Speaking of Professor Geach's belief that pronouns in natural language function like the bound variables in quantification theory, Gareth Evans, in ‘Pronouns, Quantifiers, and Relative Clauses - I’ says :I want to try to show that there are pronouns with quantifier antecedents that function in a quite different way. Such pronouns typically stand in a different grammatical relation to their antecedents, and; in contrast with bound pronouns, must be assigned a reference, so that their most immediate sentential contexts can always (...) be assigned a truth value. The relevant grammatical relation appears to be Klima's relation of ‘in construction with’. When the pronoun is in construction with its antecedent, as in [‘Some man loves his mother’] and [‘No man is happy when he is in love’] the result is a bound pronoun. (shrink)

Despite the volume of discussion on the Liar Paradox recently, there is one stream of largely British thought on the matter which is hardly represented in the wider literature. This paper points out salient aspects of the history of this tradition, from its origin in forms of propositional quantification found in Ramsey, through to more precise symbolisations which have emerged more recently. But its purpose is to exposit, with respect to a number of contested cases, the ensuing results. Thus it (...) goes on to apply the analysis to several other well known paradoxes, including one rarely discussed, which reveals more fully the consequent consistency and completeness of natural language. (shrink)

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)

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)

Recovers some of the value in the Wittgensteinian period of philosophy, using certain logical systems: Prior's theory of operators and Hilbert's epsilon calculus. This work applies, discursively, the previous largely technical results published in Prolegomena to Formal Logic (Aldershot, Gower 1989) and Intensional Logic (Aldershot, Ashgate 1994) to resolve matters of current interest in philosophy, logic and linguistics - notably attacking a variety of realisms found in comtemporary cognitive science and the philosophy of mathematics.

This paper covers the history of the development of various epsilon calculi, and their applications, starting with the introduction of epsilon terms by Hilbert and Bernays. In particular it describes the Epsilon Substitution Method and the First and Second Epsilon Theorems, the original Epsilon Calculus of Bourbaki, several Intuitionistic Epsilon Calculi, and systems that have been constructed to incorporate epsilon terms in modal, and general intensional structures. Standard semantics for epsilon terms are discussed, with application to Arithmetic, and it is (...) shown how epsilon terms give distinctive theories of descriptions and identity, through providing complete individual terms for individuals, which are rigid across possible worlds. The Epsilon Calculus' problematic thereby extends that of the predicate calculus primarily through its applicability to anaphoric reference, both in extensional and also intensional constructions. There are higher-order applications, as well, some of which resolve paradoxes in contemporary logic through allowing for indeterminacy of reference. (shrink)

Like the author's first work, this text again develops two advanced logical systems: the formalization of intensional constructions initiated by Arthur Prior, and the refinement of predicate logic instituted by David Hilbert. This book is more historical than the first, but the emphasis is still on the application of the two systems to problems in analytical metaphysics. The natures of provability and possibility are studied further, as well as the natures of opacity and intensional objects.

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)

Jean-Paul Sartre, in describing the realization of his freedom, was often inclined to say mysterious things like ‘I am what I am not’, ‘I am not what I am’ (‘as I am already what I will be …, I am the self which I will be, in the mode of not being it’, ‘I make myself not to be the past … which I am’.) He was therefore plainly contradicting himself, but was this merely a playful literary figure (paradox), or (...) was he really being incoherent? By the latter judgment I do not mean to reject his statements entirely (like many of his Anglo-Saxon contemporaries); for I believe there is an intimate link between contradiction and freedom, as I shall explain in this paper. But a minor thing we must first have out of the way is the suggestion that Sartre's language was just a rhetorical trope, designed merely to express some banal platitude in a bemusing way: ‘I am not yet what I will be’, ‘I am no longer what I was’ are sane and sensible, for instance, but cannot be the meant content of Sartre's sayings, since, while they would indeed describe the reform of some character, they would be appropriate only before or after some metamorphosis, not, as Sartre clearly intended, in the midst of some process of riddance and conversion, whether radical or otherwise. Yet, in the turmoil of such a change, ‘I am not what I am’ (or the everyday ‘I am not myself’) still, surely, cannot be true, and if that is the case, Sartre must be being inocherent, and therefore, obfuscating and deliberately obscure, and hence, it seems, must properly be rejected by all right and clear thinking men. (shrink)

In a previous issue of Philosophical Investigations Professor Radford provides a counterexample to the equation1: a word is on the tip of a man's tongue IFF (a) he can recognize the word and (b1) he believes he may be able to produce It (fairly soon).

Two uses of ‘if are discussed which do not involve conditions. The first is illustrated in the example ‘If he's here, I don't see him’, the second in ‘He's not a dunce, if a trifle stupid’. A third non‐conditional use, cognate with the first is also mentioned: it would be illustrated in the example ‘If he's a Dutchman, I'll eat my hat’. It is argued that recent attempts to formulate a logic of conditionals have distorted our understanding of ‘if, by (...) ignoring these uses, sometimes deliberately. Specifically, as a result, many arguments involving ‘if have been misjudged as invalid, because the expectation has been that ‘if expresses a condition. It is suggested that the traditional analysis of ‘necessary and sufficient conditions’ in terms of ‘if and only if, is partly to blame for these misunderstandings. And the proper understanding of ‘if’ which emerges shows it is quite fully captured in the propositional calculus. (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?

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)

Wittgenstein's Remarks on the Foundations of Mathematics was poorly received by the critics when it was first published, and only a few sympathetic commentators have made much of it since then. The book has not had a great success, because the majority of people interested in the philosophy of mathematics these days have a quite different approach to the subject from Wittgenstein. But not only that, they have a quite different logic from Wittgenstein. I believe one of the main sources (...) of the antipathy felt towards the Remarks lies in the foreignness of the logic Wittgenstein develops there. I hope, in what follows, to make that logic more understandable, and with it the philosophy of mathematics it supports. (shrink)