Introduction

Notes

Introduction

1 . See, for example, Sahlin (1990), Marion (1998), Holton and Price (2003). 2 . See McGuinness (1985) for discussion. 3 . But see Sahlin (1997) for an excellent elaboration of the kinds of influence that Ramsey’s thought may have had on the later work of Wittgenstein. 4. Interpretive questions regarding the way in which TLP ought to be read have dominated the literature on the matter for decades now. For guides from all sides regarding the nature of the distinction, see Goldfarb (1997), Williams (2004), Sullivan (2004), Conant and Diamond (2004) amongst many others. It should be noted that the distinction between resolute and traditional (or irresolute) readings of the Tr actatus should be held apart from the distinction between realist and non-realist interpretations of the work. A resolute reading certainly implies an abandonment of a realist interpretation of the work (indeed, of any interpretation of the work), but that same abandonment certainly need not imply resolution. These are orthogonal issues: as long as non-realist interpreters consider the seemingly metaphysical propositions of the Tractatus to have a content at all, they cannot be subsumed to the resolute programme. 5. See Diamond (1986) for one characterization of the realistic. 6. For persuasive arguments in favour of the positive answer, see Misak (forthcoming). 7. I mean by ‘linguistic representation’ not only utterances but thought as well, which Wittgenstein took also to occur in a language: ‘I don’t know whatt the constituents of a thought are but I know thatt it must have such constituents which correspond to the words of Language. Again, the kind of relation of the constituents of the thought and the pictured fact is irrelevant. It would be a matter of psychology to find out’ (McGuinness 2012, p. 98). 8. Peter Sullivan (2005) attributes the former view to Kenny and the latter view to Anscombe. I have been careful to remark that the objection to the latter view holds only on one conception of what a sign is. Sullivan’s view, which draws on TLPP 3.32 and diffuses the objection that I (and Kenny) make, is that a sign is the visible part of a symbol. If that is right, then there may be ‘a secondary notion’ of meaning that attaches to signs since a sign can no longer be conceived of as a mere e string but rather as something distinguishable only as a part of a meaning-bearing entity. I confess that I am suspicious of this idea: if one regards the relation of signs to symbols as something established by convention, then it seems that there must be a sense in which a sign has an existence which is independent of the symbol with which it is ultimately associated. That is, in establishing some conventional relationship between this sign and this symbol, the sign must be already distinguishable prior to its conventional correlation with the symbol. Sullivan’s article takes on renewed importance in Chapter 6; see also Kenny (1973) and Anscombe (1959).

238 Notes 239

9. Readers who are interested in more biographical detail regarding Ramsey than I have been able to incorporate into this book should see Mellor (1995), Taylor (2006), Paul (2012). I also very much recommend Mellor’s wonderful ‘Better than the Stars: a radio portrait of F.P. Ramsey’, located at http://sms.csx.cam. ac.uk/media/20145.

1 The Realistic Spirit

1 . There is a large literature on the nature, extent and commitments of realism. See Brock and Mares 2006, for an overview. Fine 2001 offers an alternative characterisation. Dummett proposed a controversial account of realism, according to which the defining mark of realism is a commitment to biva- lence for the sentences of X , anti-realism about X thus entailing the rejection of that semantic claim. See Dummett 1978 Ch. 10, 1993. See also Devitt 1983 and 1991, and Wright 1993. This meaning theoretic view of the distinction between realism and anti-realism defers questions of metaphysics, preferring an initial determination of whether or not a realist construal of the sentences in question, upon which grasp of their meaning is to be characterised by grasp of their truth conditions, makes unreasonable demands on speakers. 2 . Ramsey raises the issue of non-synonymy in F&P, p. 154. Clearly, someone might believe that ‘Lorna voted and Rob voted ... ’ was true without assenting to ‘Everyone in Cambridge voted’, simply because they do not know that the names in the conjunction exhaust the domain. That is, only if they assented to ‘Lorna voted and Rob voted and ... and Lorna, Rob, ... , are everyone in Cambridge’ would they assent also to the generalization. But all that Ramsey needs in order to support his claim is that, for any such generalization over a finite domain, there is a materially (though not logically) equivalent conjunction available. It is, in general, extremely important to remember that nobody would suggest that a sentence S that expresses the truth-conditions of some sentence T is s ynonymous with T. 3 . TLPP 4.4221, 5.535. 4 . Note that Ramsey does not construe this as merely a subjective matter, for rules can be better or worse as they conform to ‘known psychological laws’, that is, the psychological laws governing our expectations about how people will infer on the basis of their singular experience. Further, particular matters of fact might be brought into such a disagreement, insofar as they may be used to explain why one rule for judging is better supported than another. 5 . I am aware that this is not the best way in which to express the Tractarian view of universal generalisations, and I give that view more careful exposition in Chapter 9. Nonetheless, it is how Ramsey expresses the view, and as it makes no material difference to the elucidation of Ramsey’s view at this early stage, I shall continue to express thus also. 6 . In the passage, Ramsey does use the term ‘realistic’, but it is obvious from the context that he intends one of a range of views for which I am using the label ‘realist’, that is, a view which may be described as a form of realism. 7. To be more precise, it would be a conjunction of conjunctions, each of the latter consisting of a conjunction of propositions asserting the non-toxicity of each strawberry for some particular human. The main conjunction would 240 Notes

then have as its conjuncts infinitely many conjunctions, each of which concerned an object in the infinite domain of humans. These domains are infinite because the content of a statement of law is not exhausted by the actual instances of the objects in question. ‘Arsenic is poisonous’ is not taken to mean only that the sum total of arsenic in the actual world is poisonous; we would assert it even if, for instance, there were no arsenic in nature, but the properties given by its position in the periodic table assured us that, were it to exist, it would be poisonous to us. 8 . L eaving aside, that is, cases of deception, confusion, misunderstanding and such. 9. ‘What causes hesitation is the fact that, after all, Mr. Wittgenstein manages to say a good deal about what cannot be said’. TLPP p. xxiii. 10 . TLPP 5.4731, 5.5563. In a 1929 note, Ramsey wrote ‘“All our everyday prop[osition]s are in order” is absolutely false, and shows the absurdity of interpreting logic as a part of natural science’. Ramsey 1991a, p. 277; HL 002–30–01. 11 . It is not known who Mr C is – the name is illegible in the original document. 12 . This claim is hard to generalise; obviously, one is, at some point, playing bridge, even if muddling along and making some mistakes. Where one goes from learning to really playing may be, on such a view, a matter of one’s own expectations and those of the other players, as well as what oneself and others take one to be committed to in undertaking the activity. 13 . Robert Trueman has pointed out the limits of the analogy in respect of certain games, such as video games played on a console. In order to play such games, one inputs instructions via a controller, and no combination of inputs is illegitimate in any way that might be considered a contravention (though they may be stupid, counterproductive, etc.). Rather, an illegitimate input would simply be one on which nothing happened. Of course, there are ways of cheating in such games – hacking the code, for instance – and it seems at least plausible that such cheats would count as a contravention in my sense, as opposed to an illegitimate activity which was not a contravention. For imagine that the aim of the game is to complete a course in a certain amount of time. Then, whether the hack that slows the clock counts as a contravention or not will depend on whether one credits oneself (or whether one would allow someone else to credit one) with having won thatt game (as opposed to a new game in with a slower clock) in completing the course against the hacked clock. If the goal is to complete the course in 30 seconds, but one has deceived an observer, actual or potential, into thinking that 45 seconds is 30 seconds, and makes no effort to relieve him of that misapprehension, then I should say that that would be to commit a contravention in the relevant sense. For what remains are the commitments that one has undertaken and the expectations of the other players (or observers). Nothing done above relieves one of those commitments nor eliminates those expectations, in the way in which, for instance, switching the console off would (which is not to say that doing the latter would relieve one of all of one’s commitments to the other players or observers – it is bad form to throw in the towel, because it deprives others of a game, but that is not a contravention). Notes 241

