Stephen Read

Thomas Reid was one of the greatest philosophers of the eighteenth century and a contemporary of Kant's. This volume is part of a new wave of international interest in Reid from a new generation of scholars. The volume opens with an introduction to Reid's life and work, including biographical material previously little known. A classic essay by Reid himself - 'Of Power' - is then reproduced, in which he sets out his distinctive account of causality and agency. This is followed by ten original essays exploring different aspects of Reid's philosophy, as well as his relation to other thinkers, such as Kant, Priestley, and Moore

The idea of proof-theoretic validity originated in the work of Gentzen, when he suggested that the meaning of each logical expression was encapsulated in its introduction-rules. The idea was developed by Prawitz and Dummett, but came under attack by Prior under the soubriquet 'analytic validity'. Logical truths and logical consequences are deemed analytically valid by virtue of following, in a way which the present chapter clarifies, from the meaning of the logical constants. But different logics are based on different rules, confer different meanings and so validate different theorems and consequences, some of which are arguably not true or valid at all. It seems to follow that some analytic statements are in fact false. The moral is that we must be careful what rules we adopt and what meanings we use our rules to determine.

This book presents the very latest research on the medieval use of sophisms in logical and grammatical investigation by twenty-three of the leading experts in Europe and beyond. Important insights into the genre of sophismatic treatises have been gained only very recently, and the organisation of the European Symposium on this topic in 1990 led to a concentration of research and evaluation of insights. The papers are divided into three groups: one covers textual study and analysis of the role of sophisms in the medieval curriculum; another deals with grammatical sophisms; and the third covers particular logical sophisms, from 'Man is the worthiest of creatures' and problems in the theory of reference to the Liar paradox and the work of William of Ockham.

MEDIEVAL AND RENAISSANCE LOGICSIMON OF FAVERSHAM, Quaestiones super Libro Elenchorum. Text in Latin with introduction and notes in English, edited by Sten Ebbesen, Thomas Izbicki, John Longeway, Francesco del Punta, Eileen Serene and Eleonore Stump. Toronto: Pontifical Institute of Mediaeval Studies, 1984. xiv + 270 pp. $3 1.OO.JACOPO ZABARELLA, De methodis libri quatuor; Liber de regressu. Edited by Cesare Vasoli. Bologna: Editrice CLUEB, 1985. xxxviii+ 193 pp. Lire 57,000.EDITIONSG. W. F. HEGEL, Wissenschafl der Logik. Erster Teil. Die objektive Logik, Erster Band. Die Lehre von Sein. Herausgegeben von F. Hogemann und W. Jaeschke. Hamburg: Felix Meiner Verlag, 1985. x + 448 S. DM 140.BERNARD BOLZANO, Wissenschaftslehre, Sects. 1-45. Edited and introduction Jan Berg. Stuttgart-Bad Cannstatt: Friedrich Fromman, 1985. 269 pp. No price stated.MAX H. FISCH, C. J. W. KLOESEL, E. C. MOORE and DON D.ROBERTS, LYNN A. ZIEGLER, Writings of Charles S. Peirce: a chronological edition. Bloomington, Indiana: Indiana University Press. Vol. I 1857-1866. 1982. xxxv + 698 pp. $32.50. Vo l. I1 1867-1871. 1984. xlviii + 649 pp. with introductory essays by Max H. Fisch, C. F. Delaney and Daniel D. -Merrill. $35.00.ALFRED TARSKI, Logic, semantics, metamathematics. Translated by J. H. Woodger. Second edition, edited and introduced by John Corcoran. Philadelphia: Hackett, 1983, xxx+ 506 pp. $50.00/£37.50 ; $29.50/&27.50.J. MITTELSTRASS, Enzyklopadie Philosophie und Wissenschaftstheorie, Bd.2: H-0. Mannheim, Wien, Zurich: Bibliographisches Institut, 1984. 1105 pp. DM 156.LOGIC AND MATHEMATICSA. GROTE, Anzahl, Zahl und Menge. Die phanomenologische Grundlagen der Arithmetik. Hamburg: Meiner, 1983. vii + 143 pp. DM 36.VICTOR LOWE, Alfred North Whitehead: the man and his work. Volume 1: 1861-1910. Baltimore and London: The Johns Hopkins University Press, 1985. xi+ 351 pp. $27.50/£26.40.MURIEL SELTMAN and PETER SELTMAN, Piaget's logic: a critique of genetic epistemology. London, Boston and Sydney: George Allen and Unwin, 1985. ix+ 353 pp. £30.00.MORRIS KLINE, Mathemafics: the loss of certainty. New York: Oxford University Press, 1980. vi + 366 pp. $19.95.RACHEL WALLACE GARDEN, Modern logic and quantum mechanics. Bristol: Adam Hilger, 1983. xii+ 178 pp. £18.00.LOGIC AND LANGUAGEH. LEBLANC, E. MENDELSON and A. ORESTEIN, Logic, language, and mathematics. Dordrecht and Boston: D. Reidel Publishing Company, 1984, 282 pp. Dfl.90/$34.50.R. M. MARTIN, Mind, modality, meaning and method. Albany, New York: State University of New York Press, 1983. xiv+ 225 pp. $44.50 /$16.95.HERBERT HOCHBERG, Logic, ontology, and language-essays on truth and reality. Miinchen and Wein: Philosophia Verlag, 1984. 448 pp., $74.00.

