Naming the concept horse

Philosophy

Naming the concept horse Michael Price1 Published online: 6 February 2016  The Author(s) 2016. This article is published with open access at Springerlink.com Abstract Frege's rejection of singular reference to concepts is centrally implicated in his notorious paradox of the concept horse. I distinguish a number of claims in which that rejection might consist and detail the dialectical difficulties confronting the defense of several such claims. Arguably the least problematic such claim-that it is simply nonsense to say that a concept can be referred to with a singular term-has recently received a novel defense due to Robert Trueman. I set out Trueman's argument for this claim, identifying and remedying some omissions and errors of formulation therein. I then develop a response to the argument by showing, pace Trueman, that it is possible-and how it is possible-to express identities between objects and concepts. Keywords The concept horse paradox  Frege  Trueman  Concepts  Singular reference ... Coriolanus He would not answer to: forbad all names; He was a kind of nothing, titleless, Till he had forged himself a name o' the fire Of burning Rome. Coriolanus, Act V, Scene I & Michael Price firstname.lastname@example.com 1 Pembroke College, University of Oxford, Oxford, UK 123 Philos Stud (2016) 173:2727–2743 DOI 10.1007/s11098-016-0630-6 Frege's concept horse paradox has enjoyed a swell of interest in recent years.1 One of the highlights of this latest tranche of research on the paradox is Robert Trueman's 'The concept horse with no name' (Trueman 2015). Trueman presents an impressive and innovative defense of Frege's rejection of singular reference to concepts-a defense that, importantly, forgoes appeal to Wright's ill-fated Reference Principle, which has played such a central role in discussions of the justification of Frege's position on the topic.2 The rejection of singular reference to concepts is, of course, centrally implicated in the constellation of problems gathered under the rubric 'the concept horse paradox'.3 I shan't rehearse those problems in any detail here. My main concern will be with what can be said-and, in particular, with what Trueman has said-in defense of Frege's rejection of singular reference to concepts. 1 Frege against singular reference to concepts First, though, some remarks are in order concerning what that rejection amounts to. It strikes me that there are, in fact, four claims discernible in Frege's writings in each of which his rejection of singular reference to concepts might be taken to consist. The first is that reference to a concept with a singular term is impossible ('the impossibility thesis'): concepts are unnameable. Following Frege in counting something an object just in case it can be the referent of a singular term, and in counting something a concept (or property) just in case it can be the referent of a predicate, the impossibility thesis can alternatively be formulated as follows: concepts are not objects; or again as follows: singular terms and predicates cannot be pairwise co-referential. The impossibility thesis is, I think, the view on the matter standardly attributed to Frege, and on good textual grounds. We find it clearly affirmed in the following passage, for example: ... the phrase 'is a concept' requires a proper name as grammatical subject; and so, strictly speaking, it requires something contradictory, since no proper name can designate a concept... (Frege 1979b, p. 178, my emphasis)4 Yet there is reason to doubt that the impossibility thesis is Frege's most considered position on the matter. What immediately follows the passage just quoted, for example, appears to amount to a cautious recantation of the impossibility thesis just affirmed: 1 Notable recent contributions to the topic include Hale (2010), Hale and Wright (2012), Hale (2013, Hale and Linnebo (TS), Jolley (2007), MacBride (2011), Noonan (2006), Proops (2013), Rayo (TS), Textor (2010) and Trueman (2015). 2 A powerful case against the Reference Principle is presented in Oliver (2005). 3 For an excellent discussion of the distinguishable difficulties see Proops (2013). 4 I remind the reader that all singular terms count as proper names on Frege's use of 'proper name' (indeed he uses 'proper name' (Eigenname) interchangeably with 'singular term' (Einzelname): see Frege (1997a, p. 172). The expression 'unnameable' in this essay is to be understood as a cognate of Frege's 'proper name': something is unnameable just in case it cannot be the referent of a Fregean proper name. 2728 M. Price 123 ... or perhaps better still, something nonsensical. (ibid.) Better than saying that singular reference to concepts is impossible, Frege ventures, is to say that there is no sense to be made of reference to a concept with a singular term. This latter is the second claim I have in mind: it is nonsense to say that a concept might be the referent of a singular term, nonsense to say that a concept is an object ('the nonsensicality thesis'). The third is that it is impossible to think of a concept as being the referent of a singular term-impossible to suppose that a concept is an object ('the unthinkability thesis'). This follows from Frege's general pronouncement that ... concepts cannot stand in the same relations as objects. It would not be false, but impossible to think of them as doing so. (Frege 1997a, p. 175), since to think of a concept as being the referent of a singular term would be to think of a concept as standing in a relation in which objects stand. The fourth claim is that it is impossible to state that a concept is an object ('the inexpressibility thesis'). In 'On Concept and Object', Frege insists that ... what is suitably stated of the concept does not suit the object ... I do not want to say it is false to state concerning an object what is stated here concerning a concept; I want to say it is impossible, senseless, to do so. (Frege 1997c, p. 188–9, translation altered) Since, in particular, it is possible to state concerning an object that it is an object, it seems clear that Frege deemed it impossible to state concerning a concept that it is an object. The import of 'senseless' in this passage is made more explicit in an earlier draft of the paper: ... a sentence which tried to express such a thing [i.e. which tried to do the impossible and state concerning a concept what can be stated concerning an object] would be absolutely devoid of sense;... (Frege 1979a, p. 109) Since 'A concept is an object' is presumably just such a sentence, we have here a further affirmation of the nonsensicality thesis. Of these four theses, each of which constitutes a position on which singular reference to concepts is rejected, three face an exigent threat of self-stultification. The threat is perhaps most conspicuous in the case of the inexpressibility thesis. Saying 'It is impossible to state that a concept is an object' is liable to be compared to saying out loud (and with correct pronunciation) 'I cannot pronounce the word ''banana'''.5 Merely voicing the thesis appears to expose it as false. A similar problem attends the unthinkability thesis: if we are even to understand the thesis, we must be in a position to apprehend just what it is that is being claimed unthinkable, and such apprehension threatens to demand the very thinkability of the subject of the claim. The problem is that identified in the preface of the Tractatus: 'in order to set a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be 5 The example is Peter Sullivan's (Sullivan 2002, p. 76), though he deploys it to illustrate a different point. Naming the concept horse 2729 123 able to think what cannot be thought)' (Wittgenstein 1974, p. 27). The impossibility thesis faces a charge of self-stultification too. In this case the problem is the one acknowledged by Frege in our first quotation above: 'n is a concept' requires a singular term to fill its argument place; it is extremely natural to suppose that where a predicate truly applies to something, there could, in principle, be a true sentence consisting of an expression referring to that thing in the argument place of that predicate; but in that case, anything to which 'n is a concept' does truly apply is something to which a singular term can, in principle, refer-i.e. an object; but 'n is a concept' truly applies to something just in case it is a concept; so anything that is a concept is an object; granted that there are concepts, as Frege maintains, it follows that it is false that no concept is an object. This kind of problem is, of course, one distinguishable dimension of the concept horse paradox (Proops 2013, p. 84–85). The nonsensicality thesis stands out on this count, I submit: it is innocent of selfstultification. For it must be understood as a claim about a certain linguistic expression, 'a concept is an object', and as being to the effect that that expression lacks sense-i.e. expresses no thought (this is the relevant notion of nonsensicality in the present context). (Better: it must be understood as claim about a cluster of linguistic expressions-'a concept is an object', 'a concept can be the referent of a singular term', 'a singular term can co-refer with a predicate', etc.