14 . Someone who saw me playing what looked to them like bridge, without knowing that I did not know what it was to proceed in accordance with the rules, might describe me as playing bridge. But this description is irrelevant, just as someone’s failure to describe me as playing bridge were I to follow the rules of the game but use bodily gestures rather than cards would be irrelevant to the assessment of what activity it is that I am participating in. See, for instance, PI I, §200. 15 . It sometimes happens that we will accuse someone of thinking illogically when we are trying to point out that she has in some way failed to make the inference that she ought, as opposed to pointing out that she has inferred badly. Holmes might thus accuse Watson of illogicality for not having arrived at the identity of the murderer as a result of overlooking some evidence – the depth to which the parsley has sunk into the butter – or failing to make the requisite links – what this indicates about the passing of time on a sunny day. This kind of fallibility is not the sense in which I intend ‘illogical inference’ here. 16. TLPP 5.13–5.132. 17 . It is interesting to note that Ramsey was later to turn this form of criticism upon his own account of degrees of belief. In September of 1929 he wrote: ‘What is wrong with my probability is its externality. The “form of thought” which makes it impossible to think illogically is a form which thought haben soll. Das Denken hat eine solche Form nicht. Die Form is eine idea. ... All this is even clearer in my probability theory. Degree of belief is a useless scientific conception, and should not be introduced as one.’ Ramsey (1991a), pp. 277–278; HL 002–30–01. 18. Strawson (1966) considers a view upon which Kant’s theory of geometry is concerned not with physical space, but with phenomenal space – that is ‘primarily the geometry of the spatial appearances of physical things and only secondarily, if at all, the geometry of the physical things themselves’, p. 282. Amongst a series of problems raised about such an interpretation, one finds an objection aligned with Ramsey’s: ‘Or consider again: “Between any two points on a straight line there is a further point.” How can we even decide whether this accords with our visual intuition or not? What picture is relevant? Does it help just to look at a straight line? Any way we might think of for testing it against our visual intuition, or our visual intuition against it, rather suggests it is counter-intuitive’, p. 290. To be sure, Ramsey is concerned not with testing Euclidian geometry against our visual intuition but rather with testing our visual intuition against such a geometry – that is, testing the proposal that a theory that involves Euclidian points may provide a background against which stable analyses of visual reports may be conducted. Because Strawson is concerned with the idea that visual space may provide an interpretation of Euclidian geometry (and not vice-versa, as it would for Ramsey), he may go some way towards dodging the objection by conceding that the theory may involve certain idealised concepts. Ramsey’s interlocutor, however, cannot do this: either she must abandon a Euclidian description of visual space by stipulating that such a space is not infinitely divisible but atomic, in which case we shall require an account of ‘visual atoms’, or else she must, quite hopelessly, hold that phenomenal objects have non-phenomenal components. 242 Notes

19 . Someone might suggest that the view is easily modified by allowing that all that is required to warrant the claim ‘This patch is red’ is that there be a threshold proportion of adjacent, bounded points in the visual field which are red. After all, I might call a patch in my visual field red even though there is a section of it which appears white as a result of bright light that reflects upon the surface of the relevant object. That is, the analysis of ‘This patch is red’ would proceed disjunctively. But such a modification does nothing at all to address the twin hearts of the objection, namely that infinite divisibility is not, and could not be, a feature of our visual experience, and that non- finitely expressible truth conditions cannot underwrite our understanding of sentences. 20 . See, for instance, David Marr’s influential computational account of visual processes, which invokes the notion of pixels, or ordered triples of points (x and y co-ordinates) and their intensity values, in the initial stage of the deriva- tion of, e.g., shape information from the retinal image. Marr 1982. Similarly, objects frequently undergo idealisations for the sake of visual models in psychology: e.g. ‘[f]or optical purposes ... any object may be considered as a collection of point sources of light.’ Cornsweet 1970, p. 36. 21 . I use the terms ‘acquisition’ and ‘manifestation’ advisedly. There is, I think, a great deal of continuity between Ramsey’s criticisms of realist philosophical theories and Dummett’s acquisition and manifestation constraints on a theory of meaning. That should come as no surprise if one thinks, as I do – and as I shall discuss in Chapter 9 – that Ramsey’s later views had a significant influence on Wittgenstein. 22 . Some philosopher may respond thus: doesn’t the similarity in grammatical form constitute at least a prima facie plausible case for semantic continuity? In which case, isn’t the onus on Ramsey to show that there is something wrong with proceeding as though such a continuity exists? In response, I should say that the expression ‘prima facie’ is doing some illicit work here. A case is describable as prima facie plausible only against a background of assumptions which furnish it with its plausibility. In a court of law, when a judge determines whether the prosecution has a prima facie case, she does so against a background that contains the legal framework that would govern her ruling were the case to go to trial. But a case which is prima facie plausible in one jurisdiction need not be so in another. Likewise, seeing grammatical similarity as constituting a prima facie plausible case for semantic continuity simply reveals the background assumptions against which such a judgement is made.

2 Empiricism, Solipsism and the Realistic

1. ‘I do not deny the existence of material substance, merely because I have no notion of it, but because the notion of it is inconsistent, or in other words, because it is repugnant that there should be a notion of it ’(1996., p. 175). 2 . Positing such continuity is controversial as it may be said to erase the important spiritual and religious aspects of Berkeley’s work. There is also the question of the degree to which there is coincidence between the notion of a Notes 243

logical construction and Berkeley’s view of material objects. See, for example, Stack (1970), Ch. 4; Prichard (1915). 3 . Russell’s reconstructive programme is, in my view, one that Berkeley could have adopted. However, I do not wish to imply that the similarities between the two views go any further. For one thing, Russell is rather unsteady about the nature of sense data; at times, they are ideas, at other times they are char- acterized as themselves physical. The details of his ontology do not make a difference to the similarities that I am concerned to pursue. 4 . Clearly, a binary similarity relation (I am deliberately ignoring all the well- known problems with defining such a relation) will not suffice for a three-di- mensional space, because who could say whether perceptual object Y, which is slightly smaller than object X, is more or less similar to X than object Z, which is the same size but slightly different in shape? Rather, one would need significantly more complex relations in order to account for differences in shape as well as differences in distance along those planes. The picture is further complicated if one includes, for instance, differences in colour, such as shade, tone and intensity. In order to establish even a partial ordering on the union of the sets of ordered n -tuples which result, one would additionally need, it seems, at least a further binary relation on the ordered n- tuples of the original orderings. 5 . Such a relation will be subject to all of the difficulties which benight the original similarity relation on perspectives and more. Additionally, it is hard to see how one would go about ordering perspectives in terms of similarity without first picking out features of those perspective upon which to base that ordering. However, for Russell, the ordering on perspectives must be prior to any ordering of aspects because otherwise two copper circles may turn out to be aspects of the same coin even if they occupy distinct positions in space. 6 . Th is is likely to be a contentious claim. On the relation between Russell’s (1914) and his later, non-reductive view that involves neutral monism, see for example, Stace (1946), Ayer (1971), Lockwood (1981). 7 . While Russell uses the word ‘space’, I think it rather misleads because there is no requirement that perspectives themselves be spatially organized. It is intended, instead, to capture the fact that the intimate connection between, for instance, perceptual experience and bodily sensations do not, under ordinary circumstances, come apart and that, for instance, one never, in the normal case, simultaneously feels oneself drawing away from a stationary object while it looms increasingly larger in one’s visual field. 8 . For an elaboration of something like this view, see Dummett (1978), pp. 155–160. 9 . T his is a gross simplification because the expression ‘as of the apple’ requires further reduction (though it requires further reduction in the indicative disjunct of the primary reduction sentence also) to an expression that involves only reference to sense data, because the reduction sentence makes no reference to the desk and because the final conjunct requires a probably impossible elaboration which would prevent it from entailing that there is only one apple anywhere. 10. Recent contributions include Sullivan (1996), Diamond (2000), McGuinness (2001). 244 Notes

11 . Jonathan Lear (1984) has characterised the Wittgenstein of the Philosophical Investigations as a post-Kantian. We are to understand the I nvestigations as pursuing an answer to the non-sceptical, transcendental question, ‘How is language possible?’. One might see the role that Lear assigns to the notion of a form of life in his account as providing a naturalistic elaboration upon the role that I am here assigning to the metaphysical subject of T LP.

