1 RAMSEY ON UNIVERSALS Fraser MacBride Published in Ramsey’s Legacy, edited by H. Lillehammer & D.H. Mellor (Cambridge University Press, 2005), pp. 83-104. Abstract. According to philosophical folklore Ramsey maintained three propositions in his famous 1925 paper “Universals”: (i) there is no subject-predicate distinction; (ii) there is no particular-universal distinction; (iii) there is no particular-universal distinction because there is no subject-predicate distinction. The ‘first generation’ of Ramsey commentators dismissed “Universals” because they held that whereas predicates may be negated, names may not and so there is a subject-predicate distinction after all. The ‘second generation’ of commentators dismissed “Universals because they held that the absence of a merely linguistic distinction between subject and predicate does not provide any kind of reason for doubting that a truly ontological (i.e. non-linguistic) distinction obtains between particulars and universals. But both first and second-generation criticisms miss their marks because Ramsey did not maintain the three identified propositions. The failure of commentators to appreciate the point and purpose of the position Ramsey actually advanced in “Universals” results from (a) failing to consider the range of different arguments advanced there, (b) looking at “Universals” in isolation from Ramsey’s other papers and (c) failing to consider Ramsey’s writings in the context of the views that Russell and Wittgenstein held during the early 1920s. Seen from this wider perspective Ramsey arguments in “Universals” take on an altogether different significance. They not only anticipate important contemporary developmentsthe resurgence of Humeanism and the doctrine that the existence of universals can only be established a posterioribut also point beyond them. 1. Introduction 2. What the Commentators say 3. Paradox, Complex Universals and Necessary Connexions 4. Our Knowledge of Relations 5. Conclusion 1. Introduction Is there a fundamental division of objects into two classes, particulars and universals? This was the question that Ramsey set out to address in his 1925 Mind paper “Universals”. After considering a variety of different arguments in favour of a fundamental division he came to the sceptical conclusion that there was no reason to suppose such a division between particulars and universals obtained. The theory of universals, Ramsey declared, was “nothing but a muddle” (see his [1925], p. 30). 2 “Universals” has not received the critical attention it deserves. Despite the great burgeoning of interest in universals over the last twenty-five years and the fact that so many contemporary theoretical developments presuppose the existence of a fundamental division between particulars and universals, Ramsey’s views have received little or no attention.1 Why has “Universals” been so neglected? Partly because many of Ramsey’s commentators have thought it possible to say simply, shortly and decisively why the arguments of “Universals” are mistaken. But Ramsey has been ill served by his commentators. They have failed to appreciate the significance of “Universals” because they have treated its arguments in isolation not only from one another but also from arguments employed by Ramsey in other writings and the evolving views of Russell and Wittgenstein that influenced Ramsey. When placed in this wider context it is evident that the arguments of “Universals” cannot be so easily dismissed. It also becomes evident that “Universals” continues to bear significance for contemporary debate. 2. What the Commentators say One of Ramsey’s main aims in “Universals” was to undermine the view that the linguistic distinction between subject and predicate corresponds to a “difference in the functioning of the several objects in an atomic fact” (Ramsey [1925], p. 17). Indeed it is for a summary argument to this effect that “Universals” is usually remembered. According to this argument the same object may “in a sufficiently elastic language” be denoted by both subject and predicate expressions: given a sentence whose subject denotes an object t and whose predicate denotes an object t*, another sentence that “asserts the same fact and expresses the same proposition” can be found where t* is denoted by a subject expression and t by a predicate expression. Ramsey offered “Socrates is wise” and “Wisdom is a characteristic of Socrates” as a natural language example of two sentences so related (see his [1925], p. 12). He then concluded that no fundamental classification of objects could be based upon the distinction between subject and predicate. Ramsey expressed the argument in the following terms: 1 For example, “Universals” receives no mention in either David Armstrong’s two-volume work Universals & Scientific Realism (1978) or his more recent A World of States of Affairs (1997). Hugh Mellor provides the notable exception to the rule, appreciating early on both the structure and significance of Ramsey’s views on universals. See his introduction to Ramsey [1978] and Mellor [1980]. 3 “Now it seems to me as clear as anything can be in philosophy that the two sentences ‘Socrates is wise’, ‘Wisdom is a characteristic of Socrates’ assert the same fact and express the same proposition. They are not, of course, the same sentence, but they have the same meaning, just as two sentences in different languages can have the same meaning. … Now of one of these sentences ‘Socrates’ is the subject, of the other ‘wisdom’; and so which of the two is subject, which predicate, depends upon which particular sentence we use to express our proposition, and has nothing to do with the logical nature of Socrates or wisdom, but is a matter entirely for grammarians. In the same way, with a sufficiently elastic language any proposition can be so expressed that any of its terms is the subject. Hence there is no essential distinction between the subject of a proposition and its predicate, and no fundamental classification of objects can be based upon such a distinction.” (Ramsey [1925], p. 12) Despite its superficial clarity this argument resists straightforward interpretation. The argument evidently relies on an underlying conception of propositions that enables a single proposition to be expressed by sentences that differ in the subjects and predicates they contain. This conception may have been as clear to Ramsey “as anything can be in philosophy”. But unfortunately “Universals” contains no explicit guidance on the identity or character of propositions. Nor does it contain an account of the relationship between propositions and the sentences that express them and the facts they assert.2 Despite these difficulties in interpretation Ramsey’s commentators have attributed to him on the basis of this argument the following three claims: (1) there is no subject-predicate distinction (2) there is no particular-universal distinction (3) there is no particular-universal distinction because there is no subjectpredicate distinction His commentators have then dismissed “Universals” by pointing to what they take to be the errors inherent in one or other of these claims. There have been identifiable generational differences in the criticisms that Ramsey’s commentators have brought to bear upon “Universals”. What I will callby rough and ready standardsthe first generation of commentators rejected (1). They based their contrary claim that there is a subject-predicate distinction upon the observation that whereas predicates may be negated names may not. For every 2 In his critical notice of the Tractatus Ramsey articulates a conception of propositions as types of linguistic or mental representations. And, at least in his 1925 paper “The Foundations of Mathematics”, he appears to endorse it (see Ramsey [1923], [1925a], pp. 168-9). But in “Universals” Ramsey appears to drift between a linguistic conception and one whereby propositions enjoy worldly constituents (compare Ramsey [1925], p. 16 and p. 29). In his later “Facts and Propositions” Ramsey appears to adopt a multiple relation theory of belief that obviates the need to posit propositions (see his [1927], pp. 33-4). 