-that are, by virtue of our semantic stipulations, possessed of the same sense if possessed of sense at all.) As Wittgenstein stressed, '[w]hen a sentence is called senseless, it is not, as it were, its sense that is [being claimed] senseless' (Wittgenstein 2010, p. 147e); it is the sentence itself. Accordingly, when we formulate the thesis as 'It is nonsense to say that a concept is an object', the sentence 'a concept is an object' therein must be understood as mentioned and not used. Mentioned nonsense, as opposed to used nonsense, is quarantined: it does not infect its surroundings with nonsensicality. So the thesis can simply be true, much as it can simply be true to say 'Finally Carroll said ''And the mome raths outgrabe'''.6 Whereas the inexpressibility of a thought threatens to render it inexpressible that that thought is inexpressible, so that one's success in stating that that thought is inexpressible would confute that very statement, and whereas the unthinkability of a thought threatens to render it unthinkable that that thought is unthinkable, so that one's success in supposing that that thought is unthinkable would confute that very supposition, the nonsensicality of a sentence, by contrast, does not risk rendering it nonsensical to say that that sentence is nonsensical; so one's success in sensefully saying so does not confute one's saying.7 6 See also Moore (1997, p. 157). 7 The two uses of 'threatens' in this sentence may look like undue caution. One reason I think caution is due, however, is that there are ways of referring to and apprehending thoughts that do not require the expressibility or thinkability of those thoughts. Suppose, for example, that the truth fathomed by Siddhārtha Gautama on the night of his enlightenment is inexpressible and unthinkable (at least to the benighted likes of us). That that truth is inexpressible and unthinkable, though, need be neither inexpressible nor unthinkable (even to us), providing that truth can be referred to, and apprehended under, the definite description in the preceding sentence. It is quite unclear, however, how this expedient for making inexpressibility claims and unthinkability claims respectively expressible and thinkable (even if true) could be used to surmount the charge of self-stultification facing Frege's inexpressibility and unthinkability theses above. 2730 M. Price 123 2 Trueman against singular reference to concepts If one is going to argue for a Fregean rejection of singular reference to concepts, there are, then, prima facie grounds for arguing for it in the form of the nonsensicality thesis. This is what Trueman does. The conclusion of his paper is 'that it is nonsense to say that a property is an object' (Trueman 2015, §8). (Trueman favours 'property' over 'concept'; we'll switch to the former in what follows to accord with his formulations.) Interestingly, though, he sets about establishing that conclusion by arguing, in the first instance, for the inexpressibility thesis: we are prevented, in principle, he argues, 'from so much as expressing the thought that a property is an object' (Trueman 2015, §3). If, for the moment, we prescind from the self-stultification problem afflicting it, the inexpressibility thesis does look fit to serve as intermediate conclusion en route to the nonsensicality thesis. For suppose that, contrary to the nonsensicality thesis, it does make sense to say that a property is an object-i.e. that one does succeed in expressing a thought in saying so. Whatever thought is thereby expressed is, trivially, not inexpressible; but, 'It is impossible to express that a property is an object' says of that thought that it is inexpressible, and is thus false. If 'It is impossible to express that a property is an object' is false, then it is not impossible to express that a property is an object. So if it makes sense to say that a property is an object, it is possible to express that a property is an object. By contraposition, if it is not possible to express that a property is an object, then it is nonsense to say that a property is an object: the inexpressibility thesis implies the nonsensicality thesis.8,9 However, even ignoring the self-stultification of the inexpressibility thesis, we are now confronted with the fresh oddity that the inexpressibility thesis is stultified by the conclusion for which it serves as lemma-the nonsensicality thesis: after all, 'a property is an object' is used, not mentioned, in 'it is impossible to express that a property is an object'; so, if the former is nonsense, the latter is too. But if the latter is nonsense, how can it serve as a lemma en route to the nonsensicality thesis? Trueman acknowledges that he is in 'a precarious dialectical position' (Trueman 2015, §8). He denies that his position need be 'ultimately unstable', however. The argument is to be understood, according to Trueman, as an attempt to show his opponents-those who think it does make sense to say that a property is an object- by their own lights that it does not make sense. It need not, to that end, succeed in 8 Cf. Moore (1997, p. 198). 9 The unthinkability thesis also features in Trueman's paper. Like the nonsensicality thesis, it is affirmed as a consequence of the inexpressibility thesis: ''unless we can find a way of expressing Benno's thought [the thought that a certain concept is an object], we cannot suppose that it might actually be true'' (Trueman 2015, §4). The inference of the unthinkability thesis from the inexpressibility thesis is mediated by a 'ground rule' Trueman lays down (Trueman 2015, §4) of not entertaining the suggestion that the thinkable outstrips the expressible. Though my main focus in this paper will be with Trueman's argument for the inexpressibility thesis as intermediate conclusion en route to the nonsensicality thesis, what I say will equally bear on whether Trueman has established the unthinkability thesis via the same route. Incidentally, Trueman ascribes the unthinkability thesis to Frege, claiming that 'he was clear' that this thesis was 'the proper formulation of his position' (Trueman 2015, §4). I suggest that the brief survey of relevant passages in Sect. 1 does not in fact disclose a single, official formulation of Frege's position. Naming the concept horse 2731 123 showing this by the lights of those sharing his view, who indeed need not (and as we've seen, cannot) even accept the meaningfulness of the argument. For what it is worth, I'm sympathetic to Trueman's response. We should, I believe, recognize the legitimacy of arguments that are only intelligible by the lights of those on whose position they are an attack. Such arguments are, I think, just extreme examples of good ad hominem arguments: arguments whose cogency depends upon assumptions accepted by opponents of, but not proponents of, the view they are intended to support. In any case, it is not with the ultimate stability of Trueman's dialectical position that I shall take issue here. Rather, my concern is to argue that Trueman does not show, even by his opponent's lights, that it is impossible to express that a property is an object. Let us turn, then, to the details of the argument that purports to show that. 2.1 The basic argument Suppose that it is possible, in principle, to express the general thought that a property is an object-or equivalently, that a property is identical to some object. (Throughout, 'a property is an object' is to be understood as an existential generalisation-i.e. as 'some property is an object'-rather than a universal generalisation or a generic; similarly for its equivalents.) In that case, it must also be possible, in principle, to express the thought (call it Benno's thought, in honour of Frege's critic) that a particular property-say, the one 'n is a horse' refers to-is identical to a particular object-say, the one 'the property horse' refers to. Benno's thought is an identity, so the natural way to attempt to express it is by use of the identity predicate, 'n = f'. But while 'the property horse' can be introduced into an argument place of the identity predicate, 'n is a horse', whose referent we wish to identify with the property horse, cannot be introduced into the remaining argument place. The point is not, Trueman is keen to stress, merely that the parochial grammatical strictures of English forbid substituting 'n is a horse' for 'n' in 'n = the property horse'. Rather, the kind of sense possessed by 'n is a horse', qua predicate, is such that, unlike a singular term, it cannot combine solely with 'n = the property horse', given the kind of sense it has, to yield the expression of a thought. This, Trueman thinks, is just a consequence of the general consideration that the contrasting kinds of sense respectively possessed by terms and predicates prevent them from being substituted for one another. If we are to express Benno's thought, then, we must complete 'n = the property horse' with a singular term. Clearly, we must select one that co-refers with 'n is a horse'. Let 'a' be whichever such term we select. The problem, however, Trueman claims, is that even if 'a' indeed co-refers with 'n is a horse' (and to assume that it could not, or that it is nonsense to say that it does, would be to beg the question in the present context), 'a = the property horse' will nevertheless fail to express Benno's thought. The reason is that 'a', qua singular term, will not present its referent in the right way-namely, as a property, something to which predicate reference can be made. Trueman illustrates this point by way of comparison with the following case. Suppose that there is a philosopher, the Misguided Metaphysician, who maintains that the number 3 is identical to Julius Caesar. The Misguided 2732 M. Price 123 Metaphysician attempts to express that view not with the sentence 'Julius Caesar = 3' but rather by saying '2 ? 