3 Pragmatism and the Realistic

1. I should note that in my limited exegesis of Peirce, I restrict myself to mate- rials to which we know that Ramsey had access. 2. For a fine example of Ramsey’s astuteness at even the young age of 18, see his meticulous review of Keynes’ A Treatise on Probability, first published in January 1922 in The Cambridge Magazine, reprinted by Hugh Mellor as Ramsey 1989. 3 . It should be noted that Ramsey does not prove the theorem, but see Sahlin (1990), pp. 26–34 for an excellent discussion. 4 . As I pointed out in Chapter 1, Ramsey appears to have subjected his own T&P account of partial belief to a criticism which stems from his later commitment to self-conscious reflection in philosophical theorising, writing in September of 1929: ‘What is wrong with my probability is its externality. The “form of thought” which makes it impossible to think illogically is a form which thought haben s oll. Das Denken hat eine solche Form nicht. Die Form is eine idea. ... All this is even clearer in my probability theory. Degree of belief is a useless scientific conception, and should not be introduced as one.’ Ramsey (1991a), pp. 277–278; HL 002–30–01. 5 . Peirce (1878), reprinted as Ch. 3 of Peirce (1923). 6 . Peirce has a truly unique way of dealing with the single-case problem that sometimes bothers frequentists. For him, it is a condition of rationality that a rational thinker be capable of extending her reason beyond the single case of her inference to the inferences of a community of thinkers as a whole and beyond her own interests to everyone’s interests: what I do in making this choice should be determined by what it would be best for everyone to do in those circumstances. See Peirce (1923), pp. 69–75, Misak (1991), pp. 108–110. 7 . Peirce (1878), reprinted as Ch. 4 of Peirce (1923). 8. ‘We may, nevertheless, speak of the chance of an event absolutely, meaning by that the chance of the combination of all arguments in reference to it which exist for us in the given state of our knowledge’ (1923. p. 87). Peirce is here using the term ‘chance’ in a technical sense for what we would now call ‘odds’, i.e. the ratio of positive cases to negative cases (as opposed to the ratio of positive cases to total cases, the frequentist interpretation of probability), ibid., p. 86. 9. He writes, for instance, that ‘having degrees of belief obeying the laws of probability implies a further measure of consistency, namely such a consistency between the odds acceptable on different propositions as shall prevent a book being made against you’, T&P, p. 183. But nowhere does he equate resistance to such a book being made against one with rationality. At any Notes 245

rate, one might imagine cases in which, for instance, the instinct (as opposed to the desire) to protect one’s children resulted in the absence of such resistance without inviting a judgement of irrationality. 10. I am emphasizing degrees of belief in this discussion, though it should be remembered throughout that, for Peirce, degrees of belief are, in an account of probability, secondary to objective relative frequencies in respect of inference types. Nonetheless, he does, as discussed earlier in this section, posit a relation between such frequencies and degrees of belief. 11. As Cheryl Misak has pointed out to me in discussion, Peirce’s view is more moderate than this, insofar as he determinedly does not refer to an ideal person . 12. See Misak (forthcoming) for an argument to the contrary. 13. While Ramsey refers to Peirce in the context of his discussion of self-control, he does not name a text. Nonetheless, it is discussed at various points in Peirce (1906). 14. Clearly Ramsey’s account will have to be complicated in order to deal with cases of generalisation, e.g. ‘John believes that everything Cassandra says is true’, and such cases seem unlikely to be amenable to the schematicc analysis proposed above. In F&P, Ramsey takes truth and falsity to be ascribable to propositions, and offers two accounts of these kinds of sentence. The first involves quantification over propositions, while the second eliminates propositional quantification in favour of quantification over names and forms of propositions. The view thus differs significantly from that offered in OTT, but what is common to both is that Ramsey takes the question of real philosophical significance to be that of the analysis of judgement, rather than truth. See F& P, p. 143. 15 . In his introduction to On Truth, Rescher claims that Ramsey intended to detail his account of propositional reference in a missing sixth chapter, provisionally titled ‘On Judgement’ but that that material was ‘absorbed into the revised version of chapter III, “Judgement”, which was now no longer qualified as Preliminary y and which discussed “the object of judgement” (viz. propositional reference) at considerable length. It is thus probable that the On Truth material as we have it represents an effectively complete, albeit unpolished, version of Ramsey’s book’ (p. xii). If this is so, then On Truth would have been a book with a gap where the most work was owed, namely in giving a full account of the individuation of particular beliefs. The chapter that Rescher refers to in fact supplies arguments in favour of Ramsey’s broad construal of the term judgementt in work on characterising propositional reference that was presumably to come but which was never carried out. 16 . Ramsey provides no reference but simply appends the note ‘Wanted: Note on Peirce’. Since we know that he read Chance, Love and Logic, it is highly likely that this is what he would have referred to, and it is quite easy to find, in the two papers mentioned, passages which, together, express the idea that Ramsey is articulating here. 17 . ‘It is certainly best for us that our beliefs should be such as may truly guide our actions so as to satisfy our desires’, Peirce (1923), p. 16. 18. Ramsey (1991), pp. 91–93 criticises the view that James presents in James (1907). 19. See also Ramsey (1991), pp. 33–34. 20. ‘The Nature of Propositions’, in Ramsey (1991), p. 107. 246 Notes

4 Ramsey and Wittgenstein: First Encounters

1. It seems to me that it is precisely on the basis of such a slide that McGuinness (1956) sees himself at odds with Ramsey with regard to the relation between reference and representation. See p. 142, ff. 3 in Copi and Beard (1966). 2 . TLP, p. xi. Russell here ignores Wittgenstein’s own proclamation that his ‘fundamental thought’ was that the logical constants are not names. But clearly, different things are meant by ‘fundamental’ – Potter suggests that Wittgenstein meant by fundamental merely that the idea constituted a guiding methodological principle and not that it is the central idea of the theory (2009, p. 54). This is supported by the fact that its expression occu- pies a rather peripheral place in TLP ’s numbering system, namely 4.0312, and by the fact that Wittgenstein upbraided Russell in a letter for not seeing that ‘the main point is the theory of what can be expressed by propositions – i.e. by language – (and, which comes to the same, what can be thought) and what can not be expressed by propositions, but only shown; which, I believe, is the cardinal problem of philosophy’ (McGuinness 2012, p.96). It is not an enormous leap to suppose that a logically perfect language might be intended to solve that problem. Indeed, see McManus (2006) for a defence of this view. 3 . Note that my disagreement with Potter has nothing to do with the contrast between conceiving of a picture as a fact and conceiving of it as a pictorial complex. That distinction is both right and useful. Rather, my disagreement is the involvement of an act of cognition in the seeing it as the picture that it is. 4 . Diamond (2013) contains an instructive discussion of several interconnecting themes and intentions present in Anscombe’s approach to TLP, offering both a compelling reading of her treatment of the picture theory as well as the suggestion that the book is itself a working through of the philosophical prescriptions of TLP, as understood by Resolute readers. 5 . Anscombe notes that the original Italian translator of the T LP, Father Colombo, raises a similar question: if correlation were mere isomorphism, why should not a fact picture a proposition rather than vice versa? Since Anscombe holds that representation involves an asymmetric component, namely the correlation by us of objects with objects, and since isomorphism is symmetric, correlation cannot be equivalent to representation (p. 67). But this hardly answers the question because if the asymmetric component of representation is the act of cognition that she supposes, then there is nothing essential to our seeing a proposition as a picture of a fact rather than the other way around. It is a consequence of her view that a fact could picture a proposition if we chose to see it in the right kind of way. 6 . Anscombe remarks that this line is derived from a poor rendering of 2.1513 in the Ogden translation of the TLP: that translation, ‘the representing relation ... also belongs to the picture’, is a mistake which ‘throws Wittgenstein’s quite straightforward idea into obscurity’ (p. 68f). While I agree that the line is poorly rendered, I reject the claim that Ramsey’s idea is a mistake; or, at least, if it is, it is an interestingg one. 7 . Matters are further complicated by Wittgenstein’s occasional use of ‘Form der Darstellung’, which Ogden also renders as ‘form of representation’. Pears and McGuinness use ‘form of representation’ only for ‘Form der Darstellung’. Notes 247

