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.

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

In his recent study, Concepts, Fodor identifies five nonnegotiable constraints on any theory of concepts. These theses were all shared by the standard medieval theories of concepts. However, those theories were cognitivist, in contrast with Fodor’s: concepts are definitions, a form of natural knowledge. The medieval theories were formed under two influences, from Aristotle by way of Boethius, and from Augustine. The tension between them resulted in the Ockhamist notion of a natural language, concepts as signs. Thus conventional signs, spoken and written, signify things in the world by the mediation of concepts which themselves form a language of thought, signifying those things naturally by their similarity. Indeed, later thinkers realised that everything signifies itself and what is like it naturally in a broad sense by means of the concept of its natural likeness

One of the manuscripts of Buridan’s Summulae contains three figures, each in the form of an octagon. At each node of each octagon there are nine propositions. Buridan uses the figures to illustrate his doctrine of the syllogism, revising Aristotle's theory of the modal syllogism and adding theories of syllogisms with propositions containing oblique terms (such as ‘man’s donkey’) and with ‘propositions of non-normal construction’ (where the predicate precedes the copula). O-propositions of non-normal construction (i.e., ‘Some S (some) P is not’) allow Buridan to extend and systematize the theory of the assertoric (i.e., non-modal) syllogism. Buridan points to a revealing analogy between the three octagons. To understand their importance we need to rehearse the medieval theories of signification, supposition, truth and consequence.

_ Source: _Page Count 21 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.

I. SUPPOSITION AND SIGNIFICATIONIn an insightful article on the medieval theory of supposition, Elizabeth Karger noted a remarkable development in the characterization of the material mode of supposition between William of Ockham and his contemporaries in the early fourteenth century and Paul of Venice and others at the turn of the fifteenth century.1. E. Karger, “La Supposition Materielle comme Supposition Significative: Paul de Venise, Paul de Pergula,” in A. Maierú, ed., English Logic in Italy in the 14th and 15th Centuries (Naples, 1982), pp. 331–41. For William, material supposition is explicitly ‘non-significative’, while for Paul, every mode of supposition is a kind of signification.2. Paul of Venice, Logica Magna (Tractatus de Suppositionibus), ed. and trans. A. Perreiah (St. Bonaventure, 1971), p. 4: “nam omnis suppositio est significatio.” In particular, we can set these definitions in opposition.

Thomas Bradwardine makes much of the fact that his solution to the insolubles is in accordance with Aristotle's diagnosis of the fallacy in the Liar paradox as that of secundum quid et simpliciter. Paul Spade, however, claims that this invocation of Aristotle by Bradwardine is purely "honorary" in order to confer specious respectability on his analysis and give it a spurious weight of authority. Our answer to Spade follows Bradwardine's response to the problem of revenge: any proposition saying of itself that it is false says more than does Bradwardine's proposition saying of it that it is false, and so follows from that other proposition only in respect of part of what it says, and not simpliciter.

MEDIEVAL LOGICCARLOS A. DUFOUR, Die Lehre der Proprietates Terminorum. Sinn und Referenz in mittelalterlicher Logik. München, Hamden, Wien: Philosophia, 1989. 312 pp. 148 DM.NORMAN KRETZMANN and BARBARA ENSIGN KRETZMANN The Sophismata of Richard Kilvington. Oxford: Published for the British Academy by Oxford University Press, 1990. xx + 156 pp. £27.50.LOGIC AND MATHEMATICSSOULEYMANE BACHIR DIAGNE, Boole. Paris: Editions Belin, 1989. 262pp. 75 Ffr.M.-M. TOEPELL, Über die Entstehung von David Hilberts “Grundlagen der Geometrie”. Göttingen: Vandenhoeck und Ruprecht, 1986. vii + 293 pp. 82 DM.VOLKER PECKHAUS, Hilbertprogramm und Kritische Philosophie. Das Göttinger Model1 interdisziplinarer Zusammenärbeit zwischen Mathematik und Philosophie. Gottingen: Vandenhoeck und Ruprecht, 1990. vi + 291 pp. 78 DM.E. WELTI, Die Philosophie des Strikten Finitismus, Entwicklungstheoretische und mathematische Untersuchungen iiber Unendlichkeitsbegriffe in Ideengeschichte und Mathematik, Bern, Frankfurt am Main und New York: Peter Lang, 1986. xxix + 652pp. $79.90.Philosophy of logicMARK A. NOTTURNO, Perspectives on psychlogism. Leiden, New York, Copenhagen and Cologne: E. J. Brill, 1989. viii + 504 pp. 225 Dfl/$112.50.ROBERT N. MCLAUGHLIN, On the logic of ordinary conditionals. Albany: State University of New York Press, 1990. xvii + 202 pp. $54.50 /$17.95.JAAKKO HINTIKKA and MERRILL HINTIKKA, The logic of epistemology and the epistemology of logic: selected essays. Dordrecht, Boston and London: Kluwer Academic Publishers, 1989.J. NORMAN and R. SYLVAN, Directions in relevant logic. Foreword by N. D. Belnap. Dordrecht, Boston and London: Kluwer Academic Publishers, 1989. xii + 453 pp. £72.00.LOGIC AND LANGUAGEC. J. F. WILLIAMS, What is identity? Oxford: Clarendon Press, 1989. xx + 207 pp. £25.00.GREGORY MCCULLOCH, The game of the name. Oxford: Oxford University Press, 1989. xvi + 320pp. £30.00, £9.95.GRAEME FORBES, Languages of possibility. Oxford: Basil Blackwell, 1989. x + 181 pp. £27.50.