1 = 3'. The natural verdict is that the Misguided Metaphysician's attempt to express her claim in this way is unsuccessful. Moreover, her attempt would be unsuccessful even if she were right, and '2 ? 1' did indeed refer to Julius Caesar. If she were right, her utterance would say de re of Julius Caesar that he is identical to the number 3; but her utterance would nevertheless fail to express the thought that Julius Caesar is identical to the number 3. This is witnessed by our being able to accept what the Misguided Metaphysician says without agreeing with her that Julius Caesar and the number 3 are identical. Trueman's diagnosis of the failure is that '2 ? 1', even if it refers to Julius Caesar, does not present its referent as Julius Caesar. The attempt to use the sentence 'a = the property horse' to express Benno's thought is comparable, Trueman thinks, to the Misguided Metaphysician's attempt to express her thought using '2 ? 1 = 3'. Benno's thought is that a certain property-something that can feature as the referent of a predicate-is identical to a certain object. But the singular term 'a', even if it succeeds in picking out the intended property, does not present its referent as something to which predicate reference can be made. Thus, while 'a = the property horse' may succeed in saying de re of the referent of 'n is a horse' that it is identical to a certain object, it nevertheless fails to express Benno's thought. In order, Trueman thinks, to present the property we wished to identify with an object as a property, we would have to refer to it with a predicate. But we cannot both do this and employ the predicate 'n = the property horse' to express Benno's thought. Quite generally, we cannot do this and employ the identity sign 'n = f', or any expression with the same sense, to express Benno's thought: 'n = f' requires-once again, as a matter of sense-that each of its argument places be supplied with a singular term. But then how can Benno's thought be expressed? Conclusion: it cannot. And if it cannot, nor can the general thought that a property is an object. 2.2 Can't terms present their referents as properties? Trueman considers two broad kinds of objection to this argument. The first is to the effect that a singular term can present its referent as a property, so that Benno's thought can after all be expressed by use of the identity predicate. The second is to the effect that Benno's thought admits of expression without use of the identity predicate, by some means that allows for the use of 'n is a horse' itself to pick out the property to be identified with an object, rather than a surrogate singular term. I shall, in fact, ultimately push versions of both these objections against Trueman's argument, though my version of the second objection will be quite different from the version Trueman treats and will, in a sense, be parasitic upon my defense of the first objection.10 Let us then, give substance to the first objection and hear Trueman's response to it. 10 The version of the second objection Trueman discusses consists in the proposal that Benno's thought can be stated by means of a lopsided analogue of the identity predicate, 'U * n', admitting a predicate into one argument place and a term into the other. I shan't pursue this proposal here. Naming the concept horse 2733 123 Two terms that do appear to present their referent as a property, and are excellent candidates for co-referring with 'n is a horse', are 'the referent of ''n is a horse''' and 'the property horse'. It appears that the latter quite explicitly presents its referent as a property, while the former presents its referent as a property- something to which a predicate can refer-by presenting it as something to which a particular predicate does refer. If we substitute either for 'a' in 'a = the property horse', won't the result suffice to express Benno's thought? For closely related reasons Trueman thinks neither expression is fit to task. I shall focus on 'the referent of ''n is a horse'''. This looks like a singular term, one naturally analysed as the result of using a definite description operator to bind a term variable in the argument place of the predicate '''n is a horse'' refers to f', where this predicate is in turn the result of inserting the predicate name '''n is a horse''' into the first argument place of 'n refers to f'.11 The problem with this analysis, Trueman thinks, is that 'refers', used when speaking of predicates referring, should not be understood as the very same first-level dyadic predicate, 'n refers to f', used when speaking of terms referring. The reason has to do with the possibility of specifying, by disquotation, what an expression refers to. Disquotation sentences like (i) The referent of 'Julius Caesar' = Julius Caesar capture, Trueman maintains, something essential about reference-roughly, that when we pass from using a referring expression to talking explicitly about what that expression refers to, we continue to talk about the same thing. So if we are to count predicates as referring expressions,12 it must correspondingly be true that when we pass from referring to something using a predicate to explicitly speaking of what that predicate refers to, we continue to talk about the same thing; and it must be possible to capture this for any particular predicate, as (i) captures this for the term 'Julius Caesar'. It must be possible, that is, to furnish a disquotation sentence that is to 'n is a horse', for example, as (i) is to 'Julius Caesar'. However, if 'refers to' in discourse about predicate reference is to be understood as 'n refers to f', Trueman thinks, it would not be possible to furnish any such sentence. For in that case, 'the referent of ''n is a horse''' would indeed be the singular term it appears to be, but then in order to state an analogue of (i) for 'n is a horse' we would have to express the thought that something referred to with that singular term is identical to something referred to with a predicate, 'n is a horse'. That is, we would have to express an object-property identity. So we are confronted once more with the above argument that this cannot be done. We cannot use the predicate 'n is a horse' to pick out the property whose identity with a certain object we wish to express: the sense of the identity predicate prohibits that. So we would have to resort to the use of a co11 I shall assume, in Fregean spirit, that if 'the referent of ''n is a horse''' is the definite description it appears to be, it is a referring expression and is not to be analysed in Russellian fashion. 12 It is, of course, far from uncontroversial that we are to count predicates as referring expressions; but I shall follow Trueman (2015, §2) in assuming that, in some significant sense, at least some predicates do refer. We will shortly see that Trueman himself presents an argument to the effect that, in another significant sense, predicates do not refer. 2734 M. Price 123 referring singular term in its stead; but no singular term we choose will be fit for the expression of our target thought: even if the term we select refers to the property, it will not present its referent as a property, as would be required to express the thought. The possibility of giving an analogue of (i) for a predicate can only be secured, Trueman thinks, if the relational expression for predicate reference permits us to specify what a predicate refers to using a predicate-that is, if 'refers to' for predicates is to be understood as 'n refers to U' (where 'U' marks an argument place open to predicates). There is no uncontroversial rendering of 'n refers to U', Trueman acknowledges13; but unless talk of predicates referring can be interpreted in this way, he thinks, an essential feature of reference, captured in the case of terms by the likes of (i), cannot even be said to obtain in the case of predicates. However, we cannot understand 'the referent of ''n is a horse''' as the result of using a definite description operator to bind a term variable in the argument place of '''n is a horse'' refers to U', because only a predicate variable could be bound in that argument place. Trueman notes that we may wish to countenance ... a higher-level definite description operator which binds (first-level) predicate variables rather than term variables; such an operator would take a second-level predicate and return a first-level predicate standing for the unique property which satisfies that second-level predicate, if there is such a unique property. We could then use this operator to form a higher-level definite description by binding the variable in '''n is a horse'' refers to U', which we could write as 'the F such that ''n is a horse'' refers to F'. But crucially, 'the F such that ''n is a horse'' refers to F' would itself be a predicate, and so we could no more plug it into the gap in 'n = the property horse', which is a gap for singular terms, than we could plug 'n is a horse' into that gap. (Trueman 2015, §5) Thus, Trueman thinks, with 'refers to' for predicates understood as it must be, the appearance that 'the referent of ''n is a horse''' is a singular term presenting its referent as a property dissolves. 