AN “i” FOR ANi: SINGULAR TERMS, UNIQUENESS, AND REFERENCE

In this essay I argue that given Donnellan’s formulation of the attributive uses of definite descriptions, as well as Kripke’s [6] and Salmon’s [10] generalized accounts, most uses of definite descriptions that are taken to be attributive turn out not to be so. In building up to my main thesis, I first consider certain problematic cases of uses of definite descriptions that do not neatly fit into any category. I then argue that, in general, a complete definite description we use is complex, in which there is an embedded singular term that is used referentially. From this I conclude that an attributive use of a definite description is an extremely rare linguistic phenomenon, much less frequent than what Donnellan, Kripke, and Salmon have presupposed; so much so that the standard examples given by Donnellan of the attributive use of definite descriptions do not qualify as attributive

We introduce new proof systems for propositional logic, simple deduction Frege systems, general deduction Frege systems, and nested deduction Frege systems, which augment Frege systems with variants of the deduction rule. We give upper bounds on the lengths of proofs in Frege proof systems compared to lengths in these new systems. As applications we give near-linear simulations of the propositional Gentzen sequent calculus and the natural deduction calculus by Frege proofs. The length of a proof is the number of lines (or formulas) in the proof.A general deduction Frege proof system provides at most quadratic speedup over Frege proof systems. A nested deduction Frege proof system provides at most a nearly linear speedup over Frege system where by “nearly linear” is meant the ratio of proof lengths is O(α(n)) where α is the inverse Ackermann function. A nested deduction Frege system can linearly simulate the propositional sequent calculus, the tree-like general deduction Frege calculus, and the natural deduction calculus. Hence a Frege proof system can simulate all those proof systems with proof lengths bounded by O(n . α(n)). Also we show that a Frege proof of n lines can be transformed into a tree-like Frege proof of O(n log n) lines and of height O(log n). As a corollary of this fact we can prove that natural deduction and sequent calculus tree-like systems simulate Frege systems with proof lengths bounded by O(n log n).

Preface. Abbreviations. Part 1: Philosophy of Language. The Social Aspect of Language D. Davidson. Singular Terms B. Hale. Philosophical Theorizing and Particularism: Michael Dummett on Wittgenstein's Later Philosophy of Language D. Pears. Convention and Assertion E. Picardi. Meaning Theory and Anti-Realism D. Prawitz. Part 2: Philosophy of Mathematics. Anti-Realism and the Philosophy of Mathematics G. Oliveri. Dummett and Wittgenstein's Philosophy of Mathematics C. Penco. Vestiges of Realism G. Sundholm. About 'the Philosophical Significance of Godel's Theorem': Some Issues C. Wright. Part 3: Philosophy of Mind, Time and Religion. Dummett, Realism and Other Minds A. Bilgrami. Truth, Time and Deity B.F. McGuinness. Leaving the Past Where it Belongs J. Schulte. Part 4: Dummett's Replies. Reply to Davidson. Reply to Hale. Reply to Pears. Reply to Picardi. Reply to Prawitz. Reply to Oliveri. Reply to Penco. Reply to Sundholm. Reply to Wright. Reply to Bilgrami. Reply to McGuinness. Reply to Schulte. Bibliography. Index.

Some recent work in the philosophy of language has rightly emphasized the role which contextual factors play in the use of language. An adequate theory about how language operates, we are told, must distinguish between (a) that which expressions, constructions and sentences carry with them from one context to another and (b) that which is added by a context of utterance. The features which carry from one context to another have been referred to as context-independent factors, and those which are added contextually as contextdependent factors. This distinction is not, of course, a new one; but it is fair to say that it has not always been given its due in discussions of logical form. Notably, it is not given its due in Russell's famous theory of definite descriptions. In this paper I will propose an alternative way of analyzing sentences containing definite descriptions which does do justice to this distinction. Before I present this theory, however, I want to distinguish three things: referring, language, and what I will call the referential link. By referring I mean the identification of some object by a speaker (as a subject for communication). By the link I mean the semantical connection between a token of a singular term (e.g., a proper name or a definite description) and an object which makes the utterance containing that token literally about that object. By language I mean singular terms or sentences containing singular terms. Typically, a speaker refers to an object by producing

