Such a misconception of grammar characterises a very popular approach to indexicality which has been current since the 1970s, stemming from the work of Casteñeda, and Kaplan. Gareth Evans was inclined to allow, for instance, that one could say ‘“To the left (I am hot)” is true, as uttered by x at t iff there is someone moderately near to the left of x such that, if he were to utter the sentence “I am hot” at t, what he would (...) thereby say is true’ (Evans 1985: 358). But not only does this disturb the proper relation between direct and indirect speech, it continues a Fregean tradition which these very cases show to be quite mistaken about the logic of intensions. (shrink)
I have become more convinced, over the years, by the truth of Wittgenstein’s characterisation of philosophy as arising through misconceptions of grammar. Such a misconception of grammar characterises a very popular approach to indexicality which has been current since the 1970s, stemming from the work of Casteñeda, and Kaplan. Gareth Evans was inclined to allow, for instance, that one could say ‘“To the left (I am hot)” is true, as uttered by x at t iff there is someone moderately near (...) to the left of x such that, if he were to utter the sentence “I am hot” at t, what he would thereby say is true’ (Evans 1985: 358). But not only does this disturb the proper relation between direct and indirect speech, it continues a Fregean tradition which these very cases show to be quite mistaken about the logic of intensions. In this paper, however, I want primarily to point out how this misconception of grammar has distorted our view of people. For some of the above thinkers have tried to make out that human motivation is related to the possession of a certain category of indexical belief, by Lewis called ‘de se beliefs’. I shall look here at how the matter arises in Hugh Mellor’s work on Time. In connection with Time, indexicality arises in McTaggart’s ‘A-series’, and Mellor treats this indexicality in parallel with Evans’ language. First, therefore, I aim to show how Mellor’s discussion of Time grammatically misconceives the situation, and leads to a misrepresentation of the motivation of human action. But a larger conclusion about Fregean intensions is also then immediately available. (shrink)
'Philosophy arises through misconceptions of grammar', said Wittgenstein. Few people have believed him, and probably none, therefore, working in the area of the philosophy of mathematics. Yet his assertion is most evidently the case in the philosophy of Set Theory, as this paper demonstrates (see also Rodych 2000). The motivation for twentieth century Set Theory has rested on the belief that everything in Mathematics can be defined in terms of sets [Maddy 1994: 4]. But not only are there notable items (...) which cannot be so defined, including numbers and mereological sums, the very notion of a set, as formalized within this tradition, is based on a series of grammatical confusions. (shrink)
One of the claims made for C. S. Peirce's existential graphs has been that they are a deductively complete formulation of first-order logic with identity. As Peirce presented them, this is true only for certain versions of first-order logic :those which do not include terms for individuals. I amend Peirce's rules here, showing, in particular, how they are capable of demonstrating that, for instance, ?Jack is in the kitchen? contradicts ?Jack is not in the kitchen?
I have written a number of articles recently that have a rather remarkable character. They all point out trivial grammatical facts that, at great cost, have not been respected in twentieth century Logic. A major continuous strand in my previous work, with this same character, I will first summarise, to locate the kind of fact that is involved. But then I shall present an overview of the more recent, and more varied (...) points I have made, which demonstrate the far larger extent of basic grammar that has been overlooked or suppressed. I end with some remarks about how this phenomenon can have arisen – principally through logicians not being attentive enough to their own language, and occupying themselves, instead, with often quite imaginary languages. (shrink)
This paper starts by criticising some olderaccounts of conditionals based on the so-called `Ramsey Test', and ends by proposing their replacement, in part with a material account, in part with a probabilistic account using epsilon terms. The combined replacement is in fact closer to Ramsey's ideas. But there is also a resemblance between the latter and a more recent account of conditionals, which relates some of them to causality. The comparison (...) provides a basis for assessment of the proposed replacement. (shrink)
P.M.S. Hacker, recounting some of Wittgenstein's views, says (Hacker 1996, p134): [T]he pervasive conception of behaviour that has informed philosophical psychology for the last three centuries has misrepresented human behaviour as 'bare bodily movement', from which it is supposed we infer, by analogy or inference to best explanation, the inner state and so on from which the behaviour might be thought to arise … But we see the pain in a person's face hear the glee in his chortles, (...) perceive the affection in the looks and gestures of lovers. In this paperIexplain how this can be, before meeting several objections. (shrink)
Routley?s Formula says, for instance, that if it is believed there is a man then there is something which is believed to be a man. In this paper I defend the formula; first directly, but then by looking at work by Gensler and Hintikka against it, and at the original work of Routley, Meyer and Goddard for it. The argument ultimately reduces to a central point about the extensionality of objects in Routley, Meyer and Goddard?s intensional system, i.e. in its (...) formulation of transparency. (shrink)
Fregean logic has difficulty with certain arguments in which there is cross-reference between premises and conclusion. In this paper I describe a method of handling arguments of the troublesome kind: It involves replacing standard quantifiers with explicit existential statements, and turns standard logic into a free one. A validation procedure is provided for the logic.
The paper presents and applies Hilbert's Epsilon Calculus, first describing its standard proof theory, and giving it an intensional semantics. These are contrasted with the proof theory of Fregean Predicate Logic, and the traditional (extensional) choice function semantics for the calculus. The semantics provided show that epsilon terms are referring terms in Donnellan's sense, enabling the symbolisation and validation of argument forms involving E-type pronouns, both in extensional and intensional contexts. By providing for transparency in intensional constructions they support a (...) Model Conceptualism to contrast with traditional intensional logic's Modal Realism. But epsilon-terms also symbolise fictions, and through their difference from iota terms enable the solution of a number of outstanding puzzles about Direct Reference and de re beliefs. (shrink)
Gary Kemp defends Realist approaches to the paradox of analysis. Other, prima facie equally viable approaches to this problem are the Nominalist one of Langford and Camap and the Conceptualist one of Prior and Stalnaker. In the context of a fuller survey focus is set on the realist attempt. This puts one in a better position to arbitrate between these approaches and give a more final assessment of the realist one, including an assessment of Kemp's defence of it. The Conceptualist (...) one, as it turns out, triumphs over the others, and is the basis for a Wittgensteinian vie w of the a priori which is analyzed in the second part of the paper. (shrink)
In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant *c* in a given logic: its operational meaning, given by the operational rules for *c* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing *c* which can be proved in the same calculus. Subsequently, we use (...) the same strategy to counter Quine's meaning variance argument against deviant logics. In a nutshell, we claim that genuine rivalry between (similar) logics *L* and *L* is possible whenever each constant in *L* has the same operational meaning as its counterpart in *L* although differences in global meaning arise in at least one case. (shrink)
B. H. Slater has argued that there cannot be any truly paraconsistent logics, because it's always more plausible to suppose whatever negation symbol is used in the language is not a real negation, than to accept the paraconsistent reading. In this paper I neither endorse nor dispute Slater's argument concerning negation; instead, my aim is to show that as an argument against paraconsistency, it misses (some of) the target. A important class of paraconsistent logics — the preservationist logics (...) — are not subject to this objection. In addition I show that if we identify logics by means of consequence relations, at least one dialetheic logic can be reinterpreted in preservationist (non-dialetheic) terms. Thus the interest of paraconsistent consequence relations — even those that emerge from dialetheic approaches — does not depend on the tenability of dialetheism. Of course, if dialetheism is defensible, then paraconsistent logic will be required to cope with it. But the existence (and interest) of paraconsistent logics does not depend on a defense of dialetheism. (shrink)