3 Initial reflections Oddly, Trueman does not actually deliver the predicate analogue of (i) that is allegedly only available if the relational expression for predicate reference takes a predicate in accusative position. This omission can be remedied, however, using resources he accepts. We've just seen Trueman countenance a second-level analogue of the definite description operator; later in the paper he follows Frege in countenancing a second-level analogue of the identity predicate, which takes a predicate in each of its argument places and which I shall notate '=2'. (As with 'n 13 One candidate, Trueman notes, is Dummett's 'Vx(x is what n refers to $ Ux)', where the 'is' therein is meant to be the 'is' of predication rather than identity (Dummett 1981, p. 217). Naming the concept horse 2735 123 refers to U', there is no uncontroversial rendering of '=2'. Frege favoured 'Vx(Ux $Wx)'; Trueman suggests 'hVx(Ux $Wx)'.) Using the second-level analogues of the identity predicate and the definite description operator, an analogue of (i) for 'n is a horse' may be given as follows: (ii) The F such that 'n is a horse' refers to F = 2 is a horse. The admission of a second-level analogue of the identity predicate opens up a possibility for pursuing the second of the two kinds of objection mentioned at the start of Sect. 2.2. Specifically, it presents the option, not discussed in Trueman's paper, of stating Benno's thought using '=2' in conjunction with two predicates. Using '=2', we could employ 'n is a horse' itself to pick out the property to be identified with an object, rather than a surrogate singular term. Of course, this strategy of stating Benno's thought as a higher-level identity confronts a mirror image of the problem set out in Sect. 2.1: a singular term cannot fill an argument place of '=2', only a predicate; so in this case it is requisite to use a surrogate predicate to pick out the object we wish to identify with a property. But whichever predicate we select, Trueman will presumably claim, it will not present its referent as an object; so the resulting second-level identity sentence will fail to express Benno's thought. The challenge, if we are to maintain that Benno's thought can be expressed with a second-level identity sentence, is to find a predicate that presents its referent as an object, just as the challenge, if we are to maintain that Benno's thought can be expressed with a first-level identity sentence, is to find a term that presents its referent as a property. I hope to show in Sect. 4 that both of these challenges can be met, that Benno's thought is accordingly susceptible of expression either as a firstor as a second-level identity claim, and hence that Trueman's case against singular reference to properties fails. First, though, I want to raise a lesser objection to Trueman's argument: the argument does not, I submit, establish that it is nonsense to say that a property is an object; at most it establishes the disjunctive thesis that it is either nonsense or false to say that a property is an object. This disjunction of the nonsensicality and impossibility theses would still be a remarkable result. If Trueman were to have established the disjunction, he would have succeeded in ruling out singular reference to concepts (as either impossible or unintelligible). Nevertheless, it is worth making clear that, for all Trueman has shown, saying that a property is an object may at least escape the ignominious fate of being not even wrong. This emerges from an observation that will also provide inspiration in Sect. 4: even granting Trueman's claim that '''refers' for predicates must be read as 'n refers to U''' (Trueman 2015, §5), we can still insert the name of a predicate into the first argument place of 'n refers to f'; and when the second argument place is also filled with a singular term, the result will, at least, make sense. The sense of 'n refers to f' is only such as to require that the expressions introduced into its argument places have the characteristic kind of sense possessed by singular terms14; the name of a 14 Might it be objected that 'n refers to f' semantically requires more of the expressions admitted into its argument places than that they have the sense of singular terms? Perhaps: the introduction of certain singular terms into the first argument place of 'n refers to f' will produce sentences that might seem to be category mistakes-e.g. 'The Baltic Sea refers to Socrates'-and there are those who have wished to 2736 M. Price 123 predicate has that kind of sense.15 The sentence '''n is a horse'' refers to Socrates', for example, is perfectly meaningful. In that case, so is the generalization 'Ax(x is a predicate ^ x refers to Socrates)', as is its modalization 'eAx(x is a predicate ^ x refers to Socrates)'. The conjunction (iii) eAx(x is a predicate ^ x refers to Socrates) ^ eAy(y is a singular term ^ y refers to Socrates) must also make sense, since there is no doubt about the meaningfulness of the latter conjunct. Moreover, the result of existentially generalizing this conjunction in the position of 'Socrates' also makes sense: (iv) Az(eAx(x is a predicate ^ x refers to z) ^eAy(y is a singular term ^ y refers to z)) However, given the way in which 'object' and 'property' were introduced, (iv) is a very natural reading of 'A property is an object'. So there is a very natural way of taking 'A property is an object' on which it is perfectly meaningful.16 What, then, is the import of Trueman's claim that 'refers' for predicates must be read as 'n refers to U'? This: when we speak of predicates referring, it is a condition of the truth of what we say (not the meaningfulness of what we say) that 'refers' mean 'n refers to U'. Thus, the complaint against (iv) to which Trueman is entitled is not that it is nonsense, but that it is false-false because nothing satisfies the predicate 'eAx(x is a predicate ^ x refers to n)'. These considerations also bear upon the interpretation of 'the referent of ''n is a horse''' and the possibility of employing this expression to articulate Benno's Footnote 14 continued classify category mistakes as nonsense. However, firstly, it is not clear that the likes of 'The Baltic Sea refers to Socrates' really are category mistakes, at least if a category mistake represents an attempt to ascribe a property to an object that is of the wrong the kind to exemplify that property. After all, can't any object, in principle, serve as a name (see e.g. Lewis 1986, p. 145–6)? If so, the Baltic Sea is not of the wrong kind to instantiate the property of referring to Socrates. Secondly, there is a strong case to be made against the view that category mistakes are nonsense (see Magidor 2009; Magidor 2013), and the popularity of the view has certainly waned. Thirdly, even if there were categorial restrictions on the kind of thing a name of which can meaningfully appear in the first argument place of 'n refers to n'- restrictions that exclude objects like the Baltic Sea-those restrictions would have to be very stringent to exclude predicates: a predicate is a linguistic expression; is a linguistic expression not the kind of thing that can refer to Socrates, for example? Though I cannot address these issues in detail, I think this suffices to indicate the difficulties confronting the view that names of predicates cannot be meaningfully substituted for 'n' in 'n refers to f'. 15 I am, of course, here assuming that predicates can be named-i.e. that predicates are objects. Trueman also makes this assumption, though he evinces a suspicion that it is false (Trueman 2015, fn. 11). I shall only say that this is not a suspicion I share. Some commentators, of whom Geach is a notable example (Geach 1976b, pp. 59–61), (Geach 1961, p. 144), (Geach 1976a, p. 440)), have maintained that Frege himself deemed this assumption false and conceived of incomplete expressions (of which predicates are a species) as linguistic functions mapping singular terms or sentences to singular terms or sentences. I think these commentators are wrong. Several things Frege says indicate that he conceived of incomplete expressions as objects-e.g. Frege (1980, p. 136). 