Many-valued logics are standardly defined by logical matrices. They are truth-functional. In this paper non truth-functional many-valued semantics are presented, in a philosophical and mathematical perspective.

Graham Priest presents an expanded edition of his exploration of the nature and limits of thought. Embracing contradiction and challenging traditional logic, he engages with issues across philosophical borders, from the historical to the modern, Eastern to Western, continental to analytic.

This is a philosophical investigation of the nature of the limits of thought. Drawing on recent developments in the field of logic, Graham Priest shows that the description of such limits leads to contradiction, and argues that these contradictions are in fact veridical. Beginning with an analysis of the way in which these limits arise in pre-Kantian philosophy, Priest goes on to illustrate how the nature of these limits was theorised by Kant and Hegel. He offers new interpretations of Berkeley's (...) master argument for idealism and Kant on the antimonies. He explores the paradoxes of self reference, and provides a unified account of the structure of such paradoxes. The book concludes by tracing the theme of the limits of thought in modern philosophy of language, including discussions of the ideas of Wittgenstein and Derrida. (shrink)

A number of important philosophical problems are problems in the overlap of logic and ontology. Both logic and ontology are diverse fields within philosophy, and partly because of this there is not one single philosophical problem about the relation between logic and ontology. In this survey article we will first discuss what different philosophical projects are carried out under the headings of "logic" and "ontology" and then we will look at several areas where logic and ontology overlap.

Our aim in this article is to attempt to discuss propagating organization of process, a poorly articulated union of matter, energy, work, constraints and that vexed concept, “information”, which unite in far from equilibrium living physical systems. Our hope is to stimulate discussions by philosophers of biology and biologists to further clarify the concepts we discuss here. We place our discussion in the broad context of a “general biology”, properties that might well be found in life anywhere in the cosmos, (...) freed from the specific examples of terrestrial life after 3.8 billion years of evolution. By placing the discussion in this wider, if still hypothetical, context, we also try to place in context some of the extant discussion of information as intimately related to DNA, RNA and protein transcription and translation processes. While characteristic of current terrestrial life, there are no compelling grounds to suppose the same mechanisms would be involved in any life form able to evolve by heritable variation and natural selection. In turn, this allows us to discuss at least briefly, the focus of much of the philosophy of biology on population genetics, which, of course, assumes DNA, RNA, proteins, and other features of terrestrial life. Presumably, evolution by natural selection—and perhaps self-organization—could occur on many worlds via different causal mechanisms. Here we seek a non-reductionist explanation for the synthesis, accumulation, and propagation of information, work, and constraint, which we hope will provide some insight into both the biotic and abiotic universe, in terms of both molecular self reproduction and the basic work energy cycle where work is the constrained release of energy into a few degrees of freedom. The typical requirement for work itself is to construct those very constraints on the release of energy that then constitute further work. Information creation, we argue, arises in two ways: first information as natural selection assembling the very constraints on the release of energy that then constitutes work and the propagation of organization. Second, information in a more extended sense is “semiotic”, that is about the world or internal state of the organism and requires appropriate response. The idea is to combine ideas from biology, physics, and computer science, to formulate explanatory hypotheses on how information can be captured and rendered in the expected physical manifestation, which can then participate in the propagation of the organization of process in the expected biological work cycles to create the diversity in our observable biosphere. Our conclusions, to date, of this enquiry suggest a foundation which views information as the construction of constraints, which, in their physical manifestation, partially underlie the processes of evolution to dynamically determine the fitness of organisms within the context of a biotic universe. (shrink)

The conjunction of process and reality is familiar from the original theory of A. N. Whitehead and the subsequent development of process philosophy and metaphysics by Nicholas Rescher. Classical logic, however, is either ignored or stated to be inappropriate to a discussion of process. In this paper, I will show that the value of a process view of reality can be enhanced by reference to a new, transconsistent logic of reality that is grounded in the physical properties of energy in (...) its various forms. These properties justify a principle of dynamic antagonism or opposition that explicates the phenomena of change at all levels of reality. It can be, accordingly, a preferred logic for understanding the dynamics of real processes. (shrink)

I. Le dualisme antagoniste et les exigences historiques de l'esprit. -- II. Essai d'une nouvelle théorie de la connaissance.