluated only for kinds of objects that can have volumes then any set of objects which satisfy T2 will have to be physical or at least extended objects Thus our commitments here will be to extended objects and this in virtue of our being committed to a certain open sentence being satis ed by some objects where the relation in question can hold only between objects of a certain kind Of course when we have a theory that makes existential statements involving predicates it is easier to see what some of our commitments are If we assert something of the form EIxFx then clearly for this to be true x must take on as a value an Fthing But even here matters are perhaps not quite so straightforward Suppose someone says Elxx is a person In this case of course one is committed to persons at least one But might one not also be committed to other types of things For example it might be thought that nothing could be a person that was not embodied in which case we would also be committed to the existence of physical objects in being committed to the existence of persons This is one reason we can t simply say that our ontological commitments are given by what predicates appear in existentially quantif1ed statements in our theory One might perhaps say that a theory is committed to all and only those kinds of entity K such that the theory implies a sentence of the form Elxx is of kind K Even here there might be some difficulty though for it might be that one has a theory which has too limited a vocabulary to formulate a sentence about all the kinds to which it is committed For example T2 above might have only L2 in its nonlogical vocabulary we would still want 7 I borrow this example from Richard Cartwright s Quine and Ontology in his Philosophical Essays 13 Spring 2009 to say that it is committed to the existence of physical objects In a richer theory it would imply an appropriate sentence but not as presently formulated There are then quite a lot of questions that still have to be answered in order to uncover the ontological commitments of a theory even after we have settled on Quine s criterion of ontological commitment In asking questions we have been availing ourselves of the apparatus of rst order logic though we have hardly been using a purely formal language One reason this helps is that it allows us to ignore questions about the semantics of ordinary language locutions like everything something etc Properly though if we are to investigate our ontological commitments in the language we speak we need to consider what the semantics of ordinary language statements are This introduces another level of complexity in guring out what our ontological commitments are Quine is Ithink aware of this and would urge us to formulate our theories in a canonical language whose semantics was already laid out and ideally in a rst order formal language though this choice itself would carry ontological commitments since we would not be allowing quanti cation into predicate places I want to turn now to an internal criticism of Quine due to Richard Cartwright8 Quine as we ve already noticed rejects as unintelligible the notions of necessity and possibility and all other modal notions as well as those of involving the propositional attitudes Now this raises a dif culty it turns out for his own criterion of ontological commitment In passage b and c it is clear that Quine is appealing to a modal notion in formulating the principle Why The reason is that we want to be able to count false theories as possibly having distinct ontological commitments If a theory is false it is clear that there are no values of its variables that makes it true So if we count commitment by what kinds of values of variables there are in every set of objects which makes the axioms of the theory true every false theory will have the same ontological commitments namely none Consider the theory T3 Al There are supernatural beings A2 Every supernatural being is the ruler of Olympus or a member of his court Now Al and A2 might be reckoned by many people to be false Suppose it is Does it have no ontological commitments Of course it does To capture its commitments however in terms of what values its variables take on we have to consider counterfactual situations since we are assuming there aren t actually any supernatural beings Thus Quine s criterion really ought to read a theory is committed to those and only those sorts of entities to which the bound variables of the theory would refer were the af rmations made in the theory true But this way of stating it is not available to Quine We should conclude that Quine has not succeeded in stating a criterion that meets his own standards of clarity 8 Op cit


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