The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL ew of the substructural logic FL ew. The main result of Part I of this series [41] shows that the equivalent variety semantics of N and the equivalent variety semantics of NFL ew are term equivalent. In this paper, the term equivalence result of Part I [41] is lifted to the setting of deductive (...) systems to establish the definitional equivalence of the logics N and NFL ew. It follows from the definitional equivalence of these systems that constructive logic with strong negation is a substructural logic. (shrink)

Розкрито сутність поняття «рейтинг». Доведено значущість рейтингової оцінки для суб’єктів фінансового ринку, зокрема для страхових компаній, потенційних страхувальників, інвесторів та кредиторів.

We consider the class of pointed varieties of algebras having a lattice term reduct and we show that each such variety gives rise in a natural way, and according to a regular pattern, to at least three interesting logics. Although the mentioned class includes several logically and algebraically significant examples (e.g. Boolean algebras, MV algebras, Boolean algebras with operators, residuated lattices and their subvarieties, algebras from quantum logic or from depth relevant logic), we consider here in greater detail Abelian ℓ-groups, (...) where such logics respectively correspond to: i) Meyer and Slaney’s Abelian logic [31]; ii) Galli et al.’s logic of equilibrium [21]; iii) a new logic of “preservation of truth degrees”. (shrink)

"Williams's masterful translation satisfies (at last!) a long-standing need. There are lots of good translations of Augustine's great work, but until now we have been forced to choose between those that strive to replicate in English something of the majesty and beauty of Augustine's Latin style and those that opt instead to convey the careful precision of his philosophical terminology and argumentation. Finally, Williams has succeeded in capturing both sides of Augustine's mind in a richly evocative, impeccably reliable, elegantly readable (...) presentation of one of the most impressive achievements in Western thought--Augustine's Confessions." --Scott MacDonald, Professor of Philosophy and Norma K. Regan Professor in Christian Studies, Cornell University. (shrink)

The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL ew of the substructural logic FL ew . In this paper, it is shown that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL ew (namely, a certain variety of FL ew -algebras) are term equivalent. This answers a longstanding question of Nelson [30]. (...) Extensive use is made of the automated theorem-prover Prover9 in order to establish the result. The main result of this paper is exploited in Part II of this series [40] to show that the deductive systems N and NFL ew are definitionally equivalent, and hence that constructive logic with strong negation is a substructural logic over FL ew. (shrink)

This book offers a critical introduction to the work of American philosopher D. G. Leahy (1937-2014). Leahy's fundamental thinking can be characterized as an absolute creativity in which all creating is 'live' -- a happening occurring now that manifests a supersaturated polyontological actuality that is essentially created by the logic that characterizes it. Leahy leaves behind the categorial presuppositions of modern thought, eclipsing both Cartesian and Hegelian subjectivities and introducing instead an essentially new form of thinking founded in a nondual (...) logic of creation. The new thinking delineates the absolute unicity of existence as a creative interactivity beyond all traditional dichotomies (such as one vs. many, unity vs. plurality, identity vs. change): a fully "digitized" actuality that is nothing but newness, which inherently implies nothing but change. Through this new form of thinking, change itself is revealed to be the very essence of reality and mind. Any reader looking for a quantum leap beyond the thrall of modern and postmodern fixations is invited to hear and apprehend this new thinking that refuses to be conditioned by paradigms, categories, species, genera, walls, bridges, boundaries, or abstractions: an essentially free thinking that embodies creative novelty itself. (shrink)

This article answers two questions (posed in the literature), each concerning the guaranteed existence of proofs free of double negation. A proof is free of double negation if none of its deduced steps contains a term of the formn(n(t)) for some term t, where n denotes negation. The first question asks for conditions on the hypotheses that, if satisfied, guarantee the existence of a double-negation-free proof when the conclusion is free of double negation. The second question asks about the existence (...) of an axiom system for classical propositional calculus whose use, for theorems with a conclusion free of double negation, guarantees the existence of a double-negation-free proof. After giving conditions that answer the first question, we answer the second question by focusing on the Lukasiewicz three-axiom system. We then extend our studies to infinite-valued sentential calculus and to intuitionistic logic and generalize the notion of being double-negation free. The double-negation proofs of interest rely exclusively on the inference rule condensed detachment, a rule that combines modus ponens with an appropriately general rule of substitution. The automated reasoning program Otter played an indispensable role in this study. (shrink)

A discriminator logic is the 1 -assertional logic of a discriminator variety V having two constant terms 0 and 1 such that V ⊨ 0 1 iff every member of V is trivial. Examples of such logics abound in the literature. The main result of this research announcement asserts that a certain non-Fregean deductive system SBPC, which closely resembles the classical propositional calculus, is canonical for the class of discriminator logics in the sense that any discriminator logic S can be (...) presented as an axiomatic extension of SBPC by a set of extensional logical connectives taken from the language of S. The results outlined in this research announcement are extended to several generalisations of the class of discriminator logics in the main work. (shrink)

In this first paperback edition, a new introduction by Tom Burke establishes the ongoing importance of Sleeper's analysis of the integrity of Dewey's work and ...

Political liberals ask citizens not to appeal to certain considerations, including religious and philosophical convictions, in political deliberation. We argue that political liberals must include a demanding requirement of intellectual modesty in their ideal of citizenship in order to motivate this deliberative restraint. The requirement calls on each citizen to believe that the best reasoners disagree about the considerations that she is barred from appealing to. Along the way, we clarify how requirements of intellectual modesty relate to moral reasons for (...) deliberative restraint. And we argue against attempts to weaken our requirement of intellectual modesty by emphasizing those moral reasons. (shrink)

Locke is the first English philosopher to be considered in this series, and that fact of itself is worthy of attention. Philosophy, of course, like science, knows no frontiers and no national boundaries. Yet it is true to say that Locke’s contribution to philosophy is typically and peculiarly English. His moderation, his emphasis upon experience, his tolerant spirit of compromise, his dislike of mystical extravagance and of metaphysical speculation, even that elusive quality of his which people call his “common sense”, (...) are English traits. His very defects, illogicality leading to inconsistency and an awkward disorderliness of thought so abhorrent to the. (shrink)

The Nature of God explores a perennial problem in the philosophy of religion.

This book is not a study of Plato's philosophy, but a contribution to the literary interpretation of the dialogues, through analysis of their formal structure, ...

The Hellenistic philosophers and schools of philosophy are emerging from the shadow of Plato and Aristotle and are increasingly studied for their intrinsic philosophical value. They are not only interesting in their own right, but also form the intellectual background of the late Roman Republic. This study gives a comprehensive and readable account of the principal doctrines of the Stoics, Epicureans and various sceptical traditions from the death of Alexander the Great in 323 B.C. to around 200 A.D. Discussions are (...) arranged topically in order to address underlying issues and to make clear what the different schools have in common and how they differ. At the same time the coherence of each system as a whole is emphasized. (shrink)

Overdenkingen in proza en poëzie over filosofische vraagstukken door de in ongenade gevallen Romeinse ex-consul (480-524).