4 predicate F, they claimed, there is another, its contradictory ~F, such that when each is attached to a common subject a the result is a pair of contradictory sentences (Fa and ~Fa); but there are no such contradictory pairs of names (see Geach [1950], pp. 474-5, [1975], pp. 143-4, Anscombe [1959], p. 108 and Dummett, [1973], pp. 63-4). The first generation of commentators adhered to a broadly Fregean conception of ontology. According to this conception it is the logical behaviour of the expressions that denote a thing that determines the ontological category to which it belongs. By contrast, the second generation of Ramsey commentators self-consciously rejected the Fregean conception (see Simons [1992], Dokic & Engel [2002], pp. 40-1, Lowe [forthcoming], sec. 3). Instead they adhered to an alternative conception that denies language the role of authoritative guide to ontology. According to this conception the categorial status of an entity is determined quite independently of the behaviour of expressions that denote it. Consequently the second generation of commentators rejected (3) because the absence of a linguistic distinction between subject and predicate hardly providesgiven the conception of ontology adhered toa reason for supposing an ontological distinction between particular and universal to be absent too.3 This view of things is encapsulated in Peter Simons’ judgement on “Universals”: The supreme questionable presupposition of Ramsey’s paper…is that the logical structure of language is (or is meant to be) our infallible guide to ontology. Personally I consider it fundamentally mistaken to try to read important ontological or metaphysical theses out of logical or linguistic ones; it is one place where much of analytical philosophy, of which Ramsey is such a prime exponent, went wrong. It is pleasing that modern realists about universals, such as David Armstrong have come to accept this, and have abandoned the bad old linguistic arguments” (see Simons [1992], p. 159). Unfortunately both generations of commentators have got it wrong. They have failed to interpret “Universals” properly and consequently their criticisms miss their mark. They miss their mark because Ramsey did not advance any of the three claims (i)-(iii) attributed to him. The first clue that their interpretations have gone awry arises in the sentence that immediately succeeds the above argument from “Universals”, a sentence that provides Ramsey’s own commentary on its significance: 3 “Universals” may, of course, be criticised in other ways. Braithwaite [1926] and Strawson [1959], pp. 160-1 argue that the particular-universal distinction may be understood in (roughly) spatio-temporal terms. MacBride [1998] and [2001] raise a variety of considerations that speak against this line of criticism. Wisdom [1934], pp. 208-9 responds to Ramsey’s scepticism about the particular-universal distinction by claiming that the identity of indiscernibles applies to universals but not particulars. 5 “I do not claim that the above argument is immediately conclusive; what I claim is that it throws doubt upon the whole basis of the distinction between particular and universal as deduced from that between subject and predicate, and that the question requires a new examination” (Ramsey [1925], p. 13). This indicates that we cannot expect to come a proper appreciation of the position that he actually advance without also examining the other arguments that Ramsey provides in “Universals”. 3. Negation, Complex Universals and Necessary Connexions Where did the first generation of commentators go wrong? They took Ramsey to deny that there is any logical distinction that obtains between subject and predicate. But Ramsey did not deny anything so strong. He sought only to cast doubt upon the assumption that differences that obtain between the linguistic expressions “Socrates” and “is wise” correspond to differences amongst the constituents of the proposition that “Socrates is wise” expresses and the fact that makes the sentence true (if it is). Moreover, there is evidence to suggest that Ramsey would have treated with equanimity the observation that whereas predicates may be negated names may not. For Ramsey did deny that a predicate sign that contains a negation corresponds to a constituent of an atomic fact. He affirmed instead that predicate signs that contain a negation are to be treated as “incomplete symbols”. Incomplete symbols are expressions thatlike definite descriptions conceived à la Russellmake a systematic contribution to the sentences in which they occur but do not do so by indicating a constituent of the propositions these sentences express or the facts that make them true (if they are). Once this move is made it is no longer possible to simply read off a distinction between the constituents of atomic factsbetween particulars and universalsfrom a distinction between expressions that can be negated (predicates) and expressions that cannot (names). The passage that supplies evidence for this interpretation occurs in the penultimate paragraph of “Universals”. In this passage Ramsey asserts that the possibility cannot be ruled out that there are atomic facts consisting of two objects of the same type. Ramsey then considers an objection: “It might be thought that this would involve us in a vicious circle contradiction, but a little reflection will show that it does not, for the contradictions due to letting a 6 function be its own argument only arise when we take for argument a function containing a negation which is therefore an incomplete symbol not the name of an object” (Ramsey [1925], pp. 29) In this passage Ramsey is alluding to the class of paradoxes that Russell discovered in 1902 and that now bear his name. The most famous, the paradox of the class of all classes that are not members of themselves, arose from an examination of Cantor’s proof that there is no greatest cardinal number. However, it is a consideration of another version of what Russell called “the Contradiction” that will most readily enable us to appreciate the significance of the above passage from “Universals”: “If x is a predicate, x may or may not be predicable of itself. Let us assume that “not predicable of oneself” is a predicate. Then to suppose either that this predicate is, or that is not, predicable of itself, is self-contradictory” (Russell [1903], §101) Russell asks us to consider a function sign “not predicable of oneself” that contains a negation. He then shows that a contradiction arises when this function sign is applied to itself (allowed to figure in its own argument position). Russell took it to be “obvious” what conclusion to draw: “‘not predicable of oneself’ is not a predicate”. Ramsey’s contention that function signs that contain a negation are incomplete symbols contains the germs of a related solution to the contradiction. It is because these symbols are not names but contribute to the sentences in which they occur in some different way that functions sign containing a negation are not capable of selfascription. Ramsey does not elaborate on the kind of semantic contribution he supposes these symbols to make. But one obvious thought is that when a function sign containing a negation appears to occur within an atomic sentence “(~F)a” its semantic contribution