One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley-Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing (...) a general conception of conditionality that may unify the three given conceptions. (shrink)

Relevant Logics and their Rivals, Volume II extends the material of the first volume in two ways.

Richard Sylvan died suddenly at the age of 60, when he had just completed this major text. But though this volume is the mature expression of one of our foremost modern philosophers, it remains, like all his work, pioneering, eclectic and controversial. Sylvan's theory of 'plurallism', the culmination of his life's work, is the subject of this important text. In his own characteristically provocative words, 'There is not merely a plurality of correct theories and more or less satisfactory worldviews: there (...) is a corresponding plurality of actual worlds. Plurality penetrates deeper in full plurallism than linguistic surface or than conceptual or theoretical structure, to worlds...There is no single fact of the matter, there are facts and matters.'. (shrink)

Da Costa's C systems are surveyed and motivated, and significant failings of the systems are indicated. Variations are then made on these systems in an attempt to surmount their defects and limitations. The main system to emerge from this effort, system CC , is investigated in some detail, and dual-intuitionistic semantical analyses are developed for it and surrounding systems. These semantics are then adapted for the original C systems, first in a rather unilluminating relational fashion, subsequently in a more illuminating (...) way through the introduction of impossible situations where and and or change roles. Finally other attempts to break out of impasses for the original and expanded C systems, by going inside them, are looked at, and further research directions suggested. (shrink)

The problems of the meaning and function of negation are disentangled from ontological issues with which they have been long entangled. The question of the function of negation is the crucial issue separating relevant and paraconsistent logics from classical theories. The function is illuminated by considering the inferential role of contradictions, contradiction being parasitic on negation. Three basic modelings emerge: a cancellation model, which leads towards connexivism, an explosion model, appropriate to classical and intuitionistic theories, and a constraint model, which (...) includes relevant theories. These three modelings have been seriously confused in the modern literature: untangling them helps motivate the main themes advanced concerning traditional negation and natural negation. Firstly, the dominant traditional view, except around scholastic times when the explosion view was in ascendency, has been the cancellation view, so that the mainstream negation of much of traditional logic is distinctively nonclassical. Secondly, the primary negation determinable of natural negation is ·relevant negation. In order to picture relevant negation the traditional idea of negation as otherthanness is progressive) refined, to nonexclusive restricted otherthanness. Several pictures result, a reversal picture, a debate model, a record cabinet (or files of the universe) model which help explain relevant negation. Two appendices are attached, one on negation in Hegel and the Marxist tradition, the other on Wittgenstein's treatment of negation and contradiction. (shrink)

Da Costa's C systems are surveyed and motivated, and significant failings of the systems are indicated. Variations are then made on these systems in an attempt to surmount their defects and limitations. The main system to emerge from this effort, system $CC_{\omega}$ , is investigated in some detail, and "dual-intuitionistic" semantical analyses are developed for it and surrounding systems. These semantics are then adapted for the original C systems, first in a rather unilluminating relational fashion, subsequently in a more illuminating (...) way through the introduction of impossible situations where and and or change roles. Finally other attempts to break out of impasses for the original and expanded C systems, by going inside them, are looked at, and further research directions suggested. (shrink)

The proposed synthesis is set within general object-theory. The underlying idea of the synthesis is that the alternative worlds semantics — arrived at in pursuit of a universal semantics (a general semantics for all languages, including relevant ones) and, connectedly, as part of a comprehensive object-theory — be applied also in fundamental physics, most importantly to the matter of the origin, history, and physical features of the cosmos, but as well, again connectedly, elsewhere, in particular in the interpretation of quantum (...) theory. The universal semantics is a many worlds — a many nonexistent worlds — theory. The point of applying such an interpretation in cosmology also is explained by way of examples, concerning the understanding of the contingency of existence and the improbability of present arrangements. A resolution of the basic question, 'Why does anything at all exist?' is sketched, leading to the further question why the fundamental constants of physics have the particular surprisingly sensitive values they appear to have. Chauvinistic answers through anthropic principles are critically rejected, in favour of resolution by way of world selection. (shrink)

Richard Sylvan died in 1996, he had made contributions to many areas of philosophy, such as, relevant and paraconsistent logic, Meinongianism and metaphysics and environmental ethics. One of his trademarks was the taking up of unpopular views and defending them. To Richard Sylvan ideas were important, wether they were his or not. This is a book of ideas, based on a collection of work found after his death, a chance for readers to see his vision of his projects.

