Stephen Read

In his article "Verdades antiguas y modernas" (in the same issue, pp. 207-27), David Miller criticised Thomas Bradwardine’s theory of truth and signification and my defence of Bradwardine’s application of it to the semantic paradoxes. Much of Miller’s criticism is sympathetic and helpful in gaining a better understanding of the relationship between Bradwardine’s proposed solution to the paradoxes and Alfred Tarski’s. But some of Miller’s criticisms betray a misunderstanding of crucial aspects of Bradwardine’s account of truth and signification.

Desde que Tarski publicó su estudio sobreel concepto de verdad en los años 30, hasido una práctica ortodoxa el considerarque t oda i nst anci a del esquema T esverdadera. Sin embargo, algunas instanciasdel esquema son falsas. Éstas incluyen lasi nst anci as paradój i cas ej empl i f i cadaspor la oración del mentiroso. Aquí sedemuestra que un esquema mejor permiteun tratamiento uniforme de la verdad enel que las paradojas semánticas resultanser simplemente falsas.Si nc e Ta r s ki publ i s he d hi s s t udy ofthe concept of truth in the 1930s, it hasbeen orthodox practice to suppose thatevery instance of the T-schema is true.However, some instances of the schemaare false. These include the paradoxicalinstances exemplified by the Liar sentence.It is shown that a better schema allows auniform treatment of truth in which thesemantic paradoxes turn out to be simplyfalse

The ?no???no? paradox (so-called by Sorensen) consists of a pair of propositions each of which says of the other that it is false. It is not immediately paradoxical, since it has a solution in which one proposition is true, the other false. However, that is itself paradoxical, since there is no clear ground for determining which is which. The two propositions should have the same truth-value. The paper shows how a proposal by the medieval thinker Thomas Bradwardine solves not only the Liar paradox, but also symmetric paradoxes like the ?no???no?, the descending ?no???no?, and the Truth-teller paradoxes

Gabriel Nuchelmans, Dilemmatic arguments. Towards a history of their logic and rhetoric. (Verhandelingen der Koninklijke Nederlandse Akademie van Weten-schappen, Afd. Letterkunde, Nieuwe Reeks, deel 145.) Amsterdam, New York, Oxford, Tokyo:North-Holland, 1991. 152pp. No price stated Francis P. Dinneen (trans.), Peter of Spain:language in dispute. Amsterdam and Philadelphia: John Benjamins Publishing Company, 1990. xxxix + 271 pp. Hfl. 110/$58.00 Charles H. Manekin, The logic of Gersonides. A translation of Sefer ha-heqqesh ha-yashar (The Book of the Correct Syllogism) of Rabbi Levi ben Gershom with introduction, commentary and analytical glossary. Dordrecht, Boston and London:Kluwer Academic Publishers, 1992. xii + 341 pp. £61.00 F. P. Ramsey, Notes on philosophy, probability and mathematics. Edited by Maria Carla Galavotti. Naples:Bibliopolis, 1991 [published 1992]. 349 pp. No price stated Thomas Drucker (ed.), Perspectives on the History of Mathematical Logic. Boston, Basel, Berlin; Birkhäuser, 1991. xxiii 4- 195 pp. 108 SFr./128 DM J.P. Cleave, A study of logics. (Oxford Logic Guides, volume 18.) Oxford:Clarendon Press, 1991. xiii + 417 pp. £65.00 Hartry Field, Realism, mathematics and modality. Oxford (UK) and Cambridge (USA):Blackwell, 1989 (paperback 1991). viii + 290 pp. £14.95 T.E. Forster, Set theory with a universal set, exploring an untyped universe. Oxford:Clarendon Press, 1992. viii + 152 pp., £25.00 Mark Sainsbury, Logical forms:an introduction to philosophical logic. Cambridge, Mass, and Oxford: Basil Blackwell Publishers, 1991. viii + 398 pp. £40.00 (cloth), £11.95 (paper) L.C. Burns, Vagueness. An investigation into natural languages and the sorites paradox. (Reason and Argument, Volume 4.) Dordrecht, Boston and London:Kluwer, 1991. xii + 202 pp. dollar;130.00/£74.00/dfl 130 Douglas Walton, Slippery slope arguments. Oxford:The Clarendon Press, 1992. xi + 296 pp. £35.00 Bas Van Fraassen, Quantum mechanics. An empiricist view. Oxford:Clarendon Press, 1991. xvi + 541 pp. £50.00 (hardback)/£17.50 (paper) R. Giuntini, Quantum logic and hidden variables. (Grundlagen der exakten Naturwissenschaften, Bd. 8.) Mannheim, Vienna and Zürich:BI-Wissenschaf ts-verlag, 1991. x + 184 pp. No price stated W. Spohn, B.C. Van Fraassn And B. Skyrms (eds.), Existence and explanation:essays presented in honor of Karel Lambert. Dordrect, Boston and London: Kluwer Academic Publishers, 1991. xii 4- 243 pp. £56.00 Michele Di Francesco, Il realismo analitico. Logica, ontologia e significato nel primo Russell (Saggi, 28.) Milan:Guerini, 1991. 269 pp. 30,000 Lire Kenneth Blackwell and Carl Spadont (eds.), A detailed catalogue of the second archives of Bertrand Russell. Bristol:Thoemmes Press, 1992. xxvi + 433 pp. £60.00.