is perspicuously displayed by a sentence in which the function sign and the negation are pulled apart and the negation assigned wide scope “~(Fa)”. It is because negation is resolutely assigned wide-scope that function signs that contain negation are never genuinely self-ascribed and contradiction is thereby circumvented. Ramsey’s solution to “the Contradiction” merits conviction only to the extent that there is independent reason to hold that function signs that contain a negation are incomplete symbols. Unfortunately the above passage supplies no reason of this kind, offering only the assurance that a “little reflection” will suffice to show that these symbols are incomplete. In fact this situation is doubly to be regretted. It not only leaves us without the means to assess Ramsey’s solution to “the Contradiction”. It 7 also leaves us without motivation for the claim that a distinction between the constituents of atomic facts cannot be read off the distinction between expressions that are capable of being negated (predicates) and expressions that are not (names). Fortunately, an argument that appears earlier in “Universals" yields up some of the motivation missing. Ramsey begins his examination of the subject-predicate distinction by considering such sentences as “Either Socrates is wise or Plato is foolish” (Ramsey [1925], p. 13). Prima facie the subject-predicate distinction does not apply to this sentence or the proposition it expresses. But one might still contend that the distinction does gain application, the subject being any term, the predicate the complex remainder. For example, “Socrates” may be taken to be the subject and “being wise unless Plato is foolish” the predicate. If so, the predicate appears to be a name for a complex universal asserted to characterise Socrates. Ramsey seeks to discredit the theory that universals correspond in this way to complex predicates with a reductio ad absurdum: “In order to make things clearer let us take a simpler case, a proposition of the form ‘aRb’; then this theory will hold that there are three closely related propositions; one asserts that the relation R holds between the terms a and b, the second asserts the possession by a of the complex property of ‘having R to b’, while the third asserts that b has the complex property that a has R to it. These must be three different propositions because they have different sets of constituents, and yet they are not three propositions, but one proposition, for they all say the same thing, namely that a had R to b. So the theory of universals is responsible for an incomprehensible trinity, as senseless as that of theology” (Ramsey [1925], p. 14) In this passage propositions, like facts, have worldly items as constituents (elsewhere in “Universals” propositions take on a linguistic guise). Ramsey assumes that these propositions are distinct if their constituents are different. Absurdity results when this assumption is combined with the admission that complex predicates are names for complex universals. This is because more than one complex predicate may be isolated in a sentence of the form ‘aRb’predicates that may be represented by “ξRζ”, ‘ξRb” and “aRζ”. If these predicates are names of different universals then the sentence ‘aRb’ expresses no less than three propositionspropositions that are distinct because 8 they correspond to the three different collections of constituents (i) ξRζ, a, b, (ii) ξRb, a and (iii) aRζ, b. But this is absurd because “aRb” says only one thing: that aRb.4 This argument can be generalised to rule out the possibility that negated predicate are names of complex universals (negative ones). This is because more than one predicate may be isolated in a sentence of the form “∼Fa”the complex predicate that may be represented by “∼Fξ” and the simple predicate “Fξ”. If these predicates are both names of universals then the sentence “∼Fa” expresses no less than two different propositionsone that denies that Fξ characterises a and another that asserts ∼Fξ to do so. This too is absurd because “∼Fa” also says only one thing: that ∼Fa. If this argument is effective then it follows that neither relational nor negated predicates are names of complex universals. This supplies the missing motivation for Ramsey’s thesis that functions signs that contain a negation are incomplete symbols. But this argument relies not only upon the assumption that propositions with different constituents are distinct but also the assumption that sentenceslike “aRb” and “∼Fa”say only one thing. And, unfortunately, Ramsey provides no explicit motivation for either of these assumptions.5 So if we are to understand Ramsey’s reasons for doubting that the distinction between particular and universal may be deduced from that between subject and predicate then we must enquire further into the (implicit) grounds for these assumptions. It may appear, however, that Ramsey’s argument against complex universals does not rely upon any special assumptions. On one such interpretation the argument comes down to a judicious employment of Ockham’s razor. On this interpretation Ramsey is merely pointing out that there is no need to posit complex universals in addition to simple ones. This is because simple universals (and particulars) provide an adequate supply of constituents to construct the propositions our sentences express and the facts that make them true. So complex universals are nothing but an excrescence to our ontology. On a related interpretation, Ramsey’s argument depends 4 Mellor revives a version of Ramsey’s argument against complex universals in his [1991], p. 179. See Oliver [1992] and Mellor [1992] for a criticism and a defence of this argument. 5 Several of Ramsey’s critics have rejected these assumptions, arguing that the same proposition may admit multiple parsings where different parsings reveal the presence of different constituents (ξRb on one parsing, aRζ on another etc.) but where the proposition nevertheless still says the same thing. See Moore [1962], p. 297, Anscombe [1959], p. 95, Geach [1975], pp. 146, Dummett [1981], pp. 264-6 and Oliver [1992], pp. 95-6. But unless we enquire into the underlying motivations that shape Ramsey’s argument we will be unable to assess the relative merits of endorsing or rejecting alternative views. 9 ultimately upon the ‘robust sense of reality’ that Russell exhorted us to maintain when doing philosophy. This sense of reality can be seen to be at work when Russell argues that asymmetric relations (before, greater, up) are identical to their converses (after, less, down). Russell begins from the reflection that there is an important difference between “before” and “after”, namely that “A is before B” may not be inferred from “A is after B”. But, he continues, “it may be inferred that B is after A, and so it would seem that this is absolutely the same ‘fact’ as is expressed by saying that A is before B. Looking away from everything psychological, and considering only the external fact in virtue of which it is true to say that A is before B, it seems plain that this fact consists of two events A and B in succession, and that whether we choose to describe it by saying ‘A is before B’ or by saying ‘B is after A’ is a mere matter of language” (Russell [1913], p. 85). In this argument Russell appeals to our robust sense of reality to assure us that the external fact in virtue of which the sentence “A is before B” is true admits of only A and B in succession. And certainly Russell has intuition on his side when he makes this claim. Consider a situation in which a cup is on top of a saucer. Intuitively the cup’s being on top of the saucer is the same external state of the environmentthe very same ‘chunk of reality’as