In recent years, speech-act theory has mooted the possibility that one utterance can signify a number of different things. This pluralist conception of signification lies at the heart of Thomas Bradwardine’s solution to the insolubles, logical puzzles such as the semantic paradoxes, presented in Oxford in the early 1320s. His leading assumption was that signification is closed under consequence, that is, that a proposition signifies everything which follows from what it signifies. Then any proposition signifying its own falsity, he showed, also signifies its own truth and so, since it signifies things which cannot both obtain, it is simply false. Bradwardine himself, and his contemporaries, did not elaborate this pluralist theory, or say much in its defence. It can be shown to accord closely, however, with the prevailing conception of logical consequence in England in the fourteenth century. Recent pluralist theories of signification, such as Grice’s, also endorse Bradwardine’s closure postulate as a plausible constraint on signification, and so his analysis of the semantic paradoxes is seen to be both well-grounded and plausible.

The correspondence theory of truth has experienced something of a revival recently in the form of the Truthmaker Axiom: whatever is true, something makes it true. We consider various postulates which have been proposed to characterize truthmaking, in particular, the Disjunction Thesis (DT), that whatever makes a disjunction true must make one or other disjunct true. In conjunction with certain other assumptions, DT leads to triviality. We show that there are elaborations of truthmaking on which DT holds (which must therefore take steps to avoid the triviality); but that there are more plausible accounts of truthmaking on which DT fails.

In this article, we discuss the notion of merely confused supposition as it arose in the medieval theory of suppositio personalis. The context of our analysis is our formalization of William of Ockham's theory of supposition sketched in Mind 86 (1977), 109-13. The present paper is, however, self-contained, although we assume a basic acquaintance with supposition theory. The detailed aims of the paper are: to look at the tasks that supposition theory took on itself and to use our formalization to relate them to more modern ideas; to explain the notion of merely confused supposition and to defend it against certain criticisms; and to discuss two issues closely related to the idea of merely confused supposition which we could not broach in a shorter article: the mode of supposition of terms in intensional contexts, and the possible existence of a fourth mode, often called suppositio copulatim

Michael Dummett and Dag Prawitz have argued that a constructivist theory of meaning depends on explicating the meaning of logical constants in terms of the theory of valid inference, imposing a constraint of harmony on acceptable connectives. They argue further that classical logic, in particular, classical negation, breaks these constraints, so that classical negation, if a cogent notion at all, has a meaning going beyond what can be exhibited in its inferential use. I argue that Dummett gives a mistaken elaboration of the notion of harmony, an idea stemming from a remark of Gerhard Gentzen's. The introduction-rules are autonomous if they are taken fully to specify the meaning of the logical constants, and the rules are harmonious if the elimination-rule draws its conclusion from just the grounds stated in the introduction-rule. The key to harmony in classical logic then lies in strengthening the theory of the conditional so that the positive logic contains the full classical theory of the conditional. This is achieved by allowing parametric formulae in the natural deduction proofs, a form of multiple-conclusion logic

Frege’s project has been characterized as an attempt to formulate a complete system of logic adequate to characterize mathematical theories such as arithmetic and set theory. As such, it was seen to fail by Gödel’s incompleteness theorem of 1931. It is argued, however, that this is to impose a later interpretation on the word ‘complete’ it is clear from Dedekind’s writings that at least as good as interpretation of completeness is categoricity. Whereas few interesting first-order mathematical theories are categorical or complete, there are logical extensions of these theories into second-order and by the addition of generalized quantifiers which are categorical. Frege’s project really found success through Gödel’s completeness theorem of 1930 and the subsequent development of first- and higher-order model theory