8. Ramsey (1925b), 43:4. Notes of these lectures exist thanks to one of Ramsey’s students, L.H. Thomas. Peter Sullivan has transcribed the original notes and was kind enough to share his electronic version with me. 9. McManus endorses the ‘superstitious view’, though in a rather complicated fashion. On his view, TLPP is to be understood as showing that a particular view of the nature of thought, language and reality, which he names the ‘con-formist view’, is self-undermining. So the claims that Wittgenstein makes regarding the nature of objects, propositions, facts and so forth are the claims that might be made by an advocate of the con-formist view that Wittgenstein wishes to show inadequate. Part of the con-formist view is that objects are internally relatedd to the names that name them; that is, that being so named by that name is an essential property of an object, and thus nothing can be said d about that relation. See McManus (2006), pp. 29–42. 10. Pears and McGuinness drop the definite article from the original ‘die Logische Form’, but Ogden retains it. I have used the Pears and McGuinness version here, but have reinserted the article as it is relevant to Ramsey’s discussion of logical form. 11. Birmingham Notes, para. 33; see Potter (2009), p. 280. 12. See, for example, Quine (1951). 13 . My thanks to Michael Potter for helping me to get clear on this point. 14 . ‘Now it is clear why I thought that thinking and language were the same. For thinking is a kind of language.’ Wittgenstein (1961), p. 82. 15. Indeed, Wittgenstein was utterly uninterested in the nature of that language: ‘I don’t know what the constituents of a thought are but I know that it must have such constituents which correspond to the words of Language. Again the kind of relation of the constituents of thought and of the pictured fact is irrelevant. It would be a matter of psychology to find it out.’ McGuinness (1995), p. 125. 16 . Or like a sentential complex open to the kinds of syntactic ambiguity present in ‘Afghan hounds like hunting dogs’. Likewise, Potter considers the unbrack- eted sentence of a propositional language ‘not p or q’ in which there is ambiguity as to the scope of the negation sign. Potter (2009), p. 211. 17. Ramsey is perhaps a little strong in asserting that, on this view, ‘that Germans use “nicht” for not becomes part of the definition of such words as “believe”, “think” when used of Germans’ (loc. cit.) since our aim is not to define those terms. But he is correct in holding that the proposed solution will entail that the sign that Germans use to express what is expressed by me when I assert ‘not p ’ will become a part of the analysis of those terms in the sentential contexts that we have considered. And since the use by Germans of the word ‘nicht’ for no t is contingent (‘significant’ is the term Ramsey uses), it is implau- sible to suppose that it is analytic of those terms when used of Germans. 18 . See also Wittgenstein’s discussion of ‘kilo’ in 1914: ‘How is it possible for “kilo” in code to mean: “I’m all right”? Here surely a simple sign does assert something and is used to give information to others’ (1961, p. 8). ‘At any rate it is surely possible to correlate a simple sign with the sense of a sentence’ (p. 9). 19. In order for the notation to work, a convention regarding the ordering the truth-values in the truth table must be agreed upon in advance. ‘(TTTF)((p, q)’ agrees with that truth table where the assignment of values to p goes, from top to bottom, TTFF, and to q, TFTF. 20. See, e.g. Potter (2009), Ch. 17–18. 248 Notes

21 . Wittgenstein’s N-operator, from which all propositions are supposed to be derivable by repeated application of it, exploits precisely this fact insofar as what it express is joint denial of the propositions which it takes as its bases in a single application. 22 . Nor could we suggest that it is the world as a whole which provides a sense for ‘~~ p’. On that view, it is equivalent to a disjunction of propositions that describe the logically possible situations of the milk but that exclude the case where it is on the table. First, we are attempting to characterise disjunction in terms of the, hopefully, less problematic notions of negation and conjunction. But second, such a proposal leads to intractable difficulties in the case that the world is infinitely complex.

5 The Mystical

1 . In Chapter 7, I discuss Ramsey’s treatment of mathematics in ‘The Foundations of Mathematics’. A large part of that discussion is concerned with Ramsey’s notion of a propositional function in extension (a PFE). I conclude that the Tractarian logicism that Ramsey presents in that article fails because the only stable understanding of PFEs is one which commits him to an ontology of objects which far surpasses any describable as ‘logical’. I wish to note here that Ramsey’s discussion of propositions in F oM is rather at odds with how he understands the relation between a propositional sign and a proposition (conceived of as a type of propositional-sign tokens) in C N. For there he allows Ĝ that the propositional sign token ‘ e(Socrates)’ may belong to the proposition Ĝ type of which the token ‘Queen Anne is dead’ is a token (here the symbol ‘ e’ Ĝ indicates a PFE), that is, that ‘ e(Socrates)’ means that Queen Anne is dead. Ĝ But ‘ e(Socrates)’ appears to exhibit none of the internal properties required for expressing that Queen Anne is dead. In essence, this is simply another way of expressing what is unstable in Ramsey’s account of PFEs. 2 . Note significance and not truth-value. The significance of ‘The King of France is bald’ depends upon the significance of ‘a is bald’, for some a. But its truth- value is, of course, independent of there being merely some object which satisfies ‘x is bald’. 3 . Note that the ‘therefore’ refers to the claim that identity is not a ‘relation between objects’ (5.5301), from which Wittgenstein takes it to follow that it should be eliminable from the notation. See Chapter 7 for more on this matter. 4. I am not able within the compass of this chapter to discuss in any detail the relation between Ramsey’s treatment of Tractarian nonsense and Carnap’s. Ramsey’s recourse to semantic ascent in order to explain our mistaking various forms of nonsense for sense may put a reader in mind of Carnap’s general strategy of reading pseudo-propositions in the material mode as syntactic propositions in the formal mode (Carnap, 1937). But Ramsey’s idea is merely that the syntactic claim is sometimes what we wish to say when we say ‘a exists’; at other times, it is the product of a genuine confusion over appropriate completions of the schema ‘— exists’. Whereas Carnap sees the possibility of systematic ascent from the material to the formal mode in statements concerning the ‘logic of science’, Ramsey is much more amenable to the thought that such constructions may also be straightforwardly nonsensical. Notes 249

5 . There is some debate about whether Wittgenstein really does regard mathematical equations as nonsensical or whether he categorises them, with logical propositions, as senseless. And there is also debate about whether the distinction between nonsense and senselessness can be clearly made out. As Ramsey clearly considered that Wittgenstein took equations to belong with other species of nonsense, I am ignoring these issues here. But see Kremer (2002). 6 . TLP 6.02. Following Potter (2000), I have modified Wittgenstein’s presentation in order to tidy up his idiosyncratic notation. See p. 178. 7 . What we still require is an account of what ‘Ωu + v’ is supposed to indicate. Wittgenstein gives an account of multiplication at 6.241, such that Ωu x v(p) = $(Ωv)u ( p). Addition is then given by Ωu + v(p) = Ωu(Ωv)((p). 8 . See Potter (2000) pp. 177–185 for a fuller exposition. 9 . Or, even, as Kremer prefers, recordingg those practices. See Kremer (2002), pp. 293–295.