the saucer’s being underneath the cup.6 Similarly, it may be argued, looking away from everything psychological and concerning only the external fact in virtue of which it is true to say that aRb, it seems plain that this fact consists of just a, R and b, and that whether we choose to describe it as “R holds between the terms a and b”, “a possesses the complex property of ‘having R to b’” or “b has the complex property that a has R to it” is a mere matter of language. Consider a situation in which a cup is next to a saucer. Intuitively the holding of the next to relation between the cup and the saucer, the possession by the cup of the property being next to the saucer, and the saucer’s having the property that the cup is next to it, are the very same state of the external environment, a chunk of reality that consists of nothing but the cup and the saucer in adjacency. Whatever the intrinsic merits or defects of these arguments they cannot suffice as interpretations of Ramsey. It is critical to the structure of Ramsey’s argument that the admission of complex universals results in “an incomprehensible trinity” of propositions. After all, the argument is intended to be a reductio ad absurdum of the assumption that complex universals exist. But neither of the interpretations offered 6 See Fine [2000], pp. 2-6 for a similar argument against converse relations. 10 make sense of this. The trinity of propositions (or facts) that result from the admission of complex universals areso far as these interpretations goredundant or superfluous rather than incomprehensible. In order to understand why Ramsey should have thought that the admission of complex universals results in “an incomprehensible trinity” it is necessary to appreciate the influence that Wittgenstein exerted upon him during the period “Universals” was composed. In his Notebooks 1914-16 Wittgenstein set out to investigate whether negative propositions correspond to negative facts. Raphael Demos, one of Russell’s students, had proposed that a proposition of the form “∼p” does not correspond to a negative fact, but rather to some true proposition ‘q’ that is incompatible with “p” (see Demos [1914]). Russell was later to criticise Demos’ account on the grounds that “it makes incompatibility a fundamental and objective fact which is not so much simpler than allowing negative facts” (see Russell [1918], p. 213). Russell therefore admitted negative facts alongside positive facts to correspond to negative and positive propositions respectively. However, just as Demos’ account provides no explanation of the incompatibility of the propositions “p” and “q” but leaves this a brute fact of nature, Russell’s account likewise provides no explanation of the incompatibility of the positive and negative facts p and ∼p. When Wittgenstein came to reflect upon these issues he found that fundamental incompatibilities of this kind offended against his Humean scruples. Just as Hume could not understand how there could be brute necessary connexions between causes and effects, Wittgenstein could not understand how brute necessary incompatibilities could obtain between positive and negative facts. At first Wittgenstein struggled to find a way to avoid such incompatibilities: “The question is really this: Are there facts beside the positive ones? (For it is difficult not to confuse what is not the case with what is the case instead of it.)” (Wittgenstein [1961], 25.11.14) “It is the dualism, positive and negative facts, that gives me no peace. For such a dualism can’t exist. But how to get away from it?” (Wittgenstein [1961], 25.11.14). But Wittgenstein was soon to light upon an account of the role of ‘∼’ and the other logical constants that obviated the need to posit a dualism of positive and negative facts, an account that addressed his Humean concerns. The account was to become the Grundgedanke of the Tractatus: 11 4.0312 … My fundamental idea is that the ‘logical constants’ are not representatives; … (Wittgenstein [1919]). It was the assumption that the negation sign contributes to the content of “∼p” that lead Demos and Russell to affirm fundamental incompatibilities between propositions and facts. By both accounts “∼” combines with “p” to produce a representation of a fact different to peither a positive fact q that is incompatible with p or the negative fact ∼p. A dualism of incompatible facts is thereby induced. To avoid this dualism Wittgenstein denied that the negation sign contributes to the content of the sentences in which it occurs. He proposed instead that both “p” and “∼p” have the same content only that they represent this content in different modes. On Wittgenstein’s account “∼” switches the mode in which the content is represented; what “p” represents to obtain, “∼p” represents to be absent. The influence of Wittgenstein is evident in Ramsey’s 1927 paper “Facts and Propositions”. In this paper Ramsey endeavours to combat the idea that the logical constants are representatives of logical objects. Suppose, for the sake of argument, that the negation sign is the name of a logical object not. Then the sentence “~~p” expresses a proposition that contains a constituent not that is missing from the proposition expressed by “p”. “p” and “~~p” therefore express different propositions (see Ramsey [1927], p. 43). But if they express different propositions then it appears impossible to explain the fact that they are mutually entailing; the account that treats logical constants as representatives of logical object leaves this a brute necessary connexion between distinct propositions. Ramsey concluded that the logical constants “must function in some different way”: “I find it very unsatisfactory to be left with no explanation of formal logic except that it is a collection of ‘necessary facts’. The conclusion of a formal inference must, I feel, be in some sense contained in the premises and not something new. I cannot believe that from one fact, e.g. that a thing is red, it should be possible to infer an infinite number of different facts, such as that it is not not-red, and that it is both red and not not-red. These, I should say, are simply the same fact expressed by other words; nor is it inevitable that there should be all these different ways of saying the same thing. We might, for instance, express negation not by inserting a word ‘not’ but by writing what we negate upside down” (Ramsey [1927], p. 42; cf. Wittgenstein [1922], 5.43). 12 Ramsey thus seeks to avoid brute necessary connexions by insisting that the conclusion of an inference must be contained in its premises.7 In this way Ramsey tries to ensure that the connexions between propositions are intelligible rather than brute. The underlying Humean concerns that shape Ramsey’s perspective re-emerge later in “Facts and Propositions” when he shifts his attention from the logical constants to the quantifiers. Frege and Russell had maintained that the universal and existential quantifiers denote higher-order properties. Their theory assigns quantified sentences the form ‘F(f)’: according to the theory a universal quantification “For all x, fx” ascribes the higher-order property of universal application to the lower-order property f whereas an existential quantification “There is an x such that fx” ascribes the higher-order property of merely having application to f. Ramsey rejects this account in favour of Wittgenstein’s theory that “For all x, fx” is equivalent to the infinite conjunction of all the values of “fx” (“fa & fb & fc & …”) whereas “There is an x such that fx” is equivalent to their infinite disjunction (“fa v fb v fc v …”). Ramsey endorses Wittgenstein’s account because, “It is the only view which explains how ‘fa’ can be inferred