A study in philosophical logic of the meaning of 'true'. Dr Williams demonstrates the shortcomings of various analyses which interpret 'true' as a predicate or truth as a relational property, and clears up a number of important points about propositions, quantification, definite descriptions and correspondence. This 'deflationary metaphysics' is interwoven with a positive theory of his own, which seeks to develop ideas about the late Arthur Prior. The work is marked throughout by great clarity, precision and thoroughness.

A study in philosophical logic of the meaning of 'true'. Dr Williams demonstrates the shortcomings of various analyses which interpret 'true' as a predicate or truth as a relational property, and clears up a number of important points about propositions, quantification, definite descriptions and correspondence. This 'deflationary metaphysics' is interwoven with a positive theory of his own, which seeks to develop ideas about the late Arthur Prior. The work is marked throughout by great clarity, precision and thoroughness.

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the first (...) two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...) emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

The first solid bit of argumentation you get in Plato's Phaedo goes something like this: Whatever comes to be, comes to be from its opposite . If at a certain time t a given thing a begins to be F , before that time t it must have been non- F . Wherever a pair of predicates, F and G , are genuine contradictories; where, that is, they stand to each other in the same relation as F stands in to (...) non- F ; it is necessarily true that if a began to be F at t before then a was G . The only trouble comes from the difficulty of finding substitutes for F and G that people will allow to be genuine contradictories. It the butter began to be soft at four o'clock, we may suggest, before four it was hard. A tiresome opponent will retort that there is a state in which butter cannot properly be called either hard or soft. We try again: If Ann began to be asleep at eight, before eight she was awake; if my shirt became dirty on Tuesday, before Tuesday it was clean; if Bonzo died last week, before last week he was alive. And when the advocate of the borderline state reminds us of the various twilight areas of consciousness or cleanliness, we are reduced to legislation: “asleep” shall henceforth apply to every mental state short of complete wakefulness, “alive” to every condition of the body before the onset of putrefaction, “clean” to every shirt incapable of producing a certain measurable discoloration in the water in which it is washed. “Let F and G be contradictories”, we still guardedly maintain: “then if a comes to be F at time t , before time t a was G ”. (shrink)

The first solid bit of argumentation you get in Plato's Phaedo goes something like this: Whatever comes to be, comes to be from its opposite. If at a certain time t a given thing a begins to be F, before that time t it must have been non-F. Wherever a pair of predicates, F and G, are genuine contradictories; where, that is, they stand to each other in the same relation as F stands in to non-F; it is necessarily true (...) that if a began to be F at t before then a was G. The only trouble comes from the difficulty of finding substitutes for F and G that people will allow to be genuine contradictories. It the butter began to be soft at four o'clock, we may suggest, before four it was hard. A tiresome opponent will retort that there is a state in which butter cannot properly be called either hard or soft. We try again: If Ann began to be asleep at eight, before eight she was awake; if my shirt became dirty on Tuesday, before Tuesday it was clean; if Bonzo died last week, before last week he was alive. And when the advocate of the borderline state reminds us of the various twilight areas of consciousness or cleanliness, we are reduced to legislation: “asleep” shall henceforth apply to every mental state short of complete wakefulness, “alive” to every condition of the body before the onset of putrefaction, “clean” to every shirt incapable of producing a certain measurable discoloration in the water in which it is washed. “Let F and G be contradictories”, we still guardedly maintain: “then if a comes to be F at time t, before time t a was G”. (shrink)

C. J. F. Williams; VI*—Is Identity a Relation?, Proceedings of the Aristotelian Society, Volume 80, Issue 1, 1 June 1980, Pages 81–100, https://doi.org/10.1093/.

We present a pole expansion for the propagators in the framework of normalized quantum electrodynamics and compare it with the more canonical results from S-matrix theory.

Kaplan claims that (1) ‘I am here now’, though analytic, is not a necessary truth. But this sentence is not a proposition, in a sense of proposition in which some, but not all, sentences are propositions. Since it is not a proposition, it is not true, and consequently not analytic. It is in fact a fragment of a proposition, the same fragment as ‘he was there then’ in (2) ‘CJFW said in Oxford on 23 September 1991 that he was there (...) then’. Sentences containing indexicals in general owe their sense to the corresponding fragments of sentences containing ‘quasi‐indexicals’(‘then’, for example, is the quasi‐indexical to ‘now’ as indexical). Someone uttering (1) assertively will thereby make a proposition like (2) true. (2) entails (3) ‘CJFW said in Oxford on 23 September 1993 that CJFW was in Oxford on 23 September 1991′. So by uttering (1) in the appropriate circumstances I made it true that I had asserted the proposition (4) ‘CJFW was in Oxford on 23 September 1991′. What is analytic and necessarily true is the proposition ‘If (3) then (4)’. (shrink)

In this article I shall argue for an interpretation of Odyssey 19.393–466 as a flash-back taking place in the mind of Eurykleia at the moment she recognises Odysseus' scar. That Eurykleia somehow forms the connection between main story and digression has been suggested before, but so far other interpretations have been defended with more fervour. Most famous of these interpretations is the one given by E. Auerbach in the first chapter of his Mimesis. He had chosen 19.393–466 to illustrate his (...) thesis that in Homer everything is ‘fully externalized’ and that there is no background, only a ‘uniformly illuminated’ foreground. According to Auerbach the digression on the scar stands in complete isolation to its context. It is meant to ‘relax the tension’, to make the hearer/reader ‘forget what had just taken place during the footwashing’, and although it might have been presented as a recollection of Odysseus , this ‘subjectivisticperspectivistic procedure, creating a foreground and background’ was not chosen, being ‘entirely foreign to the Homeric style’. Some twenty years later this interpretation was challenged by A. Köhnken, who, however, stuck to the idea that the digression is not told from the restricted perspective of one of the characters but from the perspective of the omniscient narrator; he claims that foreground and background are marked as such through a difference in narrative style: ‘berichtende Erzählung’ for the digression itself and ‘szenische Darstellung’ for the context. I disagree with both points. (shrink)

In his celebrated article on the narrative technique of Odysseus' Wanderings W. Suerbaum concludes that this character's narration is not essentially different from that of the primary narrator of the Odyssey . Even though Odysseus is a first-person narrator and hence is subject to certain restrictions, these are almost completely counterbalanced by his ex eventu knowledge. For example, he can even report a conversation which took place on Olympus , because it was afterwards reported to him by Calypso, who heard (...) it from Hermes . He can also tell what went on in the minds of his companions , because they later told him what they had felt . Suerbaum's conclusion is shared by M. Fusillo and A. Heubeck, p. 11. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...) emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

This collection of essays, addresses, and one interview come from the years 1966-73 and cover a wide spectrum of interest, dealing with such general topics as 'The Absence of God in Modern Culture' and 'The Future of Christianity.'.

Bertrand de Jouvenel was a renowned French philosopher and political economist. In Sovereignty he turned his attention to the relationship between the distribution of power and the creation of an ethical society. More specifically, he was concerned with the potential confusion of the body politic resulting from the development of increasingly dynamic and nebulous social conditions. The text is written in an exploratory fashion, reflecting the authorial perception of an ambiguity in modern political structures. This translated Cambridge edition, which was (...) first published in 1957, was derived from a 1955 French original. It constitutes an important contribution to post-war political theory that will remain of value to anyone with an interest in questions relating to political structures and the nature of authority. (shrink)