6 Truth and Meaning

1 . Dokic and Engel (2002), p. 50 refer to any view which allows such beliefs as mentalism, but dismiss it out of hand as a ‘suspect thesis’. Mellor (2012) addresses these concerns by holding that saying g something is an action based upon beliefs and desires, so that any belief which might under some circumstances be stated may be characterised in terms of the standard success semantics account. Restrictions of space do not allow me to address these issues here, but see Whyte (1990) and (1997), Mellor (1991) and (2012) for defences of the view, and see Brandom (1994), Nanay (2012), Blackburn (2005), Daly (2003), Godfrey-Smith (1994) and Bermudez (2003) for criticisms. 2 . First published as ‘Der Gedanke: Eine logische Untersuchung’ in Beiträge zur Philosophie des deutschen Idealismus 2, 1918–1919. My references throughout are to Frege (1956). 3 . Frege is not at all clear about whether to judge a thought is to t ake it to be true or to recognise (in the factive sense of that word) that it is true. Certainly, the text of the essay lends weight to the latter reading, though that is unfortunate since it transforms ‘judge’, ‘assert’, etc. into factive verbs, but they are not in ordinary use. Such a reading strikes me as distinctly uncharitable, so I have modified the locution in favour of the weaker throughout. 4 . First published by G. Allen and Unwin (1921). My references throughout are to Russell (1995). 5 . I think it is clear that Russell gave up the multiple relation theory of judgement under the influence of Wittgenstein (see Chapter 4). However, Russell’s claim here is that the positive theory expounded in The Analysis of Mindd owes something to Wittgenstein as well. 6 . Surprisingly, Ramsey has been understood here as endorsing exactly y Russell’s by-then abandoned multiple-relation theory. See, for example, Le Morvan (2004). 7. There are cases where we might prefer our own hypothesis to the agent’s reports: if we have reason to suppose him deceptive, if he has no explanation for his own action (‘I don’t know w hat I was thinking!’) or if we think him insufficiently articulate or conceptually impoverished, as in the case of small children. 250 Notes

8. Not only explanatory contexts, but ethical, aesthetic and epistemic contexts too, amongst others. What I mean is that we attribute beliefs to others in order to explain why people do the things that they do, but we also do so in order to criticise people’s ethical views or to make criticisms of their actions. We make similar aesthetic judgements with regard to their tastes and predilections, and we also attribute or withhold the qualities of rationality, wisdom and education on the basis of such attributions. 9. ‘Evidently, name, meaning, relations and object may be really all complex, so that the fact that the name means the object is not ultimately of the dual relational form but far more complicated. Nevertheless, just as in the study of chess nothing is gained by discussing the atoms of which the chessmen are composed, so in the study of logic nothing is gained by entering into the ultimate analysis of names and the objects they signify’. F&P, p. 145. 10 . McGuinness (1981) likewise rejects the bottom-up view. 11 . This, along with the view that there is a ‘fixed grid of possible states of affairs’ in which objects are set, is what Pears (1987) calls ‘uncritical realism’ (p. 9). 12 . And a general logical atomism may still be upheld even across a range of languages for which the notion of an object is relativised. The claim that the truth-conditions of any sentence S of any language is to be given by its analysis to simple names and their arrangement can still do its work as the keystone of a semantic theory. 13 . ‘What is novel about general propositions is simply the specification of the truth-arguments by a propositional function instead of by enumeration’. F&P, p. 153. 14 . I have removed the obviously erroneous quotation marks which appear around ‘p ’ and ‘not--p’ in the original. 15. S korupski (1980), pp. 74–75. Skorupski’s version of Wallace’s proposal (Wallace 1972, p. 86) is intended as an analysis of de re beliefs and is presented as a version of Russell’s theory. So on his version, the members of the sequence are not names but objects. Further, the relation is named by ‘x , y [ xRyy]’, where the square brackets represent Quinean intensional abstraction. Since my version (B) involves a relation on names, I don’t require intensional abstraction. 16 . Ramsey (1925b), 44:4. 17 . Sullivan (2005) also makes reference to this passage but describes it as a ‘temporary retreat’ (p. 67) with regard to the difficulty I discuss in the next section. 18 . Sullivan (2005) and Geach (1957). 19 . This isn’t really y an admission, since my claim is that F&P P is a development of CNN, not an extension or addendum to it.

7 The Foundations of Mathematics

1. See also Ramsey (1991a), p. 84, HL 005–14–01. 2. How one best understands Wittgenstein’s treatment of mathematical truths in TL P is a matter of some dispute. I am here taking it that Wittgenstein considered mathematical equalities to be pseudo-propositions, and that this Notes 251

is how Ramsey understood the TLP too. But see Kremer (2002) for a view not in keeping with that which I attribute to Ramsey. 3 . For discussion, see Fogelin (1983). 4. I don’t wish to say that Wittgenstein does not also endorse QP in some moods – see, for instance, 3.328: ‘If a sign is u seless, it is meaningless’. My point is just that this particular argument need not be seen to be making use of it. 5 . For discussion. see Hacker (2001), Ch. 7. 6 . See TLP 4.062; Wittgenstein’s account of truth exhibits, for this reason, all the hallmarks of the redundancy component of Ramsey’s view. Since ‘““p” is true’ says nothing more than p, then in grasping the sense of p, one must have grasped the conditions for its truth. 7 . See, for instance, Frege (1997), pp. 51, 244–245. 8 . See, for instance, ‘Some Remarks on Logical Form’: ‘By syntax in this general sense of the word, I mean the rules which tell us in which connections only a word gives sense, thus excluding nonsensical structures ... where ordinary language disguises logical structure, where it allows the formation of pseudo- propositions, where it uses one term with an infinity of different meanings, we must replace it by a symbolism which gives a clear picture of the logical structure, excludes pseudo-propositions, and uses its terms unambiguously’. Wittgenstein (1929), pp. 162–163. 9 . Note that Ramsey’s argument is rather different from Wittgenstein’s in that it is what I have called a Quinean argument, turning on the principle that if a sign is eliminable from the notation, then that sign does not stand for anything in the world – the principle I earlier called QP. 10 . See also Wehmeier (2012) and Trueman (2014). 11 . Ramsey appears to have attempted his own proof of the expressive adequacy of a Tractarian Logic in ‘Identity’ by providing a number of translation rules. In a passage that he later struck out (p. 159), he wrote: ‘Now we have made this convention clear we can examine whether, as Wittgenstein asserts, it is adequate to express all possible propositions without using a sign of identity. We shall see that this is possible, and facilitated by a certain trick’. The trick that Ramsey is referring to is that of introducing a tautology function, which allows for the explicit exclusion as the value of a variable those values which are to be excluded given the convention. Such functions are to be taken as primitive and incorporated into the formula when

one translates a L= formula into a Tractarian formula. 12 . This feature of Tractarian propositions is key to Ramsey’s treatment of the semantic paradoxes and subsequent rejection of the ramified theory. 13 . Sullivan (1995), Potter (2000), Trueman (2011). 14. Bear in mind that Sullivan means by ‘objective predicate’ what Ramsey means by ‘predicative function’. 15 . For the argument, see Sullivan (1995). See also Trueman (2011) §§4, 5 for a discussion and elaboration upon Sullivan’s argument. 16. For an elaboration upon this concern, see Trueman (2011), pp. 298–300. 17. There is, in fact, a further assumption built into the view, namely that every individual has a name. I take this, however, following the discussion in Chapter 6, to be a fundamental component of Ramsey’s understanding of TLP. 252 Notes