16 'A property is identical to some object' would be more naturally read as 'Az Av (eAx (x is a predicate ^ x refers to z) ^ eAy(y is a singular term ^ y refers to v) ^ z = v)'. Naming the concept horse 2737 123 thought. This expression can be interpreted as the result of first inserting the predicate name '''n is a horse''' into the first argument place of 'n refers to f', and then using a definite description operator to bind a term variable in the argument place of the resulting predicate, '''n is a horse'' refers to f'. Moreover, if 'the referent of ''n is a horse''', thus interpreted, were to refer, it would, in one sense, present its referent as something to which a predicate can refer. Letting 'refers1' mean 'n refers to f' and 'refers2' mean 'n refers to U', 'the referent of ''n is a horse''', thus construed, would present its referent as something to which a predicate can refer1. Moreover, if 'referred' in the stipulation, 'a property is anything that can be referred to with a predicate' (Trueman 2015, §2), is understood to be 'referred1', the resulting sense of 'property' is one on which 'the referent of ''n is a horse''', as presently construed, would present its referent as a property. Let 'property1' mean 'property' in this sense. If Benno's thought concerns the property1 referred to by 'n is a horse', there is, then, no problem in presenting it as such with a singular term, and therewith identifying it with an object, as follows: the referent of 'n is a horse' = the property horse. But the import of Trueman's claim that 'refers' for predicates must be read as 'n refers to U' is that (a) there is no property1 referred to by 'n is a horse', since (b) there are no properties1 at all, because predicates do not refer1, and hence (c) 'the referent of ''n is a horse''', on its present reading, lacks a referent, as 'n is a horse', in particular, does not refer1. It does not follow that 'the referent of ''n is a horse'' = the property horse' is nonsense, but the emptiness of the singular term left-flanking the identity sign renders the sentence at least untrue, a fate shared by Benno's thought if this sentence indeed expresses it. 4 In defense of singular reference to concepts 4.1 How to state object-property identities I: second-level operators If Benno's thought is to be neither inexpressible nor untrue, what appears to be requisite is a singular term that presents its referent as something to which a predicate can refer2. I propose that there is a way of construing 'the referent of ''n is a horse''', neglected in Trueman's paper, on which this expression is just such a singular term. This expression cannot, we have seen, be understood as the result of applying the standard term-variable-binding definite description operator to the predicate '''n is a horse'' refers to U': the argument place of this predicate cannot accommodate a term variable. But nor can it be understood, if it is to be singular term, as the result of applying to this predicate the second-level definite description operator Trueman countenances in the quotation at the end of Sect. 2.2: though this operator can bind a predicate variable in the argument place of '''n is a horse'' refers to U', it produces a predicate, not a singular term. However, these two operators do not, I submit, exhaust our options. In addition to a term-variable-binding, termforming operator and a predicate-variable-binding, predicate-forming operator, we can recognize a predicate-variable-binding, term-forming operator-one that (roughly) yields a complex name of the unique value of the predicate variable it binds (if there is one) that satisfies the relevant second-level predicate. This operator 2738 M. Price 123 would, firstly, be fit to bind a variable in the argument place of the second-level predicate '''n is a horse'' refers to U'; secondly, produce, when applied to that second-level predicate, a singular term that co-refers with 'n is a horse'; and thirdly, produce, crucially, a singular term that presents its referent as a property in the required sense-that is, as something to which a predicate might refer2. If there is such an operator, 'the referent of ''n is a horse''' may be understood as the result of applying this operator to the second-level predicate '''n is a horse'' refers to U'. If Trueman's argument is to go through, therefore, he requires that there can be no such operator. But what reason have we to preclude such a term-forming operator? Needless to say, variable-binding operators need not yield expressions of the same logical type as the variables they bind.17 Prima facie, the term-forming operator seems just as intelligible as the predicate-forming operator Trueman recognises. Neither operator is readily rendered in English (though I note that 'the F such that ''n is a horse'' refers to F' is much more straightforwardly heard as a singular term than a predicate). Are there any grounds for denouncing the operator I propose? There is at least one reason one might be concerned about it. Let's introduce some notation for the two predicate-variable-binding operators now on the table. Let Ip be the higher-level definite description operator Trueman recognizes (the subscript indicating that it is predicate-forming) and let It be the higher-level operator I propose that we recognize (the subscript indicating that it is term-forming). Call an Ip-predicate any predicate that results from binding a predicate variable in the argument place of a second-level predicate with Ip. Similarly, call an It-term any term that results from binding a predicate variable in the argument place of a second-level predicate with It. The proposal is to state the desired object-property identity, Benno's thought, as follows: (v) It F ('n is a horse' refers to U) = the property horse. Here is the concern.18 If we are to introduce It then we shall have to state its semantics. That means giving a principle that settles, given an arbitrary It-term, to what it refers. In the case of the standard definite description operator-which we now symbolize as i -we give some such principle as the following: (vi) For all x ('ix(Fx)' refers to x iff for all y (Fy iff x = y)). 17 More than one predicate-variable-binding, term-forming operator appears in Frege's own work. Firstly, since he thinks that sentences are names, the second-order quantifiers, on Frege's analysis, will surely count as such operators. Secondly, Frege will presumably want to recognise a second-level counterpart to his first-level notation for the value-range of a first-level function. The first-level notation features an operator (a Greek letter with a smooth breathing) that binds a first-order variable (the same letter without the smooth breathing) in the argument place of a function expression. Applied to 'f' the operator yields a name of the value-range of f0-viz. 'e9 f (e)'. See Frege (1997b, p. 136–7). The secondlevel counterpart of this notation will feature an operator that binds a function variable (e.g. a predicate variable) in the argument place of a second-level function expression 'Q', and yields a name of the valuerange of Q. This operator will thus be both predicate-variable-binding and term-forming. 18 I'm grateful to Robert Trueman for impressing the following kind of worry upon me in correspondence. Naming the concept horse 2739 123 Roughly, this tells us that the result of applying i to a first-level predicate 'Fn' refers to any object, and only that object, that uniquely satisfies 'Fn'. Likewise, in the case of Ip we can give the following principle for an arbitrary Ip-predicate: (vii) For all F ('Ip F(QF)' refers to F iff for all G (QG iff G = 2F)). Roughly, this tells us that the result of applying Ip to a second-level predicate, 'QU', refers to any property, and only that property, that uniquely satisfies 'QU'. However, we run into difficulty when we attempt to state a corresponding principle for It. The temptation is to offer something like the following: (viii) For all x ('It F(QF)' refers to x iff for all G (QG iff G = x)). But, of course, this is nonsense: no sense has been given to '=' that would permit it to receive a predicate (variable or constant) into one argument place and a singular term (variable or constant) into the other. So then how are we to give the intended semantics of It? A more promising attempt to state a corresponding principle for It is as follows: (ix) For all F ('It F(QF)' refers to F iff for all G (QG iff G = 2F). In the left-hand clause of the bi-conditional, 'refers to' is 'n refers to U'. This might seem aberrant, since 'ItF(QF)' is intended to be a singular term, not a predicate. However, there is, of course, no syntactic obstacle to our inserting the name of a singular term into the first argument place of 'n refers to U', and the results of doing so are perfectly meaningful, just as-we saw in Sect. 3-the results of inserting the name of a predicate into the first argument place of 'n refers to f' are perfectly meaningful. Note that the strategy of inserting the name of a singular term into the first argument place of 'n refers to U' also affords a way of pursuing the neglected approach mentioned in Sect. 3: expressing an object-property identity using two predicates in conjunction with the second-level analogue of the identity predicate. In particular, it seems to enable us to produce a predicate that presents its referent as an object. We may insert, for example, 'the property horse'-the name of an object with which we wish to identify a property-into the first argument place of 'n refers to U'. To the predicate that results-'''the property horse'' refers to U'-we may then apply the predicate-forming operator Ip to yield: 'IpF (''the property horse'' refers to F)'. This predicate appears to present its referent as something to which singular reference can be made, and to allow us to state the desired object-property identity as follows: (x) Ip F ('the property horse' refers to F) = 2 is a horse. The concern, though, about inserting the name of a singular term into the first argument place of 'n refers to U', and thus about the proposed strategies for stating the It operator's semantics and articulating Benno's thought with the higher-level identity sentence, (x), will be this: Trueman's argument that 'refers' in talk of predicates referring must be read as 'n refers to U' will be paralleled by an argument that 'refers' in talk of singular terms referring must be read as 'n refers to f'. In brief: it is only possible to state a disquotation sentence, like (i), for a singular term using 'n refers to f', not 'n refers to U'. 