The proposed synthesis is set within general object-theory. The underlying idea of the synthesis is that the alternative worlds semantics — arrived at in pursuit of a universal semantics (a general semantics for all languages, including relevant ones) and, connectedly, as part of a comprehensive object-theory — be applied also in fundamental physics, most importantly to the matter of the origin, history, and physical features of the cosmos, but as well, again connectedly, elsewhere, in particular in the interpretation of quantum (...) theory. The universal semantics is a many worlds — a many nonexistent worlds — theory. The point of applying such an interpretation in cosmology also is explained by way of examples, concerning the understanding of the contingency of existence and the improbability of present arrangements. A resolution of the basic question, 'Why does anything at all exist?' is sketched, leading to the further question why the fundamental constants of physics have the particular surprisingly sensitive values they appear to have. Chauvinistic answers through anthropic principles are critically rejected, in favour of resolution by way of world selection. (shrink)

Whileprocess andaction are fundamental notions, in ubiquitous use, they lack satisfactory logical treatment in two critical respects: in analyses of the fundamentals themselves and in logical development. For what treatment they have so far received, under classical systematisation, leaves significant lacunae and induces much paradox. A relevant logical relocation, carried through in detail here, removes such problems, and provides solid ground-work for a satisfactory treatment.Firstly, as to fundamentals: processes should be explicated, so it is argued, as certain sorts of (time) (...) directed functions (from inputs to outputs); thus they can be represented through certain ordered pairs of relations. Significant logical structures they can enter into are investigated: notably, process lattice and coupled logics, and a generalized category theory (tolerating nonassociativity of composition). (shrink)

Curry claims that the positive paradox principle, ` A ⊃ in his elementary statement presentation, ‘is valid in any normal interpretation’ . By previous definition, ‘an interpretation of a system S is a normal interpretation just when the proposition A is true when and only when ` A’ . But his argument to normal validity is interestingly, and relevantly, invalid.

The proposed synthesis is set within general object-theory. The underlying idea of the synthesis is that the alternative worlds semantics — arrived at in pursuit of a universal semantics (a general semantics for all languages, including relevant ones) and, connectedly, as part of a comprehensive object-theory — be applied also in fundamental physics, most importantly to the matter of the origin, history, and physical features of the cosmos, but as well, again connectedly, elsewhere, in particular in the interpretation of quantum (...) theory. The universal semantics is a many worlds — a many nonexistent worlds — theory. The point of applying such an interpretation in cosmology also is explained by way of examples, concerning the understanding of the contingency of existence and the improbability of present arrangements. A resolution of the basic question, 'Why does anything at all exist?' is sketched, leading to the further question why the fundamental constants of physics have the particular surprisingly sensitive values they appear to have. Chauvinistic answers through anthropic principles are critically rejected, in favour of resolution by way of world selection. (shrink)

To leave matters in no doubt, we obligingly assert that the Russell class R, i.e. {x : x 6∈ x}, both belongs to itself and also does not belong to itself; in short, we assert R ∈ R & ∼ . To be quite explicit, we assert the contradiction r & ∼ r, where r abbreviates R ∈ R. Thus, in convenient symbols, `δ r & ∼ r, where δ is the group of dialethicians comprising Priest and Routley. Now Goldstein (...) asserts not, or not just, that we should not do what we have naughtily done, but that we cannot; it “is not that people should not assert contradictions, but that they cannot, even though they may purport to do so”. (shrink)