BOOK REVIEWS 807 Du Langage, A. Martinet et M. Merleau-Ponty. By GHYSLAIN CHARRON. Editions de L'Universite d'Ottawa, Collection Philosophica, 197~. Pp. 187. This book is a careful and intelligent piece of analysis which will be read with profit by any philosopher interested in the philosophy of language and, more particularly, in the philosophical (i.e., conceptual) investigation of contemporary linguistics. But there is something a little schizophrenic about this work. It consists of two parts which are more juxtaposed than interrelated. The first part is a careful, analytical exposition of the major conclusions of A. Martinet's work in linguistics. The second part is an exposition of the linguistic philosophy of Merleau-Ponty. The purpose of the author, as stated in the preface, is to teach philosophers something of what they need to know about contemporary linguistics and at the same time to teach the linguists why philosophers continue to be interested in the problems of language even after the creation of their new science. Why is it that even after the advent of Structuralism some questions about language still remain which the linguist is incompetent to answer? Charron takes the corpus of Martinet as typical of the structuralist approach to language as it was developing in France from 1980-1960, at the very time during which the first major philosopher of the French (or any other) tradition began to address himself to its problems in their importance for philosophy. This exposition is meant to serve as the basis for a discussion of what the structuralists, on the one side, and the phenomenologists, on the other, have in common in order to focus on the points at which they diverge (if we are hard-headed) or at which they complement one another (if we are more eirenic). The trouble is that the author is very good at putting himself in the place of and in speaking the language of each of the combatants; what does not quite come off is the dialogue which is supposed to take place between them. The section on Martinet's contributions to linguistics will be very useful for the non-specialist philosopher who is unacquainted with linguistics. It is, in fact, an excellent non-technical introduction to the methods of linguistic structuralism as exemplified in the work on phonology by this one author. But it is by the same token considerably out of date and will be of little value to those who have followed the development of linguistics past Martinet up to the present time, since a large number of the theses Martinet propounds arid defends {such as, for instance, his attempt to ·suppress the concept " word " as being insufficientJy rigorous to be useful in scientific linguistics, pp. 45 ff.) can only be fully understood in the light of later criticism, refinement, and development. It will also dissatisfy the linguist inasmuch as we are given here. only Martinet's 808 BOOK REVIEWS conclusions and none of the reasoning which led him to them. While, at the same time, the philosophical reader will remark that Martinet was only one of the structuralists whom Merleau-Ponty read and by whom he was influenced, others, like Saussure and Guillaume especially, had a much wider and deeper influence on him. Nevertheless, in spite of these criticisms, this book serves a good and important service at the present time. Merleau-Ponty was the first major philosopher we know of to concern himself with linguistics as a science and with the importance of this developing science for philosophy. By contrast, until most recently, Anglo-American philosophical analysis (in Wittgenstein, in Ryle, in Austin, in Strawson and their numerous colleagues and followers) has limited itself almost exclusively to the commonsensical analysis of speech-acts without showing much interest in the science of linguistics as such. This state of affairs has now begun to change rapidly, and we find that many of the younger American philosophers of languageparticularly as a result of the challenges of Chomsky and his students-are becoming more and more sensitive to scientific linguistics and its value for philosophy-not only because it gives us a body of scientific literature which nobody, least of all...

Étude de l’agentivité dans le discours de femmes souffrant de trouble de stress post-traumatique dans les suites de violences conjugales

Full classical S5 in natural deduction with weak normalization

The science of numbers: does language help or hinder?

A general formulation of inductive and recursive definitions in Martin-Löf's type theory is presented. It extends Backhouse's ‘Do-It-Yourself Type Theory’ to include inductive definitions of families of sets and definitions of functions by recursion on the way elements of such sets are generated. The formulation is in natural deduction and is intended to be a natural generalisation to type theory of Martin-Löf's theory of iterated inductive definitions in predicate logic.Formal criteria are given for correct formation and introduction rules of a new set former capturing definition by strictly positive, iterated, generalised induction. Moreover, there is an inversion principle for deriving elimination and equality rules from the formation and introduction rules. Finally, there is an alternative schematic presentation of definition by recursion.The resulting theory is a flexible and powerful language for programming and constructive mathematics. We hint at the wealth of possible applications by showing several basic examples: predicate logic, generalised induction, and a formalisation of the untyped lambda calculus.