2740 M. Price 123 However, I believe we now have the resources to reply to this argument and to vindicate the use of 'n refers to U' in speaking of singular terms referring. The challenge is to formulate a disquotational identity, analogous to (i), for a singular term, using 'n refers to U'. Letting 'a' be a singular term, I propose that the following meets this challenge: (xi) It F ('a' refers to F) = a. We here employ our term-forming operator It to form a term that picks out the unique property to which 'a' refers-if there is such a property-and say that that property is identical to a. The reference predicate we use is 'n refers to U'. The reader will have noticed that there is a circularity here: we have sought to vindicate the use of 'n refers to U' to specify the referent of a singular term, by giving a disquotational identity that makes use of the It operator; and we gave the semantics of It using a principle-(ix)-that itself uses 'n refers to U' to specify the referent of a singular term. However, I simply see no reason to think that this circularity is vicious. It is certainly not generally to be expected that the semantics for an expression may be given in a manner completely devoid of circularity. Absent a reason for thinking the circularity in this particular instance a cause for concern, I conclude that the use of 'n refers to U' in speaking of singular terms referring satisfies Trueman's requirement concerning the possibility of stating disquotation sentences. I have now adduced two methods of expressing Benno's thought, each exploiting a second-level variable-binding operator: firstly, with the first-level identity sentence, (v), using It; and secondly, with the second-level identity sentence (x), using Ip. So far, no reason has been given to doubt that these methods succeed. 4.2 How to state object-property identities II: first-level operators Having recognized a predicate-variable-binding, term-forming operator in addition to a term-variable-binding, term-forming operator and a predicate-variable-binding, predicate-forming operator, it is natural to complete the square and recognize a term-variable-binding, predicate-forming operator. This first-level operator, which we symbolise ip, binds a term variable in the argument place of a first-level predicate and, informally, yields a predicate referring to the unique value of that term variable (if there is one) that satisfies that first-level predicate. The semantics for ip, can more formally be captured by the following principle: (xii) For all x ('ipx(Fx)' refers to x iff for all y (Fy iff x = y)). 'ipx(Fx)' is a predicate, and the principle tells us, intuitively, that it is a predicate whose referent is the unique object that satisfies the predicate 'Fn'. But since it is a predicate, (xii) involves the appearance of a predicate in the first argument place of 'n refers to f'. Surely this falls foul of Trueman's argument that 'refers' in talk of predicates referring must be read as 'n refers to U'? However, I believe we now have the resources to reply to this argument and to vindicate the use of 'n refers to f' in speaking of predicates referring. The challenge is to formulate a disquotational identity, analogous to (i), for a predicate, using 'n Naming the concept horse 2741 123 refers to f'. Letting 'Fn' be a predicate, I propose that the following meets this challenge: (xiii) ip x ('Fn' refers to x) = 2 F. We here employ our predicate-forming operator ip to form a predicate that picks out the unique object to which 'Fn' refers-if there is such an object-and flank the second-level analogue of the identity sign with this predicate and the disquoted predicate 'Fn'. The reference predicate we use is 'n refers to f'. We find a circularity here, parallel to the circularity involved in our vindication of the use of 'n refers to U' in speaking of singular terms referring: we seek to vindicate the use of 'n refers to f' in speaking of predicates referring, by giving a disquotational identity that makes use of the ip operator; and we gave the semantics of ip using a principle-(xii)-that itself uses 'n refers to f' to specify the referent of a predicate. But again, I just see no reason to think that this circularity is in any way pathological. I conclude that the use of 'n refers to f' in speaking of predicates referring satisfies Trueman's requirement concerning the possibility of stating disquotation sentences. Having recognized the ip operator and vindicated the use of 'n refers to f' for predicates, we are, I submit, afforded two further methods for stating Benno's thought. Firstly, we may use the ip operator to construct a predicate that presents its referent as an object: 'ip x ('the property horse' refers to x)'. Therewith, we may formulate Benno's thought as the following second-level identity: (xiv) ip x ('the property horse' refers to x) = 2 is a horse. Secondly, we may use the ordinary definite description operator to construct a singular term that presents its referent as a property: 'i x ('n is a horse' refers to x)'. Therewith, Benno's thought can be naturally stated as the following first-level identity: (xv) i x ('n is a horse' refers to x) = the property horse. Exploiting the first-level operators i and ip, we can, I conclude, again either express Benno's thought as a first-level identity claim or as a second-level identity claim. 5 Conclusion I hope to have established that, pace Trueman's argument, Benno's thought does admit of expression. It can be expressed, I claim, as a first-level identity, using (v) or (xv), or as a second-level identity, using (x) or (xiv). Benno's thought was just an arbitrary object-property identity, so I conclude that it is possible to express objectproperty identities. If I am right, Trueman has failed to establish that it is nonsense to say, generally, that a property is identical to some object. But nor has he has established that it is false to say so: for no reason has been given for thinking that (v), (xv), (x) and (xiv), each of which can be understood as instances of this existential generalization, are false. I hold, then, that singular reference to properties/concepts survives Trueman's assault. If the Fregean position is to be upheld, justification must be sought elsewhere. 2742 M. Price 123 Acknowledgments Many thanks to Neil Dewar, Adrian Moore, James Openshaw, James Studd, Robert Trueman and Timothy Williamson. I'm grateful to the Arts and Humanities Research Council for awarding me a studentship, during which part of this paper was written. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. References Dummett, M. F. (1981). Philosophy of language (2nd ed.). London: Duckworth. Frege, G. (1979a). A criticism of Kerry. In H. Hermes, F. Kambartel & F. Kaulbach (Eds.), Posthumous writings (P. Long & R. White, Trans.). 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Moore, A. (1997). Points of view. Oxford: Clarendon Press. Noonan, H. W. (2006). The concept horse. In P. Strawson & A. Chakrabarti (Eds.), Universals, concepts and qualities: New essays on the meaning of predicates. Aldershot: Ashgate. Oliver, A. (2005). The reference principle. Analysis, 65(287), 177–187. Proops, I. (2013). What is Frege's 'concept horse problem?'. In P. Sullivan & M. Potter (Eds.), Wittgenstein's Tractatus: History and interpretation. Oxford: OUP. Sullivan, P. M. (2002). On trying to be resolute: A response to Kremer on the tractatus. European Journal of Philosophy, 10(1), 43–78. Rayo, A. (TS). A compositionalist's guide to predicate reference. Typescript. Available at http://web.mit. edu/arayo/www/ch.pdf. Accessed 10 May 2015. Textor, M. (2010). Frege's concept paradox and the mirroring principle. Philosophical Quarterly, 60(238), 126–148. Trueman, R. (2015). The concept horse with no name. Philosophical Studies, 172, 1889–1906. Wittgenstein, L. (1974). Tractatus logico-philosophicus. Oxford: International Library of Psychology, Philosophy, and Scientific Method. Routledge. Wittgenstein, L. (2010). Philosophical investigations. Revised fourth edition. New York: Wiley. Naming the concept horse 2743


