Stephen Read

Inferentialism claims that the rules for the use of an expression express its meaning without any need to invoke meanings or denotations for them. Logical inferentialism endorses inferentialism specically for the logical constants. Harmonic inferentialism, as the term is introduced here, usually but not necessarily a subbranch of logical inferentialism, follows Gentzen in proposing that it is the introduction-rules whch give expressions their meaning and the elimination-rules should accord harmoniously with the meaning so given. It is proposed here that the logical expressions are those which can be given schematic rules that lie in a specific sort of harmony, general-elimination harmony, resulting from applying a certain operation, the ge-procedure, to produce ge-rules in accord with the meaning defined by the I-rules. Griffiths claims that identity cannot be given such rules, concluding that logical inferentialists are committed to ruling identity a non-logical expression. It is shown that the schematic rules for identity given in Read, slightly amended, are indeed ge-harmonious, so confirming that identity is a logical notion.

Much thinking about conditionals over the last twenty years has been stimulated by the so-called 'Ramsey test'. Ramsey's idea was simple, but appealing. One should believe a conditional, 'if A then B' if one would come to believe B if one were to add A to one's stock of beliefs. The Ramsey test does not justify treating conditionals with true antecedent and consequent as true, and accepting it does not require one to accept either the similarity or probability theories of the conditional. It certainly does not justify denying truth-values altogether to conditionals. What it can do, is show how the truth- condition for conditionals should be articulated in an intensional logic, indeed, in one with a well-developed and well-tested semantics and proof-theory: the logic of relevant implication. The Ramsey test is nght, when rightly understood.

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.

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..

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

Kretzmann and Spade were led by Richard Kilvington’s proposed revisions to the rules of obligations in his discussion of the 47th sophism in his Sophismata to claim that the purpose of obligational disputations was the same as that of counterfactual reasoning. Angel d’Ors challenged this interpretation, realising that the reason for Kilvington’s revision was precisely that he found the art of obligation unsuited to the kind of reasoning which lay at the heart of the sophismatic argument. In his criticism, Kilvington focussed on a technique used by Walter Burley to force a respondent to grant an arbitrary falsehood and similar to Lewis and Langford’s famous defence of ex impossibili quodlibet. Kilvington observes that just as in obligational disputation, one may be obliged to grant a false proposition and deny a true one, so in counterfactual reasoning one may be obliged to doubt a proposition whose truth or falsity one knows, on pain of contradiction.

What makes necessary truths true? I argue that all truth supervenes on how things are, and that necessary truths are no exception. What makes them true are proofs. But if so, the notion of proof needs to be generalized to include verification-transcendent proofs, proofs whose correctness exceeds our ability to verify it. It is incumbent on me, therefore, to show that arguments, such as Dummett's, that verification- truth is not compatible with the theory of meaning, are mistaken. The answer is that what we can conceive and construct far outstrips our actual abilities. I conclude by proposing a proof-theoretic account of modality, rejecting a claim of Armstrong's that modality can reside in non-modal truthmakers.

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.

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