from ‘For all x, fx’, and ‘There is an x such that fx’ from ‘fa’. The alternative theory that ‘There is an x such that fx’ should be regarded as an atomic proposition of the form ‘F(f)’ (f has application) leaves this entirely obscure; it gives no intelligible connection between a being red and red having application, but abandoning any hope of explaining this relation is content merely to label it ‘necessary’” (Ramsey [1927], pp. 48-50). In this passage Ramsey anticipates a difficultyfashioned by contemporary Humeansthat has come to bedevil theories that conceive of laws of nature as the obtaining of higher-order relations. According to these theories, if it is a law that Fs are Gs then this is to be regarded as an atomic fact in which the higher-order relation of nomic necessitation obtains between the lower-order universals F and G. The difficulty such theories encounter is that they fail to supply an account of the connexion between (i) its being a law that Fs are Gs and (ii) some particular a that is F being also G. For whereas (i) concerns a higher order fact, the obtaining of a higherorder relation N between F and G (N(F, G)) (ii) concerns lower order facts, the 7 Of course Russell would not have been swayed by this argument. In his dispute with Bradley he wrote: “Such a view involves the assumptionimplicit in many such argumentsthat all inference is essentially analytic, that whatever can be inferred from a proposition is necessarily part of that proposition. This view appears to me to be erroneous, and to be connected with the theory of relations upon which most of my disagreements with Mr. Bradley depend” (see Russell [1911], p. 377). 13 distribution of the lower-order universals F and G over particulars like a (Fa, Ga). Since the higher-order and lower-order facts concerned are distinct the theories in question are obliged to treat the necessary connexion between a law and its instances as brute (see Lewis [1983], p. 366).8 In the same way Ramsey accuses Frege and Russell of failing to supply an account of the necessary connection between, for example, (iii) something’s being F and (iv) a’s being F. For whereas (iii) concerns a higher-order fact, the inhering of the higher-order property of having application in the lower-order universal F, (iv) concerns a lower-order fact, the inhering of F in a. Since these facts are distinct Frege and Russell are obliged to leave the necessary connection between (iii) and (iv) entirely “obscure”. By contrast, Wittgenstein’s view avoids this difficulty. The necessary connection is rendered transparent because a’s being F is a constituent of the infinite disjunction Fa v Fb v Fc v … to which the existential quantification is deemed equivalent. How do the arguments from “Facts and Propositions” illuminate Ramsey’s reasons for rejecting complex universals in “Universals”? These later arguments reveal an underlying Humean tendency to Ramsey’s thought, a tendency which can already been seen to manifest itself in his earlier argument against complex universals. According to this Humean interpretation of this argument the trinity of propositions that Ramsey declares to result from admitting complex universals is “incomprehensible” because it incorporates a commitment to the existence of brute necessary connexions. This Humean interpretation casts the argument against complex universals in the following terms. Suppose there are complex universals. Then the three sentences “R holds between the terms a and b”, “a possesses the complex property of ‘having R to b’” and “b has the complex property that a has R to it” express propositions that contain different constituents (the complex universals ξRζ, ξRb and aRζ). Therefore they express different propositions. However these three propositions are mutually entailing: if it is true that R holds between a and b then a must possess the property of ‘having R to b’ and b must have the property that a has R to it, and so on. But the 8 Of course Ramsey was later to reject theories of this kind on Humean grounds in his later 1929 paper “General Propositions and Causality”: “But may there not be something which might be called real connections of universals? I cannot deny it, for I can understand nothing by such a phrase; what we call causal laws I find to be nothing of the sort” (Ramsey [1929], p. 160). 14 theory of complex universals leaves this entirely obscure, providing no means of explaining the entailment; the entailment is an “incomprehensible” necessary connexion between three distinct propositions. The only way to explain this mutual entailment is to insist that these sentences express the same proposition (recall Ramsey’s injunction: the conclusion “must be in some sense contained in the premises and not something new” (Ramsey [1927], p. 42). But if they express the same proposition then the different predicates“ξRζ”, “ξRb” and “aRζ”embedded in these sentences cannot refer to different universals. Such complex predicates must be incomplete symbols, neither representatives nor names of complex universals. It is noteworthy that it will not do to respond to this Humean argument that one and the same proposition may say three different things at once. This relieves the pressure upon the advocate of complex universals to explain the mutual entailment between three distinct propositions. But this response still leaves in place a comparable explanatory burden: the requirement to account for the tangle of necessary connexions that still obtain between the constituents ξRζ, ξRb, aRζ, a and b even when they belong to a single proposition (the necessary connexions that oblige ξRζ to be instantiated if ξRb is, and so on). If this interpretation is correct it is an underlying Humeanism that is ultimately responsible for not only Ramsey’s rejection of complex predicates but also his claim that function signs that contain a negation are incomplete symbols. And it is because he denies that such signs are referring devices that Ramsey has no reason to suppose that the difference between signs that can be negated and those that cannot corresponds to a difference in the functioning of objects that make up atomic facts. Consequently Ramsey may accept with equanimity the claim of the first generation of commentators that there is a subject-predicate distinction based upon the distinction between expressions that can be negated (predicates) and expressions that cannot (names). He may endorse this claim whilst still doubting whether there is a fundamental division of objects into two classes, particulars and universals.9 4. Our Knowledge of Relations Where did the second generation of Ramsey’s commentators go wrong? The second generation, recall, denied the third of the claims usually attributed to Ramsey: (3) 9 See MacBride [1999] and [2001a] for further Humean arguments against the particular-universal distinction of this general kind. 15 there is no particular-universal distinction because there is no subject-predicate distinction. They denied this claim because they rejected the broadly Fregean conception that ties ontology to language. From this perspective the malady that afflicts “Universals” is one of flawed conception. It presupposes that ontological distinctions are tied to logical or linguistic ones. This appears to set Ramsey at odds with much of contemporary ontology: “Contrary to what one might call the classical stance in analytic philosophy, of which Ramsey in “Universals” is one of the most brilliant representatives, much of contemporary ontology rejects the assumption that one can get at ontological issues through linguistic distinctions, and conversely that one can get rid of the latter through the former” (Dokic & Engel [2001], pp. 40-1). It is perhaps