The proposed synthesis is set within general object-theory. The underlying idea of the synthesis is that the alternative worlds semantics — arrived at in pursuit of a universal semantics (a general semantics for all languages, including relevant ones) and, connectedly, as part of a comprehensive object-theory — be applied also in fundamental physics, most importantly to the matter of the origin, history, and physical features of the cosmos, but as well, again connectedly, elsewhere, in particular in the interpretation of quantum (...) theory. The universal semantics is a many worlds — a many nonexistent worlds — theory. The point of applying such an interpretation in cosmology also is explained by way of examples, concerning the understanding of the contingency of existence and the improbability of present arrangements. A resolution of the basic question, 'Why does anything at all exist?' is sketched, leading to the further question why the fundamental constants of physics have the particular surprisingly sensitive values they appear to have. Chauvinistic answers through anthropic principles are critically rejected, in favour of resolution by way of world selection. (shrink)

Re-explored are certain item-theory theses, major problem zones, and newer puzzles and, together therewith, prospects for liberalizing and pluralizing item-theory. Undoubtedly item-theory may be further liberalized, partly by further dissociation from object-theory and the restrictions object imposes, but primarily through substantial deregulation of the styles of characterisations permitted. Then almost anything goes; nonetheless what results is a sufficiently well-organised smooth-running sistological anarchism. Characterisation is dispersed through a federation of regions: only in old central city regions do the characterisation postulates of (...) older object-theory regularly hold; in the expanding suburbs characterisation by local assumption and postulation is a distinctive mode, while out in the country implicit intentional characterisation is a common mode. Put differently, there is a rich variety of sources yielding item specifications; only in places like the old city do structural descriptions of items enjoy formerly-imagined priority, but elsewhere alternative characterization principles may operate. However what holds in situations as a result of such local or regional characterisation may be far removed from what is actual. Characters may be only make-believe or suppositional presented character may differ from more genuine articles, and so on. Bringing the items involved into central evaluation markets, where truth value is assessed, may require preparation of the items, with pruning or regularisation of their properties. Here, at this semantical stage, full pluralization offers further freedom, that is pluralization of truth, with a plurality of actual worlds. A single assignment of truth, the truth at the actual world, is no longer de rigueur; a truth net may be differently cast, different assignments may be adopted, and a selection among alternatives perhaps made. Within this liberalized pluralized setting, resolutions of puzzles induced by certain problem-making items are ventured. (shrink)

The proposed synthesis is set within general object-theory. The underlying idea of the synthesis is that the alternative worlds semantics — arrived at in pursuit of a universal semantics (a general semantics for all languages, including relevant ones) and, connectedly, as part of a comprehensive object-theory — be applied also in fundamental physics, most importantly to the matter of the origin, history, and physical features of the cosmos, but as well, again connectedly, elsewhere, in particular in the interpretation of quantum (...) theory. The universal semantics is a many worlds — a many nonexistent worlds — theory. The point of applying such an interpretation in cosmology also is explained by way of examples, concerning the understanding of the contingency of existence and the improbability of present arrangements. A resolution of the basic question, 'Why does anything at all exist?' is sketched, leading to the further question why the fundamental constants of physics have the particular surprisingly sensitive values they appear to have. Chauvinistic answers through anthropic principles are critically rejected, in favour of resolution by way of world selection. (shrink)

Strictly speaking, intuitionistic logic is not a modal logic. There are, after all, no modal operators in the language. It is a subsystem of classical logic, not [like modal logic] an extension of it. But... (thus Fitting, p. 437, trying to justify inclusion of a large chapter on intuitionist logic in a book that is largely about modal logics).

In this article, extracted from his book Exploring Meinong's Jungle and Beyond, Sylvan argues that, contrary to widespread opinion, mathematics is not an extensional discipline and cannot be extensionalized without considerable damage. He argues that some of the insights of Meinong's theory of objects, and its modern development, item theory, should be applied to mathematics and that mathematical objects and structures should be treated as mind-independent, non-existent objects.

An appropriately unprejudiced logical investigation of causation as a type of implication relation is undertaken. The implication delineated is bounded syntactically. The developing argument then leads to a very natural process analysis, which demonstrably captures the established syntactical features. Next relevantly-based semantics for the resulting logical theory are adduced, and requisite adequacy results delivered. At the end of the tour, further improvements are pointed out, and the attractive terrain beyond present developments is glimpsed.