This is a companion to a paper by the authors entitled “Godel on deduction”, which examined the links between some philosophical views ascribed to Godel and general proof theory. When writing that other paper, the authors were not acquainted with a system of natural deduction that Godel presented with the help of Gentzen’s sequents, which amounts to Jaśkowski’s natural deduction system of 1934, and which may be found in Godel’s unpublished notes for the elementary logic course he gave in 1939 at the University of Notre Dame. Here one finds a presentation of this system of Godel accompanied by a brief reexamination in the light of the notes of some points concerning his interest in sequents made in the preceding paper. This is preceded by a brief summary of Godel’s Notre Dame course, and is followed by comments concerning Godel’s natural deduction system.

_Russell_ journal (home office): E:CPBRRUSSJOURTYPE2501\REVIEWS.251 : 2005-09-14 19:58  Reviews RUSSELL’S INFLUENCE ON INGEMAR HEDENIUS S A Theology and Religious Studies / U. of Lund  , Lund, Sweden @. Svante Nordin. Ingemar Hedenius. En filosof och hans tid [Ingemar Hedenius. A philosopher and his time]. Stockholm: Natur och Kultur, . Pp. ;  photos.  kr. en years ago I wrote a review article about Gunnar Fredriksson’s book Tabout Bertrand Russell for Russell called “Russell’s Influence in Sweden”. In it I mentioned two Swedish philosophers who introduced and established analytic philosophy in Sweden. The oldest, Ingemar Hedenius (–), was professor in practical philosophy in Uppsala from  to ; the younger, Anders Wedberg (–), was professor in theoretical philosophy in Stockholm from  to . Together they had an enormous influence on the development of Swedish philosophy, since—among other things—they had the  See the review of Bertrand Russell: en intellektuelli i politiken, Russell, n.s.  (): –. _Russell_ journal (home office): E:CPBRRUSSJOURTYPE2501\REVIEWS.251 : 2005-09-14 19:58 Reviews  power to influence most of the new professors in philosophy. And they can both be called disciples of Bertrand Russell. The formal division between theoretical and practical philosophy goes back to Aristotle and Kant and consists in a distinction between the philosophy of thinking and the philosophy of acting. In practice it means that the former subject includes metaphysics, epistemology, philosophy of language and philosophy of mathematics and logic, while the latter deals with ethics, aesthetics, social philosophy and philosophy of religion. It was Wedberg who introduced Russell as a logician and a philosopher of mathematics and for a long time theoretical philosophers primarily wrote about logic and tried to apply the symbols of mathematical logic to classical philosophical problems. Russell’s influence on Hedenius was of a more general character that showed itself in his writings on ethics and religion, but also in his general attitude to life. In  Hedenius published a collection of essays called Tro och Vetande [Faith and Knowledge] that started a public discussion about the truth of Christianity that went on for years. The book was an undisguised attack on Swedish theology and Swedish theologians that caused a lot of hard feelings and undermined the reputation of theology as a legitimate academic subject. It was such a knock out that still today many Swedish theologians suffer from a “Hedenius complex”. (One could call it a “Russell complex”.) There is only one reference to Russell in Hedenius’ book and that is to Sceptical Essays, where Russell writes: “I wish to propose for the reader’s favourable consideration a doctrine which may, I fear, appear wildly paradoxical and subversive. The doctrine in question is this: that it is undesirable to believe a proposition when there is no ground whatever for supposing it true” (SE, p. ). Of course, Russell was not the first philosopher to endorse such a doctrine, which can be traced back to the spirit of Socrates and the old Greek sceptical philosophers, but Hedenius seems to have been impressed by Russell’s humorous and elegant way of formulating it. He took it to his heart and called it “den intellektuella moralens maxim”, which translates into “the maxim of intellectual morality” and sounds like an echo of Kingdon Clifford, although Hedenius might not have heard of him. Anyway, Hedenius thought that it was morally wrong to believe any proposition without having good reasons. With this maxim in mind he examined the major tenets of Christianity and found that very few—if any—passed the test, although he never seems to have doubted that Jesus existed, which he might have done, if he had examined the reasons for believing so more critically. From now on Hedenius was the best known and feared philosopher in Sweden. Another professor in Uppsala with a big sense of humour said: “There is no God and Ingemar Hedenius is his prophet.” Hedenius took an active part _Russell_ journal (home office): E:CPBRRUSSJOURTYPE2501\REVIEWS.251 : 2005-09-14 19:58  Reviews in many public discussions and wrote hundreds of newspaper articles, essays and close to  books that could be read by anyone. The influence of Russell is obvious in many of them, although he is seldom...