8 Logical Revolt

1 . Sahlin (1990), Marion (1998), Holton and Price (2003). 2 . This is a mild simplification in that in the case that Ax contains other ^ unbound variables, xAx is functional. But this detail need not detain us. 3. Later, Hilbert prefers to use what has become known as his N-operator. A significant difference between the two operators is that N is to be charac- N Ŵ ^ terised not by the axiom A( xAx) Ax, as the -operator was, but by its Ŵ N converse, A x A( xAx). See Bell (1993) for explication; and Hilbert (1925, 1928), in van Heijenoort (1967), pp. 367–392 and pp. 464–479; and Hilbert (1929) in Mancosu (1998), pp. 227–223. One reason for this change might have been a more circumspect reading of the open formula: in 1922, given the theorems deduced from (1), Hilbert must take such a formula to express universal generality. The switch to the converse requires that it be read only Ŵ N existentially, which is unproblematic as Ax A( xAx) is, in general, equiva- Ǥ Ŵ N lent to x Ax A ( xAx). Ǣ ^ Ŷ 4. Assume ¬ x Ax. Then, by (2) and contraposition, ¬A( xAx). Let Ax ¬¬¬Ax ^ Ŷ ^ ^ Ŵ Ǥ be an axiom. Then ¬A ( xAx) ¬A ( x¬¬¬Ax). By (4), ¬ A( x¬¬¬Ax) x¬Ax. So ¬Ǣx Ax Ŵ Ǥx¬A x. 5. See also p. 184, H L 04–18–01. 6. I am referring here to a passage in F&P, pp. 153–154 and a similar criticism made in his lectures on the foundations of mathematics. Cora Diamond has pointed out to me in correspondence that Peter Sullivan once suggested that it is likely that Ramsey intended as his target Chadwick’s view of generalisations – cf. Chadwick (1927). In the Aristotelian Society symposium at which Ramsey presented F&P, his respondent G.E. Moore makes specific reference to the Chadwick view in this respect – cf. Ramsey (1927), p. 203. But see also Anscombe (1959), p. 143, who takes Ramsey’s remark to be aimed at Frege. I am in some sympathy with her view, but I will not argue for it here. 7. 5.52 – but see Chapter 9 for a discussion of the difference between specification of the arguments by enumeration and by way of a propositional function. 8. This is a contemporary formal gloss on Frege’s informal proposal. The expression ‘(F ≈ G)’ is to mean that a bijection holds between the objects which are F and the objects which are G. 9. Frege (1980a), §62–66. Someone will object that the view I am attributing to Frege is not present in his Grundlagen der Arithmetik, where he speaks only of Bedeutung. This objection is unsatisfactory on two counts: first, there is in the Grundlagen the notion of content, and it is this which Frege considers to be ‘recarved’ between the right and left side of a definition such as HP, and it is this the fixing of which fails for the so-called singular terms of the left- hand side. Second, it is not the substance of Frege’s view, but the principle as inherited certainly by Wittgenstein and, I argue, substantially by Ramsey, in which I am presently interested. 10 . I have taken some liberties with Ramsey’s bracketing, and I added the colon in the second sentence. 11. For an excellent discussion of these matters, see Blanchette (1996). 12. Robert Trueman has pointed out to me a delicious irony in this objection to Hilbert since it is precisely the objection that Wittgenstein makes to Ramsey’s Notes 253

FoM account of identity in Philosophical Grammarr, pp. 316–317: ‘For the signs “fa”, “fb” and “fc” are no more function and argument than the words “(Co) rn”, “(Co)al” and “(Co)lt” are’. See Sullivan (1995) and Trueman (2011) for elaborations upon this objection. 13. There are a number of equivalent syntactic formulations of the problem, as well as equivalent semantic versions. 14. This result follows from the fact that there are countably many sentences of the language, and all proofs are of finite length. Taken together with the completeness result for first-order logic, it is easy to show that one could, by brute force, effectively produce a proof of any valid formula of the language. See Bostock (1997), pp. 184–187, Quine (1950), pp. 213–218. 15. ‘Die zentrale Problem der mathematischen Logik, welches auch mit den Fragen der Axiomatik im engsten Zusammenhang steht, is das Entscheidungsproblem ’. Bernays (1928), p. 342. 16. See also Herbrand (1971), p. 214. 17. See, for example, Bostock (1997), pp. 115–124 for a clear presentation of a standard procedure for monadic first-order logic. For the original proof of this result, see Löwenheim (1915), in van Heijenoort (1967), pp. 228–251. 18. Behmann (1922). 19. But see Börger (2001) for a comprehensive historical account. See also Gurevich (1993), Dreben (1979) and Ackerman (1954). 20. See Fogelin (1976) for the initial criticism. Responses are offered in Geach (1981), Geach (1982) and Soames (1983). See also Jacquette (2001). 21. See, for example, Black (1964), pp. 319, 323 and Anscombe (1971), p. 137. 22. Proops (2007). Proops quotes this passage from Moore’s unpublished notes: Moore Archive, 8875, 10/7/7, 37, entry for November 25. 23. It is quite startling to see how close this last quotation comes to Hilbert’s infamous proclamation that ‘In mathematics there is no ignorabimus’. 24. The logic of TLPP is not, however, restricted to first-order logic. Without the completeness result that underwrites the semi-decidability of first- order logic, the position is even worse in respect of Wittgenstein’s claims amounting to Logical Transparencyy for propositions expressed in a higher- order notation.

9 Generality, Rules and Normativity

1. See CNN, p. 280 and Wittgenstein (1929). 2. See Methven (2014) for more on this point. 3. See Geach (1981) and (1982) for a more detailed exegesis of the N-operator and a proposal for a more perspicuous representation of it in cases of multiple generality. 4. It might be objected that ‘All c are Ĝ’ can be interpreted over an unrestricted domain, in which case, if that domain is infinite, it cannot be represented as a finite conjunction. But I take it that Ramsey is thinking of the most natural reading of such generalisations as implying a restricted reading. 5. In ‘Philosophy’, Ramsey discusses the importance of variable hypotheticals in showing that ‘in this part of logic we cannot neglect the epistemic or subjective side’ (Ph. , pp. 267–268). 254 Notes

6. The picture is more complex if I hold these beliefs in degrees; in that case, the map that one set of beliefs provides will be one that assigns a continuum of related values to a possible configuration of belief states. 7. Proops (2007) quotes this passage from Moore’s unpublished notes: Moore Archive, 8875, 10/7/7, 37, entry for November 25. Compare this to Ramsey’s view on the matter in 1925, where he is objecting to precisely this compar- ison made as a criticism against the Tractarian view of quantification by Hilbert: ‘Thus the logical sum of a set of propositions is the proposition that one at least of the set is true, and it is immaterial whether the set is finite or infinite. On the other hand, an infinite algebraic sum is not really a sum at all, but a limitt, and so cannot be treated as a sum except subject to certain restrictions’ (F oM, p. 7). 8. See also Waismann (1979), p. 70. 9. HL 004–23–01. 10 . McGuinness (2006), p. 24. 11 . Die unendliche Möglichkeit ist durch eine Variable vertreten die eine unbegrenzte [M]öglichkeit der Besetzung hat; und auf andere Art darf das Unendliche nicht im Satz vorkommen. 12 . In TLP, the natural numbers are indices on the application of an operation to an argument; the infinitude of the natural numbers thus depends on the possibility of an operation’s forever taking its value at stage n as its own argument at stage n + 1. 13 . See also Ramsey (1991a), p. 51; HL 003–31–01: ‘The logic of our language is not what Wittgenstein thought. The pictures we make to ourselves are not pictures of facts’. References