_ Source: _Volume 54, Issue 4, pp 335 - 355 Ian Rumfitt has recently drawn our attention to a couple of paradoxes of signification, claiming that although Thomas Bradwardine’s “multiple-meanings” account of truth and signification can solve the first of them, it cannot solve the second. The paradoxes of signification were in fact much discussed by Bradwardine’s successors in the fourteenth century. Bradwardine’s solution appears to turn on a distinction between the principal and the consequential signification of an utterance. However, although such a distinction played an important role in his successors’ theories, it is shown that Bradwardine’s account of signification does not admit any such distinction, no part being prior to the others. Accordingly his solution, unlike those of his successors, does not fall prey to Rumfitt’s paradoxes.

Intentional verbs create three different problems: problems of non-existence, of indeterminacy, and of failure of substitutivity. Meinongians tackle the first problem by recognizing non-existent objects; so too did many medieval logicians. Meinongians and the medievals approach the problem of indeterminacy differently, the former diagnosing an ellipsis for a propositional complement, the latter applying their theory directly to non-propositional complements. The evidence seems to favour the Meinongian approach. Faced with the third problem, Ockham argued bluntly for substitutivity when the intentional complement is non-propositional; Buridan developed a novel way of resisting substitutivity. Ockham's approach is closer to the Meinongian analysis of these cases; Buridan's seems to raise difficulties for a referential semantics. The comparision between the Meinongian and medieval approaches helps to bring out merits and potential pitfalls of each.

Logical pluralism is the claim that different accounts of validity can be equally correct. Beall and Restall have recently defended this position. Validity is a matter of truth-preservation over cases, they say: the conclusion should be true in every case in which the premises are true. Each logic specifies a class of cases, but differs over which cases should be considered. I show that this account of logic is incoherent. Validity indeed is truth-preservation, provided this is properly understood. Once understood, there is one true logic, relevance logic. The source of Beall and Restall’s error is a recent habit of using a classical metalanguage to analyse non-classical logics generally, including relevance logic.

Stephen Read - Johannes Buridanus: Summulae de Practica Sophismatum - Journal of the History of Philosophy 45:1 Journal of the History of Philosophy 45.1 157-158 Muse Search Journals This Journal Contents Reviewed by Stephen Read University of St. Andrews Fabienne Pironet, editor. Johannes Buridanus: Summulae de Practica Sophismatum. Artistarium 10–9. Turnhout: Brepols 2004. Pp. xlix + 193. Paper, €40.00. John Buridan was an unusual figure in fourteenth-century logic and philosophy. Logic was at that time largely the preserve of the young, who would lecture on logic while studying in higher faculties such as theology, before moving on to lecture in their maturity on philosophy and theology. Two notable exceptions are the Englishman Walter Burley and the Frenchman from Picardy, John Buridan. Already active in the Arts Faculty at Paris in the late 1320s, Buridan was still there thirty years later. In the meantime, among other works on metaphysics, ethics, politics, and natural philosophy, he..

In this book, Stephen Read sets out to rescue logic from its undeserved reputation as an inflexible, dogmatic discipline by demonstrating that its technicalities and processes are founded on assumptions which are themselves amenable to philosophical investigation. He examines the fundamental principles of consequence, logical truth and correct inference within the context of logic, and shows that the principles by which we delineate consequences are themselves not guaranteed free from error. Central to the notion of truth is the beguiling issue of paradox. Its philosophical value, Read shows, lies in exposing the invalid assumption on which the paradox is built. Thinking About Logic also discusses logical puzzles which introduce questions relating to language, the world, and their relationship.

Bradwardine’s solution to the the logical paradoxes depends on the idea that every sentence signifies many things, and its truth depends on things’ being wholly as it signifies. This idea is underpinned by his claim that a sentence signifies everything that follows from what it signifies. But the idea that signification is closed under entailment appears too strong, just as logical omniscience is unacceptable in the logic of knowledge. What is needed is a more restricted closure principle. A clue can be found in speech act pluralism, whereby indirect speech reports are closed under intersubstitutivity of co-referential terms. The conclusion is that solving the semantic paradoxes does not require revision of logic, thus saving logic from paradox

General-elimination harmony articulates Gentzen’s idea that the elimination-rules are justified if they infer from an assertion no more than can already be inferred from the grounds for making it. Dummett described the rules as not only harmonious but stable if the E-rules allow one to infer no more and no less than the I-rules justify. Pfenning and Davies call the rules locally complete if the E-rules are strong enough to allow one to infer the original judgement. A method is given of generating harmonious general-elimination rules from a collection of I-rules. We show that the general-elimination rules satisfy Pfenning and Davies’ test for local completeness, but question whether that is enough to show that they are stable. Alternative conditions for stability are considered, including equivalence between the introduction- and elimination-meanings of a connective, and recovery of the grounds for assertion, finally generalizing the notion of local completeness to capture Dummett’s notion of stability satisfactorily. We show that the general-elimination rules meet the last of these conditions, and so are indeed not only harmonious but also stable.

Thomas Bradwardine's solution to the semantic paradoxes, presented in his Insolubilia written in Oxford in the early 1320s, turns on two main principles: that a proposition is true only if things are wholly as it signifies; and that signification is closed under consequence. After exploring the background in Walter Burley's account of the signification of propositions, the question is considered of the extent to which Bradwardine's theory is compatible with the distribution of truth over conjunction, disjunction, negation and the conditional.

This chapter focuses on alternative logics. It discusses a hierarchy of logical reform. It presents case studies that illustrate particular aspects of the logical revisionism discussed in the chapter. The first case study is of intuitionistic logic. The second case study turns to quantum logic, a system proposed on empirical grounds as a resolution of the antinomies of quantum mechanics. The third case study is concerned with systems of relevance logic, which have been the subject of an especially detailed reform program. Finally, the fourth case study is paraconsistent logic, perhaps the most controversial of serious proposals.