not surprising that viewed from the perspective of its closing years the history of 20th century ontology should appear in this fashion. The last two decades of the century came to be dominated by a realist conception that divorces ontology from language (the philosophical systems of Mellor and Armstrong stand out as exemplars of this kind).10 However other forces dominated the period that intervened between the analytic philosophers, such as Ramsey, and the modern realists, such as Mellor and Armstrong: the forces of ordinary language philosophy and the antirealist programme that succeeded it. The contemporary revival of ontology is owed in no small part to the self-conscious attempt by modern realists to disentangle issues about meaning and ontology that ordinary language philosophy and antirealism wove together, leaving it to fundamental science to settle a posteriori what there is. It is therefore entirely natural that a contemporary metaphysician should see his (or herself) distinguished from his (or her) predecessors by the rejection of the “bad old linguistic arguments” (see Simons [1992], p. 159). However, this view of history does not do justice to the fact that the analytic philosophersnot only Ramsey but Russell and Wittgenstein as wellalso came to doubt that reflection on language could determine a priori what there is. They too came to rely upon the a posteriori investigations of fundamental science to settle what exists. Moreover, this view of history leads the second generation of Ramsey’s commentators to misinterpret “Universals”, attributing to Ramsey a claim (3) and a conception of ontology to go with it that he did not hold. 10 See Armstrong [1978], [1997] and Mellor [1991a]. 16 The awkwardness of attributing (3) to Ramsey should already be apparent from Ramsey’s discussion of incomplete symbols in “Universals”. For this discussion lead Ramsey to the conclusion that neither relational predicates nor function signs that contain negation correspond to the constituents of atomic facts (complex universals). This move already distances ontology and language in one critical respect, enjoining a distinction between what is merely a predicate and the property (if any) that it denotes.11 A further significant clue is to be found in the sentence upon which “Universals” concludes: “Of all philosophers Wittgenstein alone has seen through this muddle and declared that about the forms of the atomic propositions we can know nothing whatever.” (Ramsey [1925], p. 30) If Ramsey indeed thought there to be no particular-universal distinction because there is no subject-predicate distinction then it is entirely incongruous that “Universals” should conclude upon the epistemic reflection that we do not and cannot know whether there is an ultimate distinction amongst the worldly constituents of the atomic propositions. It is only against the backdrop of Russell’s evolving views on universals that the significance of “Universals” may be properly understood. In the second edition of Principia Mathematica (1925), Russell characterised the particular-universal distinction in the following terms.12 After defining atomic propositions as propositions of one of the series of forms (A) R1(x) R2(x,y) R3(x,y,z) .... Russell writes: Here R1, R2, R3, R4… are each characteristics of the special form in which they are found: that is to say Rn cannot occur in an atomic proposition Rm(x1, x2, … xm) unless n=m, and then can only occur as Rm occurs, not as x1, x2, … xm occur. Terms which can occur in any form of atomic proposition are called “individuals” or “particulars”; 11 Russell is also to be seen carefully separating linguistic and ontological issues in his discussion of vagueness. He writes: “There is a certain tendency in those who have realised that words are vague to infer that things are also vague… This seems to me precisely a case of the fallacy of verbalism – the fallacy that consists in mistaking the properties of words for the properties of things” (see Russell [1923], p. 85) 12 It should be noted that Russell maintained at one time or another a variety of other conceptions of the particular-universal distinction. Compare Russell [1911], p. 124, [1912], p. 53 and [1919], pp. 286-7. 17 terms which can occur as the Rs occur are called “universals”” (Russell & Whitehead [1925], p. xix; see also p. xv). Ramsey went on to offer the following gloss on Russell’s conception of the particularuniversal distinction: “[Russell] says that all atomic propositions are of the forms R1(x), R2(x,y), R3(x,y,z), etc. and can so define individuals as terms which can occur in propositions with any numbers of terms; whereas of course an n-termed relation could only occur in a proposition with n+1 terms” (Ramsey [1925], p. 29; see also his [1926], p. 31). These passages raise a number of interpretative issues.13 Nevertheless for the purpose of coming to a fuller understanding of “Universals” we mayfollowing Ramseyisolate and abstract the following account of the particular-universal distinction from the second edition of Principia. Conceive of atomic propositions as worldly complexesnon-linguistic, nonmental itemsthat actually contain the constituents they are about. Then if the space of atomic propositions consists of the sequence of forms (A) particulars (x, y, z…) may be defined as entities that can occur in propositions with any number of constituents. By contrast, universals (R1, R2, R3…) may be defined as entities that can only occur in propositions with n-ly many constituents (where n may be finite or infinite). Call those entities unigrade. Unigrade entities have a definite degree or adicity; they are either monadic or dyadic or triadic…or n-adic. Entities that enter into propositions with differing numbers of other entities are not n-adic for any number. Call these entities multigrade.14 So whereas particulars are multigrade, universals are unigrade. 13 For reasons of space I cannot offer a thoroughgoing reconstruction of the view Russell historically held in 1925. Instead I will confine myself to drawing attention to some of the interpretative issues that arise. Note first that Russell defines the particular-universal distinction relative to the occurrence of particulars and universals in “propositions”. Under the influence of Wittgenstein, Russell had adopted the view that propositions are types of mental or linguistic representations (see Russell [1918], pp. 1845, p. 196, [1919], pp. 315-9, [1921], pp. 240-2, pp. 273-4 and Russell & Whitehead [1925], pp. 406-7. According to this view, it is the symbolic representatives of the particulars and universals that occur in the propositions that concern them rather than the particulars and universals themselves. This makes Russell’s 1925 claim to define the particular-universal distinction relative to the different ways in which particulars and universals occur in propositions puzzling. Second, contra Ramsey’s gloss, Russell does not simply define particulars “as terms which can occur in propositions with any numbers of terms” and universals as n-termed relations that can “only occur in a proposition with n+1 terms” (see Ramsey [1925], p. 29, [1926], p. 31). Rather Russell invokes the further idea that universals are items that not only occur in propositions with a fixed number of constituents but also items that occur in propositions in a certain distinctive manner; they are kinds of thing that “occur as” relations. Unfortunately Russell does not make clear what it means to occur as a relation. 14 See Leonard & Goodman [1940], p. 50. 