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Ackermann, W., 107, 253 causal laws, see laws of nature action, 48, 55, 73, 132, 134–5, 142–5, Chadwick, J.A., 252 146–7, 158 character, 139–40, 142 ambiguity, 100, 102 Church, A., 208, 210 Anscombe, G.E.M., 81, 83–5, 98, clarity, 5, 9, 24, 117–20, 129–31, 150, 113–14, 238, 246, 253 235 anti-realism, 79, 148–50, 238, 239 classes, 183–4, 185–6, 195–7, 227 argument, 60 Colombo, Fr, 246 aspects, 41–4 colour exclusion problem, 218 axiom of choice, 194–5, 197, see also completeness, 211–12 multiplicative axiom complexes, 81, 99, 137 axiom of reducibility, 176, 185, 188 compositionality, 151 Ayer, A.J., 243 Conant, J., 238 conditionals, 1, 18, 43–4 Behmann, H., 253 conjunction, 17, 19, 33, 110, 112, belief, 9–10, 66–9, 73, 142–7, 148, 209–12 159–61, 161–4, 166, 221–2, 250, consciousness, 165 see also judgement consistency, 60–1, 205 attributions of, 134–5, 249, 250 context principle, 89–90 chicken beliefs, 2, 73, 134–5, 142–5, contradiction, 123–4 146, 156 correction, correctness, 30–1, 39, contents, 142, 143, 150–9 45–9, 231, 236 degrees of, 48, 54, 55–8, 58–61, counterfactuals, 19–23, 30, 70, 72, 234 62–6, 222, 241, 244, 245, 254 ‘Critical Notice of L. Wittgenstein’s dispositionalist view of, 1, 2, 73 Tractatus Logico-Philosophicus’, 6, general, 150–1 7–9, 53–4, 73, 77–8, 80–1, 86–7, Bell, J., 252 93–4, 95–6, 98–101, 103, 107, Berkeley, G., 6, 40–5, 242–3 110–11, 116–20, 120–8, 129–31, Bermudez, J., 249 171, 172, 186 Bernays, P., 207, 208–9, 253 betting, 55–8 Daly, C., 249 bipolarity, 114, 121, 126 Davidson, D., 2, 130 Black, M., 253 decidability, 209–12, 253 Blackburn, S., 249 decision problem, see Blanchette, P., 252 Entscheidungsproblem Börger, E., 253 decision procedure, 207–9 Bostock, D., 253 definite descriptions, 120–8, 139–40 Brandom, R., 249 definitions, 24–5, 107 Brock, S., 239 implicit, 203–6 Brouwer, L., 10 desires, 48, 134–5, 152, 155–6 Devitt, M., 239 Cantor, G., 172, 173 Diamond, C., 4, 6, 21–3, 40, 44–9, Carnap, R., 248 218, 234, 238, 243, 246, 252

265 266 Index disjunction, 110–11, 248 generality, 15–23, 166–7, 198, 209–11, Dokic, J., 249 217, 218, 220–3, 232, 239, 245, Dreben, B., 253 252, see also quantification Dummett, M., 78, 239, 242, 243 geometry, 205, 241 dummy names, 149 God, 41, 42–3 dutch books, 60–1 Godfrey-Smith, P., 249 Goldfarb, W., 238 ε-operator, 252 grammatical possibility, 226–8 elementary functions, 121 Grice, H.P., 158 elucidations, 149 Griffin, J., 103 empirical subject, 50, 105 Gurevich, Y., 253 empiricism, 6, 39 Engel, P., 249 habit, 65 enquiry, 22–3, 69–72, 236–7 Hacker, P., 251 Entscheidungsproblem, 11, 171, 199, Herbrand, J., 208, 253 207–9, 212–13 Hilbert, D., 11, 198, 199–203, 207, ‘Epilogue’, 51 251, 254 ethics, 50 Hintikka, J., 180, 181 evidence, 59–60 holism, 71, 154 Holton, R., 11, 222–5, 228, 238, 252 facts, 7–8, 18–21, 43, 68, 80–2, 85–8, Hookway, C., 62–3 93–5, 106–7, 110, 118, 133, Hume’s principle, 204 135–41, 153, 159–61, 246 ‘Facts and Propositions’, 2, 9, 68, ideal language, see perfect language 73–4, 132–5, 142–7, 147–51, 158, idealisation, 63–6 160, 162, 165–7, 186, 224–5, 245, ideas, 41–4 250, 252 identity, 10, 121–3, 171–3, 174–6, fantasy, see pretence 176–80, 180–3, 189, 190–7, Fine, K., 239 208–9, 248, 251 finitism, 1, 10–11, 198, 199–200, 203, indifference, principle of, 59 210 induction, 19, 25–6, 28, 30, 46–8, 60, Fogelin, R., 251, 253 65–6 form of life, 10, 157, 244 inference, 6, 24, 28–32, 45–9, 125, form of representation, see pictorial 150–1, 191–2, 199–200, 219–20, form 231, 234, 239, 241 formalism, 198, 203 infinite, infinity, 11, 194–6, 198, 218, ‘Foundations of Mathematics’, 141–2, 225–30, 254 171–2, 175, 180, 187–9, 190–7, collections, 15–17, 18, 200–1 210, 224 conjunctions, 15–17, 33, 209–12, Frege, G., 51, 78–9, 89, 100, 104, 133, 222, 228–30, 239–40, 254 135–6, 179, 192, 202, 203–6, 217, domains, 199, 218, 240, 254 249, 251, 252 operations, 223–5, 228–30 functionalism, 1 instrumentalism, 2 intensionality, 139–40, 141–2 games, 26–8, 230, 232–3, 240, 241 internal properties, 117–18, 129–31 Geach, P., 161–3, 250, 253 introspection, 45–9, 55, 165 ‘General Propositions and Causality’, Ishiguro, H., 149–50 1, 15–17, 35–8, 54, 70–1, 218, 220–2, 231–2 Jacquette, D., 253 Index 267