Review of P. Curd, The Legacy of Parmenides

Philosophy

BMCR Bryn Mawr Classical Review BMCR 1999.06.21 The Legacy of Parmenides Curd, Patricia, 1949-, The legacy of Parmenides : Eleatic monism and later presocratic thought. Princeton: Princeton University Press, 1998. x, 280 pages ; 24 cm. ISBN 9780691011820 $45.00. Review by Monte Johnson, Philosophy, University of Toronto. email@example.com If you are primarily interested in the Presocratics as analytical cosmologists, logicians, epistemologists, and scientific methodologists, then this book will be of great interest to you. If you are primarily interested in the Presocratics as enigmatic poets, prophets, healers, and law-givers, then it won't. As should be obvious from the title, The Legacy of Parmenides is a very ambitious book. Curd undertakes a thorough exposition of Parmenidean philosophy, from his influences to his immediate successors, while dealing with most of the relevant post-war secondary literature (especially Owen, Barnes, Coxon, Taran, Kahn, Mourelatos, and Robinson). The book reads somewhat like a commentary, quoting, translating, and commenting on the Greek text, according to the traditional ordering of the fragments. (The secondary sources are for the most part treated in the very extensive footnotes). In addition to the exegesis of Parmenides' poem, Curd provides interpretations (as well as relevant texts and translations) of the Ionians, the Pluralists, Zeno, the Atomists, Melissus, Philolaus of Croton, and Diogenes of Apollonia. Specialists with an interest in any of these figures and movements will need to deal with Curd's positions and will benefit from her survey of the contemporary literature. On the other hand, the book is probably too technical (and expensive) to serve students looking for an overview of the philosophical activity of Socrates' predecessors. Throughout the book, Curd seeks to situate Parmenides firmly in the debates about cosmology that occurred in Greece from the sixth through the fourth centuries BC (p. 4, 27, 64, 95, 127-8, 217, 241). According to Curd, the standard interpretation of Parmenides portrays him as an isolated figure, largely unprecedented and more or less ignored by his successors, at least until Plato's 'later' dialogues (p. 3, 10-11, 27). This interpretation, whether or not it is standard, is an extreme one and Curd's is at the opposite end. She portrays the Pre-Socratic philosophers as a tight-knit bunch with ample access to each other's positions, engaged in a continuous dialectic, the results of which were invariably cumulative and progressive. There is something productive about this methodological assumption: the texts mutually illuminate one another when their arguments are cast as entries into a huge metaphysical debate spanning multiple centuries and continents. But historical concerns threaten to undermine such an endeavor, and so Curd asks the reader to accept her chronological assumptions in exchange for the results of her interpretations (p. 15-18, 129, 19). The results are indeed impressive, and I will try to summarize some of the more important of these after stating my main complaint with the book. Curd's outlook assumes that cosmologists are Parmenides' only opponents and audience. His writing is exclusively 'philosophical' in the sense that it addresses only cosmological and scientific concerns, and scientists and cosmologists are the only people for whom he is writing. Is it not possible that Parmenides was also concerned to address other poets, politicians, sophists, doctors, laymen, and priests, as well? Of course Parmenides and his fellow 'Presocratics' were philosophers, but they were not part of an organized or exclusive discipline. What is fascinating to many of us about the Presocratic period is the total lack of consensus on what constituted philosophy, its ends, means, limits, possibilities, relation to other cultural spheres, etc. A central question for Presocratic studies in general, and Parmenidean studies in particular, is: what were they doing when they do what we now call 'philosophy'? In other words, what is philosophy? Curd's approach seems to me to preclude any discussion of this issue. For she comes to the table with a preconception of what philosophy is, and uses that preconception to determine what is important in Parmenides and his predecessors and successors. The most obvious influence on Parmenides is epic poetry. Parmenides wrote his poem in the style of Homer and Hesiod and would have expected his audience to have been educated primarily by means of their poems. If he was writing exclusively in response to, and for, other cosmologists, then why did he not write in their prose style? Xenophanes, who is often regarded as an influence on Parmenides, was a traveling bard and a performer of epic poetry as well as his own cosmological verses. There is strong reason to think that the epic poets, especially Hesiod, were Parmenides' target, and that people versed as much in epic poetry as in Ionian science were Parmenides' intended audience. Heraclitus, whom Curd claims Parmenides probably read, explicitly inveighed against the poets (fragments 40, 104, & 106). If Parmenides was in fact making a radical break with the poetic tradition in favor of the newly developing philosophical one, then it seems likely that his arguments would have been directed at the former at least as much as the latter. Curd abruptly dismisses this suggestion, which was originally Fraenkel's, in a footnote on page 117. But this is certainly too hasty. Consider the following lines of Hesiod: "the ready-voiced daughters of Great Zeus breathed into me a divine voice to celebrate things that shall be ( τὰ ἐσσόμενα) and things that were aforetime ( τὰ ἐόντα)" (29, 31-32). "let us begin with the Muses telling of things that are ( τὰ ἐόντα) and that shall be ( τὰ ἐσσόμενα) and that were aforetime ( πρὸ ἐόντα)" (36, 38). Compare Parmenides: "what-is ( ἐόν) is ungenerated and unperishable. Nor was it once ( ἤν), nor will it be ( ἔσται), since it is now ( νῦν ἔστιν), all together" (fragment 8.3-5). The Hesiodic lines come in the proem of Theogony, which contains at least three distinct preludes (beginning at lines 1, 36, and 104). By comparison, the 32 lines of proem in Parmenides' poem comprise at least a fifth of the extant lines. The proem(s) in the Theogony serve to establish the purpose of the poem and the poet's sense of his own authority and relationship to the truth. For Parmenides, concerned as he is with epistemological issues, this is a fortiori so. But although Curd's exegesis of the Parmenidean poem itself spans more than 100 pages, fewer than 6 are devoted to the proem (except for a single footnote on p. 103). Curd admits "pessimism concerning the allegorical significance of the kouros's journey" (p. 20), but is confident that the rest of the poem can be interpreted nonetheless because, "unlike other surviving pre-Parmenidean appeals to the Muses or representations of divine inspiration, Parmenides' inspired poem is a work of philosophy" (p. 20). What philosophy is, at this point, is made explicit neither by Parmenides nor by Curd. There is something wrong with using one's own conception of philosophy as a justification for eliminating a substantial part of another philosopher's text. Other commentators have advanced much more thoughtful interpretations of the proem, even in far less extensive studies. This is because the proem itself, and not just the 'rest of the poem', is philosophical. Sextus Empiricus saw it that way; he offered a detailed allegorical interpretation of the poem as the best encapsulation of Parmenides' entire philosophy ( M. VII.111ff.). More recently, commentators have used the evidence of the proem in arguments against certain interpretations of Parmenidean metaphysical or epistemological doctrines. A good example at hand is R. Waterfield's review of G. Vlastos (BMCR 95.06.17); Waterfield refers to a number of studies of the proem that conclude that the kouros's journey is from light into darkness, in order to show that Parmenides could not have simply associated Night with ignorance. Another example is P. Kingsley's recent book on Parmenides, which largely focuses on the proem ( In the Dark Places of Wisdom, Inverness, CA, 1999). So, despite her otherwise comprehensive survey of the contemporary literature, Curd all but ignores this important part of the debate about Parmenides. The result is that we are left wondering whether or not Curd could possibly be right about Parmenides' objectives, targets, and audience. But, if we take science and cosmology to be Parmenides' exclusive concern, then Curd offers a very compelling reading of the rest of Parmenides' poem (fragment 2 and following). Instead of rejecting the inquiry into nature, as he has often been thought to do, Parmenides seeks to "make it legitimate" (p. 27); thus his concern is "as much methodological as metaphysical" (p. 35). A legitimate cosmology is one that proposes "theoretically basic entities" or "natures" (p. 