What binds the constituents of a state of affairs together and provides unity to the fact they constitute? I argue that the fact that they are related is basic and fundamental. This is the thesis of Factualism: the world is a world of facts. I draw three corollaries: first, that the Identity of truth is mistaken, in conflating what represents (the proposition) with what is represented (the fact). Secondly, a popular interpretation of Wittgenstein's Tractatus, due to Steinus, whereby false propositions are taken to picture non-existent state of affairs, cannot be right. For Wittgenstein, propositions had two poles, and a proposition and its negation picture the same fact. Finally, the metaphysics of modal realism must be wrong, for there are no non-actual states of affairs to constitute any world other than the actual world. (Published Online October 13 2005).

t is often suggested that truth-preservation is insufficient for logical consequence, and that consequence needs to satisfy a further condition of relevance. Premises and conclusion in a valid consequence must be relevant to one another, and truth-preservation is too coarse-grained a notion to guarantee that. Thus logical consequence is the intersection of truth-preservation and relevance. This situation has the absurd consequence that one might concede that the conclusion of an argument was true (since the argument had true premises and was truth-preserving); yet should refuse to infer the conclusion from the premises, in the absence of demonstration of the relevance of the premises to the conclusion. The error lies in giving insufficient attention to the notion of truth-preservation. Relevance is no separable ingredient in the analysis of logical consequence, but a necessary condition of it. What we show is that if an argument really is truth-preserving, then that in itself is enough to show that the premises are (logically) relevant to the conclusion.

The recovery of Aristotle’s logic during the twelfth century was a great stimulus to medieval thinkers. Among their own theories developed to explain Aristotle’s theories of valid and invalid reasoning was a theory of consequence, of what arguments were valid, and why. By the fourteenth century, two main lines of thought had developed, one at Oxford, the other at Paris. Both schools distinguished formal from material consequence, but in very different ways. In Buridan and his followers in Paris, formal consequence was that preserved under uniform substitution. In Oxford, in contrast, formal consequence included analytic consequences such as ‘If it’s a man, then it’s an animal’. Aristotle’s notion of syllogistic consequence was subsumed under the treatment of formal consequence. Buridan developed a general theory embracing the assertoric syllogism, the modal syllogism and syllogisms with oblique terms. The result was a thoroughly systematic and extensive treatment of logical theory and logical consequence which repays investigation.

Le logicien écossais Hugh MacColl est bien connu pour ses contributions innovantes aux logiques modales et non-classiques. Cependant, jusque-là, nous disposions de peu d’informations biographiques sur son cheminement académique et culturel, sa situation personnelle et professionnelle, et sa position au sein de la communauté scientifique de la période victorienne. Le présent article présente un certain nombre de découvertes récentes à ce sujet. The Scottish logician Hugh MacColl is well known for his innovative contributions to modal and non-classical logics. However, until now little biographical information has been available about his academic and cultural background, his personal and professional situation, and his position in the scientific community of the Victorian era. The present article reports on a number of recent findings.

Logical inferentialism claims that the meaning of the logical constants should be given, not model-theoretically, but by the rules of inference of a suitable calculus. It has been claimed that certain proof-theoretical systems, most particularly, labelled deductive systems for modal logic, are unsuitable, on the grounds that they are semantically polluted and suffer from an untoward intrusion of semantics into syntax. The charge is shown to be mistaken. It is argued on inferentialist grounds that labelled deductive systems are as syntactically pure as any formal system in which the rules define the meanings of the logical constants

Hartry Field's revised logic for the theory of truth in his new book, Saving Truth from Paradox , seeking to preserve Tarski's T-scheme, does not admit a full theory of negation. In response, Crispin Wright proposed that the negation of a proposition is the proposition saying that some proposition inconsistent with the first is true. For this to work, we have to show that this proposition is entailed by any proposition incompatible with the first, that is, that it is the weakest proposition incompatible with the proposition whose negation it should be. To show that his proposal gave a full intuitionist theory of negation, Wright appealed to two principles, about incompatibility and entailment, and using them Field formulated a paradox of validity (or more precisely, of inconsistency). The medieval mathematician, theologian and logician, Thomas Bradwardine, writing in the fourteenth century, proposed a solution to the paradoxes of truth which does not require any revision of logic. The key principle behind Bradwardine's solution is a pluralist doctrine of meaning, or signification, that propositions can mean more than they explicitly say. In particular, he proposed that signification is closed under entailment. In light of this, Bradwardine revised the truth-rules, in particular, refining the T-scheme, so that a proposition is true only if everything that it signifies obtains. Thereby, he was able to show that any proposition which signifies that it itself is false, also signifies that it is true, and consequently is false and not true. I show that Bradwardine's solution is also able to deal with Field's paradox and others of a similar nature. Hence Field's logical revisions are unnecessary to save truth from paradox