James, W., 69, 245 Mellor, D.H., 239, 244, 249 judgement, 95–8, 114, 133, 135–41, mental signs, 150–6, 159–61, 165–7 158–9, 249, see also belief metalanguage, 92, 95, 124, 128–31, 150 Kant, I., 240 metaphysical subject, 7, 49–51, 77, Kenny, A., 238 98, 151 Keynes, J.M., 54, 61, 65, 244 mind, 85 Kremer, M., 249, 251 Misak, C., 62–3, 71, 72, 238, 244, 245 Kripke, S., 45 misunderstanding, 24–5 models, 33 laws of nature, 5, 15–23, 30, 35–8, 40, Moore, G.E., 225, 252, 253, 254 41, 42, 45–9, 50, 70, 72 multiple relation theory of judgement, Lear, J., 244 96–8, 133, 140–2, 159–61 Lockwood, M., 243 multiplicative axiom, 197, 198, 203, logic, 11, 25, 53, 60, 61, 63, 65–6, see also axiom of choice 209–12, 217, 230–1, 240, 254 Murdoch, I., 134, 154 logical atomism, 7, 31, 250 mysticism, 7, 9, 49–52, 104, 116–17, logical constants, 106, 108, 109–11, 124, 147, 248 115, 147, 166 logical form, 7–8, 77, 79, 90, 91–5, N-operator, 209–11, 218–20, 229–30, 97, 116 247–8, 253 logical notation, 176–80 names, 7–9, 84, 88–90, 100, 113, 118, logical products, sums, 199–203, 121, 132–3, 137, 141, 147–50, 218–20, 254 151, 153, 159–61, 161–4, 165, logical transparency, 211–12 247, 251 logical truth, 173–4 Nanay, B., 249 logicism, 10, 173–4, 196–7 necessity, 120–8, 130–1, 218 Löwenheim, L., 253 negation, 78, 79, 112–15, 121, 158–9, 247 McGinn, M., 49–50 nonsense, 3, 8, 9, 23, 24–5, 35–8, 99, McGuinnes, B., 238, 243, 246, 250, 116, 120–8, 129–31, 150, 159, 254 179, 203, 206, 229, 248, 249, McManus, D., 26, 247 250–1 Majer, U., 66 normativity, 11, 24, 26, 30–1, 39, 49, Malcolm, N., 148 217, 230–2, 235 Mancosu, P., 252 numbers, 125–6, 204, 226–7, 249, 254 Mares, E., 239 Marion, M., 171, 238, 252 objectivity, 45 Marr, D., 241 objects, 7, 41, 42, 80, 83, 84, 86–8, mathematical functions, 192–5 88–90, 106, 113, 132–3, 147–50, ‘Mathematical Logic’, 200–1 153, 162–4, 251 mathematics, 10, 124–8, 171–3, 175, Ogden, C.K., 53, 73, 246 183–4, 192–5, 198, 199–203, 228, ‘On a Problem of Formal Logic’, 209, 249, 250–1 212–13 matter, 40–4, 243 ‘On Truth’, 54, 66–9, 74, 245 meaning, 33, 40–1, 43, 45–6, 69, 78–9, operations, 108, 109–11, 125–6, 97–8, 116, 128–31, 133, 138, 149, 223–5, 228–30, 249, 254 153, 155, 204–6, 217, 230–2, 233–5, 238, 254 paradoxes, 171, 188 268 Index parsimony, 16, 21–3, 24, 35–8 propositional signs, 7–9, 49, 51, 73, Paul, M., 239 93, 97–8, 99–105, 112, 115, 116, Pears, D., 246, 250 117–20, 128–31, 133, 138, 140, Peirce, C.S., 6–7, 53–4, 58–61, 61–4, 150, 152–6, 159–60 66, 68–9, 69–72, 72–4, 98, 104, propositions, 7–8, 11, 36–7, 49, 244, 245 50–1, 51–2, 58, 61–2, 66–7, 73, perception, 32–4, 82, 242 77, 78–9, 81, 85–8, 91–5, 96–8, perfect language, 80, 101, 107, 230–1 98–101, 103–5, 106–7, 107–15, perspectives, 41–4, 243 116, 117–20, 121, 128–31, 132–3, phenomenalism, 6, 40, 41–4, 242, 243 147–50, 152, 171, 186, 190–1, Philosophical Investigations, 11, 157–8, 246, 248 217, 230–1, 241, 244 complex, 78, 108–15, 132 Philosophical Remarks, 11, 218, 226–8 ethically neutral, 56–7 ‘Philosophy’, 17, 23–6, 32–5, 73, 253 pseudo-propositions, see nonsense philosophy, 16–17, 23–38, 39–40, 49, psychological laws, 6, 11, 22, 25–6, 51, 66, 116–17, 128–31, 150, 232, 27, 28, 30, 45–59, 70, 158, 166–7, 235 186, 202–3, 217, 225, 234, 235, pictorial form, 79, 85–8, 89, 91–5 239 picture theory, 7, 77, 80–5, 88–91, psychological subject, see empirical 92–5, 106, 107–15, 123, 160–1, subject 166, 246, 247 psychology, 32–3 platonism, 171 Potter, M., 81, 84–5, 96, 98, 104, 127, quantification, 10, 11, 15–23, 171, 165, 176, 183, 193–4, 246, 249, 186, 188, 199–203, 213, 225–6, 251 see also generality practical reasoning, 55 Quine, W.V.O., 207, 211, 247, 253 pragmatism, 2, 6–7, 53–4, 55, 65, 68–9, 72–4, 132–3, 142, 166 Ramsey sentences, 1 predicative functions, 187–9, 190 rationality, 53, 54, 61–6 preferences, 55–6 realism, 2–3, 5, 15–23, 24, 31, 34–5, pretence, 19, 21–3, 31–5, 51, 73 36–8, 39–40, 43, 70, 72, 79, Price, H., 11, 222–5, 228, 238, 252 148–50, 164–7, 195, 238, 239 Prichard, H.A., 243 realistic spirit, 2–5, 10, 11, 15–23, 24, Principia Mathematica, 10, 121 31, 35, 38, 39–40, 45, 49, 51–2, privacy, 145–6 61–2, 63–6, 72–3, 104–5, 147, probability, 53, 54, 55–8, 61–6, 241 164–7, 171, 195, 217, 235, 239 axioms of, 58 reduction classes, 208 conceptualist view, 58–61 reference, 69, 78, 88–90, 133, 148–50, frequentist view, 58–9, 61, 244 153–4, 162 objective relations of, 54, 61 reflexivity problem, 128–30 subjectivist view, 58–61 relativism, 70–2 proof procedure, 207 religion, 50 Proops, I., 253, 254 representation, 10, 50, 79, 80, 81–5, propositional functions, 150–1, 166–7, 98, 105, 133, 145, 238 171, 183–4, 185–7, 190, 202, representational form, 77 209–11 Rescher, N., 66, 245 propositional functions in extension, rule-following, 11, 45–9, 157–8, 232–5 10, 176, 189, 190–7, 248 rules, 17, 25, 26–8, 61–2, 70–2, 157–8, propositional reference, 66–9, 74, 245 198, 232, 233–5, 240 Index 269

Russell, B., 6, 21, 23, 40, 41–4, 49, 73, Taylor, G., 239 80, 92, 95, 96–8, 100, 121, 133, theoretical virtues, 72 137–41, 148, 159, 171–2, 179, theories, 70–2, 205 184–6, 193, 217, 243, 246, 249 ‘Theories’, 71–2 theory of types, 171 Sahlin, N.E., 55, 238, 244, 252 Thomas, L.H., 247 scholasticism, 5, 25–6, 31, 35, 38, 39 thought, 25, 26–7, 30–2, 45–9, 85, Schönfinkel, M., 207, 208–9 100, 103, 117, 135, 150–1, 165–6, science, 70–2, 135, 240 205, 231, 236, 238, 247, 249 self-conscious reflection, 5, 24–5, Tractatus Logico-Philosophicus, 6, 7, 45–9, 65, 232, 244 11, 17, 24–5, 26–7, 30–2, 49, 50, self-control, 65, 71, 245 51, 69, 73–4, 77–9, 80–5, 86–8, semantic paradoxes, 142 89, 91, 92–5, 98–101, 103–4, semantics, 128–31, 147–50 108–15, 117, 118, 124–6, 128–31, sense, 7–9, 31, 49, 77, 78–9, 80, 89, 138, 147–50, 176–80, 201–2, 98, 99, 107–8, 109–11, 116, 204, 209–13, 218–20, 229–30, 117–20, 121, 128–31, 133, 231, 239, 240, 246, see also 148–50, 152–6, 162, 186, 193–5, Wittgenstein 204, 248 resolute reading of, 4, 9 , 124, 238 sense data, 41, 82, 243 traditional reading of, 9, 124, 238 sentences, 89–90, 98–101, 116, training, 157–8 118–19, 247 translation, 102–4 showing, 117–20 Trueman, R., 240, 251, 252–3 sign-symbol distinction, 7–9, 49, 50, truth, 30–1, 60, 61, 66–9, 77, 105–7, 51, 78, 98–105, 115, 116, 130–1, 113, 135–6, 251 147, 206, 238 correspondence theory of, 68–9, signs, 49–52, 84, 85, 141, 147, 163–4, 106–7, 138–9, 141 165 pragmatist theory of, 68–9 single case problem, 62–6 prosentential theory of, 2 Skorupski, J., 160, 165, 250 redundancy theory of, 67–8 Soames, S., 253 ‘Truth and Probability’, 53 solipsism, 7, 39, 49–52, 85 Turing, A., 208 squiggle, 161–4 type-token distinction, 7–10, 49, 53, Stace, W., 243 73, 78, 98–105, 116, 117–20, Stack, G.J., 243 130–1 strawberry-eaters, 18–20, 236, types, 88, 97 239–40 Strawson, P., 241 understanding, 24, 38, 78–9, 105, 113, subjective idealism, 40–4 135–6, 211, 231, 236 substance, 31, 149 ‘Universals’, 204 success, 60, 68–9 universals, 15–17, 18, 35–8 success semantics, 134–5, 142, 152–3 use, 25–6, 149–50 Sullivan, P., 88–90, 132, 135, 148, 159, usefulness, 16–17, 66, 68–9 161–4, 188, 190–1, 238, 243, 247, utility, 55–6, 69, 144–5 250, 251, 252, 253 symbols, 49–52, 163–4, 165, 211–12 value, 50 van Heijenoort, J., 252, 253 τ-operator, 199–200, 203, 204–6 variable hypotheticals, 1, 11, 15–23, tautology, 126, 173–4, 251 25–6, 27, 35–8, 46–9, 70, 220–3 270 Index verificationism, 43 will, 50 visual experience, 32–4, 41–4 Williams, M., 238 Wittgenstein, L., 1, 11, 21, 23, 26, Waismann, F., 254 40, 45, 47, 49, 51, 69, 73, 77, Wallace, J., 250 86, 90–1, 92–5, 96–8, 100, 105, Wehmeier, K., 180, 181–2, 251 110–11, 116, 121–2, 157–9, 195, weighting, Principle of, 59 217, 225–8, 230–5, 236, 240, 248, Weyl, H., 10, 199, 200 249, 250–1, 252, 253, 254, see also White, R., 177 Tractatus Logico-Philosophicus Whitehead, A., 121 words, 98–9 Whyte, J., 249 Wright, C., 239