81, 97) which meet certain metaphysical and epistemological criteria (p. 35, 62, 67). These criteria are outlined in the aletheia as a series of tests. Cosmologies whose basic entities do not pass the tests are deceptive, examples include those of Thales, Anaximander, Heraclitus, and the one proposed by the goddess herself in the doxa. Examples of cosmologies that might pass the tests are those of the pluralists (Anaximines, Empedocles, the Atomists, and Plato's theory of forms as presented in the early and middle dialogues). It might seem shocking that the material monists fail to pass Parmenides' test, while those of the pluralists do. This is where Curd's interpretation is most original and radical. She holds that Parmenides' brand of monism is neither material (there is only one underlying matter) nor numerical (exactly one thing exists), but predicational (each thing is only one thing). Thus pluralism is, in theory, compatible with Parmenides' brand of (predicational) monism, because "it is possible for there to be a numerical plurality of entities each of which is predicationally one" (p. 5). In fragment 2, Parmenides observes that there is a fundamental krisis between is ( ἔστι) and is-not ( οὐκ ἔστι and argues these designate two 'routes' that can be followed. The former is legitimate, the latter is not. According to Curd, there is no third or intermediate route; any attempt to think what is-not puts one on the negative route. The two questions that have most puzzled commentators are: (1) What is the subject of the ἔστι (2) What is the sense of the ἔστι ? The standard interpretation holds that the subject is 'whatever can be spoken or thought', and the sense is existential; thus 'whatever can be thought or spoken of exists'. Curd criticizes this solution, and offers her own interpretation. She suggests that the subject of the ἔστι is "what it is to be the genuine nature of something" (p. 4). The sense of the ἔστι is predicational. Whatever a cosmologist proposes as a basic entity can be inserted as the subject of the ἔστι. The point is then to determine if the subject meets the criteria required by monistic implications of the predicational ἔστι. If not, then the cosmology is metaphysically and epistemologically unsound. The criteria stem from the nature of what is. What is is neither mutable (generable, perishable, or divisible) nor incomplete. A basic entity is predicationally monistic, and thus cosmologically legitimate, only when it is immutable and complete. Thales' basic entity, water, fails, because it is generated and destroyed (p. 70-71) and, more fundamentally, because it changes from water into not water (because, on Thales' account, the fundamental entity changes from water into some phenomenal thing, p. 74). Anaximander's apeiron gives rise to something that is both hot and cold, and so fails the test by changing into both what is (hot) and what is not (hot). All dualistic cosmologies fail the test, because they assume that a fundamental entity can change into opposite things. The most explicit example of this is in Heraclitus' doctrine of the unity of opposites. (I leave aside the question of whether we should actually interpret Heraclitus as having advanced such a doctrine. Some have argued that he did not, and that he is actually very close to Parmenides on this very issue. But Curd presents a plausible, and in fact standard, interpretation of Heraclitus, one that serves as a perfect foil for her Parmenides.) Finally, the cosmology presented by Parmenides himself in the doxa is the epitome of a deceptive dualism. The basic entities or principles of the doxa, light and night, are dualistic opposites (as curd argues, "enantiomorphic" opposites). Thus the doxa serves as a pedagogical tool: by applying the criteria of the aletheia, one can determine the reason why this sort of explanation of the world, as it is presented to the senses, is false. The rest of Curd's book considers the influence Parmenides' poem had on his philosophical successors. The focus here is on the pluralists. In Anaxagoras, the chremata show themselves to be entities that meet Parmenides' criteria: they are neither generated nor destroyed, they are complete and unified, and they have a stable and immutable nature (p. 154). Empedocles' roots are Parmenidean entities, each with its own unchanging nature, not subject to generation or destruction, even if the account of phenomenal change in terms of mixture and separation (and the dualism of love and strife) follows Parmenides' model in the doxa. Now both Anaxagoras and Empedocles argue for a plurality of basic entities, but do not make explicit arguments for a pluralistic cosmology as such. For Curd, this counts as evidence for her interpretation of Parmenides as a predicational but not numerical monist. If Parmenides had been a numerical monist, then these later philosophers would have had to justify their pluralism. But their silence on this issue, and their adherence to predicational monism with respect to the basic entities, is for Curd positive evidence that Parmenides did not mean to argue that 'exactly one thing exists'. We might pause to consider if this is sound methodology: does lack of a response in a subsequent thinker imply that the thinker accepts a predecessor's argument? This is a particularly questionable inference when the subsequent thinker's work survives only in fragments. At any rate, Curd argues that, for Parmenides' successors at least, it does. See pages 8, 128, 171, 242. Some of the most interesting results turn up in Curd's treatment of Zeno and the Atomists. Zeno's paradox about divisibility applies to any corporeal entity. It threatens the pluralistic accounts not because they posit a numerical plurality of entities, but because they posit corporeal entities as really existing. Curd has already argued that a plurality of corporeal entities is consistent with Parmenides' arguments so long as they are predicational monads. Curd argues that Zeno's arguments could actually be used against Parmenides' account insofar as it allows for the real existence of corporeal entities (p. 177). So, on Curd's account, the pluralists (who are traditionally assumed to be in direct opposition to Eleaticism) seem to advance fundamentally Parmenidean positions, while Zeno (traditionally taken to be the 'faithful servant of Parmenides' views' - p. 171-2) might be a critic of the whole lot! Consequently, we need to revise our concept of Eleaticism to make room for critical developments within the school (p. 179). Curd's account of the Atomists is more or less standard, since it serves her story well that a major motivation for Atomism was evidently to posit entities that avoid Zeno's divisibilty paradoxes and meet Parmenidean criteria for what-is. With respect to the void she argues that the Atomists endeavored to show that it is real and exists, despite having no character of its own, and so tried to revise the Parmenidean criteria for what-is (p. 197ff.). Melissus is a more radical monist than Parmenides, Curd argues, because he takes both numerical and predicational monism to be a consequence of the rejection of generation and destruction (p. 209-11). Thus the traditional interpretation of Parmenides applies rather to Melissus, and a comparison of the differences between the two is further evidence that Parmenides himself was not committed to numerical monism. Curd next deals with Philolaus of Croton and Diogenes of Apollonia. Here again Curd's intention is to demonstrate their concern to abide by the Parmenidean criteria for what is. Finally, Curd argues that Plato was "the last presocratic" (p. 228ff.) insofar as the theory of forms as presented in the early and middle period dialogues conforms to Parmenidean criteria. This is most evident in the account of the form of beauty in the Symposium (210e6-211b5, Curd, p. 229). In a provocative, but severely underdeveloped argument, Curd claims that Plato's criticisms of Parmenides in later dialogues, such as Sophist and Parmenides mistakenly assume that Parmenides' monism is numerical, and that this assumption had a pernicious influence on all subsequent Parmenidean interpretation (p. 240). This argument is asserted but not developed, and Curd unfortunately does not deal with Plato's arguments from the later dialogues in any detail. Although it is reasonable for the author to circumscribe her own area of concentration, the book seems incomplete without some reference to Timaeus. The speech of Timaeus is effectively a Peri Physeos, complete with an invocation of the relevant gods, methodological prologue, theory of elements, cosmology, astronomy, psychology, human physiology, and embryology. All of these are topics with which Parmenides dealt in the second (presumably longer) philosophical poem. This summary is intended to give readers of this journal a glimpse of the daring interpretations and farreaching implications of Curd's work. The reviewer only wishes that Curd would have also advanced an interpretation of the poetic, religious, medical, and rhetorical aspects of Parmenides' 'philosophical poem', for these too constitute no small part of Parmenides' legacy.