18 Russell neglected to provide any direct motivation in Principia for the view that particulars are multigrade, universals unigrade. But this leaves one wondering from where his insistence derives that the space of atomic propositions exhibits the structure (A). If no assurance can be given that atomic propositions are one or other of the forms (A) depicts then this conception of the particular-universal distinction can carry no conviction. For all that has been established so far the space of atomic propositions may exhibit an indefinite variety of other structures contrary to (A). For example, Russell has not shown that there is anything to prevent the atomic propositions all exhibiting the same n-adic form. Nothing has been done to rule out the epistemic possibility that the atomic propositions are composed entirely of two constituents, (B) R4(x) R5(y) R6(z) … or that they are composed entirely of three constituents, (C) R7(x,y) R8(y,z) R9(z,w) .... But if either (B) or (C) obtain then all the constituents of the atomic propositions will turn out to be unigrade (monadic in (B), dyadic in (C)) and the distinction between unigrade and multigrade will fail to characterise a fundamental distinction between two classes of objects. If the space of atomic propositions exhibits a structure other than (A) then Russell will have failed to put his finger on a convincing conception of the particular-universal distinction. In order to appreciate the theoretical underpinnings of the conception of the particular-universal distinction attributed to Russell it is necessary to look back from the second edition of Principia (1925) to The Principles of Mathematics (1903) and Russell’s intervening debate with Wittgenstein and Bradley. In the Principles Russell sought to undermine the traditional logic that assumed propositions could only admit subject-predicate form. He endeavoured to do so by showing that many of the propositions of mathematics concerning “Number, Quantity, Order, Space, Time and Motion” involve asymmetric relations. Russell then set about arguing that propositions involving asymmetric relations could not be reduced to the subjectpredicate variety: 19 “We have now seen that all order depends upon transitive asymmetrical relations. As such relations are of a kind which traditional logic is unwilling to admit, and as the refusal to admit them is one of the main sources of the contradictions which the Critical Philosophy has found in mathematics, it will be desirable to make an excursion into pure logic, and to set forth the grounds which make the admission of such relations necessary” (Russell [1903], §208) Russell distinguished two ways in which relational propositions might be reduced to subject-predicate propositions. According to monadism, a relation between two terms is reducible to the properties of the terms taken separately (so a proposition of the form aRb may be perspicuously represented in the form Fa & Gb). By contrast, monism claims that the relation is a property of the whole that results from the two terms taken together (so a proposition of the form aRb may be perspicuously represented in the form R(ab)). It is because both kinds of reduction fail that Russell deemed the admission of asymmetric relations necessary. Russell’s reasons for rejecting monadism and monism are familiar. Nevertheless bringing them to mind will help make sense of the conception of the particular-universal distinction under consideration. A thumbnail sketch: against the monadist, Russell argued that no property F of a term a that does not incorporate reference to another term b can imply a relation between a and b, whilst anything that does mention b cannot be a mere property of a; against the monist, Russell maintained that an asymmetric relation R cannot merely be a property of the whole ab (= ba) because this analysis provides no basis for distinguishing between the case where R obtains between a and b (in that order) and the contrasting case where R obtains between b and a (in that order) (see Russell [1903], §214, §215). What is important to emphasise in the present context is that (B) corresponds to a form of monadism when x, y and z are distinct monads, and to a form of monism when x, y and z are one single thing. In the former case, reality consists of a collection of distinct particulars endowed with nothing but monadic features (R4(x), R5(y), R6(z)). In the latter case, reality consists of a single particular x that also lacks relational features (R4(x), R5(x), R6(x)). It is because (B) may be taken to correspond to a form of monadism or monism that Russell’s reasons for denying the credibility of monism and monadism are also reasons for dismissing (B) and thereby supply part of the missing motivation for endorsing (A). The other partnamely, a motivation for denying that (C) or its like might be necessaryemerges from Russell’s recognition that different 20 propositions require the existence of relations of different adicities. For example, projective geometry requires a four-term relation to account for the order of points on a line (see Russell [1903], §361). Russell’s conviction that there are genuinely monadic features in addition to external relations was grounded in assumptions about the character of the sense data with which we are directly acquainted (see his [1913], pp. 95-6). In this way Russell’s motivation for the conception of the particularuniversal distinction outlined becomes bound up with the reasons that Russell provided for rejecting the traditional subject-predicate logic in favour of the new logic of relations. There remain, however, important gaps in Russell’s account of the matter. If his criticisms of monism and monadism are granted then it follows that relational propositions cannot be reduced to subject-predicate ones. But it does not follow that the admission of asymmetric relations is “necessary” (Russell [1903], §208). Nor does it follow that (A) obtains. This is because it remains open that relational propositions may fail to be intelligible. It is this possibility that had exercised Russell’s idealist opponents who adhered to the traditional logic. The monist Bradley, for example, had long argued notas Russell suggests in Principlesthat relational propositions are reducible but that they are unintelligible: “a relational way of thoughtany one that moves by the machinery of terms and relationsmust give appearance, and not truth” (Bradley [1893], p. 28) There is a further difficulty. Even if such propositions are intelligible it does not follow that there actually exist the kinds or quantities of entities that are required to constitute such propositions. It is to this possibility that Wittgenstein drew attention in the Tractatus, stating that it could not be determined by logic or a priori means alone whether reality exhibited (A), (B), (C) or some other structure of atomic propositions: 4.128 5.553 Logical forms are without number. Hence there are no privileged numbers in logic, and hence there is no possibility of philosophical monism or dualism, etc. Russell said that there were simple relations between different numbers of things (individuals). But between which numbers? And how is this supposed to be decided?By experience? (There is no privileged number.) 5.554 It would be completely arbitrary to give any specific form. 5.5541 It is supposed to be possible to answer a priori the question whether I can get into a position in which I need the sign for a 27-termed relation in order to signify something. 