same properties and relations). And if so, there need not be anything very strange about giving up this requirement in the special case of definite descriptions. For if there is no unique object meeting a description, there perhaps need not be anything perverse in the idea that the different occurrences of this description may refer to different individuals. After all, different occurrences of an indefinite description like "some man" may very well refer to different individuals at their different occurrences (as, for example, in "some man is as tall as some other man"). Is it so very strange to assimilate definite descriptions to indefinite ones in those cases in which there exists no unique object answering to the description? The restriction I am proposing may thus be much more natural than first appears. Because the restriction is a very limited one, the resulting theory of definite descriptions has most of the features we should like it to have. For instance, Lambert's (23) and (26) are still available. In fact, the restriction I am proposing is in certain respects less restrictive than the one advocated by Lambert. He in effect restricts (1) by requiring that y must be a term whose bearer really exists; and this restriction affects other singular terms in addition to definite descriptions. Under the course I am suggesting, only definite descriptions are affected. As a consequence, for free individual variables we readily have some results, for example, y (Lx) (x y) which Lambert would like to have but does not have without additional assumptions.

A natural deduction system NI, for the full propositional intuitionistic logic, is proposed. The operational rules of NI are obtained by the translation from Gentzen’s calculus LJ and the normalization is proved, via translations from sequent calculus derivations to natural deduction derivations and back.

Prawitz proved a theorem, formalising ‘harmony’ in Natural Deduction systems, which showed that, corresponding to any deduction there is one to the same effect but in which no formula occurrence is both the consequence of an application of an introduction rule and major premise of an application of the related elimination rule. As Gentzen ordered the rules, certain rules in Classical Logic had to be excepted, but if we see the appropriate rules instead as rules for Contradiction, then we can extend the theorem to the classical case. Properly arranged there is a thoroughgoing ‘harmony’, in the classical rules. Indeed, as we shall see, they are, all together, far more ‘harmonious’ in the general sense than has been commonly observed. As this paper will show, the appearance of disharmony has only arisen because of the illogical way in which natural deduction rules for Classical Logic have been presented.

In 1994 Herbelin started and partially achieved the programme of showing that, for intuitionistic implicational logic, there is a Curry-Howard interpretation of sequent calculus into a variant of the λ-calculus, specifically a variant which manipulates formally “applicative contexts” and inverts the associativity of “applicative terms”. Herbelin worked with a fragment of sequent calculus with constraints on left introduction. In this paper we complete Herbelin’s programme for full sequent calculus, that is, sequent calculus without the mentioned constraints, but where permutative conversions necessarily show up. This requires the introduction of a lambda-like calculus for full sequent calculus and an extension of natural deduction that gives meaning to “applicative contexts” and “applicative terms”. Such extension is a calculus with modus ponens and primitive substitution that refines von Plato’s natural deduction; it is also a “coercion calculus”, in the sense of Cervesato and Pfenning. The proof-theoretical outcome is noteworthy: the puzzling relationship between cut and substitution is settled; and cut-elimination in sequent calculus is proven isomorphic to normalisation in the proposed natural deduction system. The isomorphism is the mapping that inverts the associativity of applicative terms.KeywordsReduction RuleNatural DeductionSequent CalculusApplicative ContextTyping RuleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.