21 (Wittgenstein [1922]) By 1924 Russell was prepared to make a dramatic shift in his position to fill the gaps Bradley and Wittgenstein identified in his argument. Instead of basing the admission of asymmetric relations on “pure logic” Russell appealed instead to “empirical grounds”: “If I am right there is nothing in logic that can help us to decide between monism and pluralism, or between the view that there are ultimate relational facts and the view that there are none. My own decision in favour of pluralism and relations is taken on empirical grounds, after convincing myself that the a priori arguments to the contrary are invalid” (Russell [1924], pp. 338-9). But what are these “empirical grounds”? In contemporary ontology it has become commonplace to rely upon the a posteriori investigations of science to determine what properties and relations there are. In a passage that prefigures this development Russell declares: “I do not believe, for instance, that those who disbelieve in the reality of relations can possibly interpret those parts of science which employ asymmetrical relations. Even if I could see no way of answering the objections raised (for example) by Mr. Bradley, I should still think it more likely than not that some answer was possible, because I think an error in a very subtle and abstract argument more probable than so fundamental a falsehood in science” (Russell [1924], pp. 339) It is then the fundamental truths of science that provide the theoretical underpinnings of Russell’s conception of the particular-universal distinction. For it is science that ultimately provides Russell with the assurance that reality consists of the variety of atomic propositions (A) depicts. Hence Russell’s pronouncement in the introduction to the second edition of Principia: “Logic does not know whether there are in fact n-adic relations (in intension); this is an empirical question. We know as an empirical fact that there are at least dyadic relations (in intension) because without them series would be impossible.” (Russell & Whitehead [1925], p. xv) Against this backdrop the significance of Ramsey’s “Universals” is thrown into relief. Ramsey did not seek to infelicitously draw ontological conclusions from linguistic premises, drawing the conclusion that there is no particular-universal distinction from the premise that there is no subject-predicate distinction. Ratherin agreement with WittgensteinRamsey doubted whether it can be settled a priori (by reflection on language or otherwise) whether (A) or some other structure obtains. Butin disagreement with RussellRamsey also doubted whether even fundamental 22 science can be relied upon to reveal a posteriori the structure of the atomic propositions. Ramsey’s denial that any fundamental classification of objects can be based upon the distinction between the subject of a proposition and its predicate is commensurate with both these points: it is because the surface features of sentences(e.g.) the subject-predicate distinctioncannot be relied upon to reveal the form of the underlying atomic propositions that neither the theoretical language of science nor the structure of ordinary speech can provide a sound basis for affirming the existence of a distinction between particular and universal. This interpretation is confirmed by Ramsey’s later reflections on “Universals” in his 1926 paper “Universals and ‘the Method of Analysis’”: “When I wrote my article [“Universals”] I was sure that it was impossible to discover atomic propositions by actual analysis. Of this I am now very doubtful, and I cannot be sure that they may not be discovered to be all of one or another of a series of forms which can be expressed by R1(x), R2(x,y), R3(x,y,z)…This I admit may be found to be the case, but no one can as yet be certain what atomic propositions there are, it cannot be positively asserted; and there is no strong presumption in its favour, for I think that the argument of my article establishes that nothing of the sort can be known a priori” (see [1926], p.31) Evidently Ramsey did not hold (3) that there is no particular-universal distinction because there is no subject-predicate distinction. He did not even hold (2) that there is no particular-universal distinction. Instead he maintained that the forms of language provide no guidance to structure of reality. Far from advocating a position that has long been superseded by contemporary ontology Ramsey anticipates its development in “Universals”. 5. Conclusion Ramsey did not hold any of the claims usually attributed to him; two generations of commentators have gone astray. Of course this does not settle what Ramsey really claimed and why he wished to claim it.15 Ultimately it will only be possible to come to a definitive judgement of the kind in the context of a fuller study that would address, amongst other things, the influence that other works of the period bore upon “Universals”. These include W.E. Johnson’s Logic (1921/2), A.N. Whitehead’s Principles of Natural Knowledge (1919) and The Concept of Nature (1920), and G.E. 15 I explore some further issues surrounding the interpretation of “Universals” in MacBride [2004] and [forthcoming]. 23 Moore’s polemic against G.F. Stout that Ramsey took to have “already sufficiently answered” the view that properties are particular tropes (see Moore [1923], Ramsey [1925], p. 9). Nevertheless it is already evident that “Universals” not only continues to bear significance for contemporary ontology but points beyond it. This may appear an unlikely claim to wish to make. Consider once more the conception of the particularuniversal distinction that Ramsey isolated in the second edition of Principia. The campaign in favour of external relations and against monism and monadism appears to have long been fought and won. Speaking from a contemporary perspective few would deny that there are external relations of different degree. And even if this cannot be known a priori many are willing to affirmas Russell did in 1924 and Ramsey came by 1926 to acknowledgethat a posteriori science provides a reliable guide to the existence of such relations. As a consequence few would seriously doubt that reality exhibits the kind of structure that (A) depicts. So unless life is somehow breathed back into a debate that appears to have been settledthe debate over the very possibility of external relationsit appears that the Russell’s 1925 conception of the particular-universal distinction has been put upon a sure epistemic footing (albeit an a posteriori one). Yet even if it is granted that external relations exist it does not follow that Russell’s conception of the particular-universal distinction is justified. Nor does it follow that Ramsey was mistaken in his scepticism about the distinction. For there may be other reasons to doubt whether (A) offers an accurate depiction of reality. There may be other universals that fail to be registered in (A)’s inventory. And if these universals are admitted alongside the ranks of n-adic universals that (A) records Russell’s conception is thrown in jeopardy once more. For example, there may be multigrade universals (Rm) that occurs repeatedly in atomic propositions of the different forms, (D) Rm(x) Rm(x,y) Rm(x,y,z) .... In “Facts and Propositions” Ramsey converted to the multiple relation theory of judgement, a theory that holds, 24 “a judgement has no single object, but is a multiple relation of the mind or mental factors to many objects, those which we should ordinarily call constituents of the proposition judged” (see Ramsey [1927], pp. 34-5). If Ramsey is right about this then there is at least one multigrade relationthe relation of de re belief that relates different numbers of objects on different occasions depending on the complexity of the proposition judged. But if there are multigrade universalsand this will need to be investigatedthen the unigrade-multigrade distinction will fail to mark out the fundamental division of objects into two classes, the particulars and universals, into which Ramsey enquired. 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