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)

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)

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)

Kant asserts that we cannot represent to ourselves the non-existence of space. In his discussion of the Ontological Argument he maintains that there is nothing whose non-existence is inconceivable. He thus seems to contradict himself. If the non-existence of space is unthinkable, so is the non-existence of a part of space — a place. Indicating a particular place, we might say "There are no objects there", but it would be nonsense to say "There doesn't exist". We can say, as Aristotle (...) saw, "There is a place where there was water and where there is now air"; but to do so is to bind an adverbial variable with a quantifier, not to attach "exists" to the name of a place. To assert of a place, or of space, that it exists or that it does not exist would be nonsense, and the unthinkable in that sense is not something whose negation is, as Kant thought, a necessary truth. (shrink)

The main problem of the Spanish local finance system derives from the existence of two opposite models: LOFCA model versus Floral system. As a result of this opposition, the Spanish system has moved some distance away from the theoretical principles of sound fiscal federalism. The analysis carried out in the article points out clearly the need to improve the fiscal mechanisms of responsibility and financial autonomy and to introduce a system of interjurisdictional responsibility which should palliate the defects detected in (...) the actual system in order to maximise the political and economic advantages of an authentic fiscal decentralisation.Le problème majeur du système espagnol de finances locales réside dans l’existence de deux modèles opposés: le modèle LOFCA et le système Floral. En raison de cette opposition, le système espagnol s’est considérablement écarté des principes affirmés par la théorie d’un authentique fédéralisme fiscal. L’analyse conduite dans l’article met en évidence la nécessité d’améliorer les mécanismes fiscaux de responsabilité et d’autonomie financière des collectivités locales espagnoles en introduisant un système de responsabilité inter-juridictionnelle capable d’éliminer les incohérences du système ; ce qui permettra de tirer pleinement partie des avantages politiques et économiques inhérents à la décentralisation fiscale. (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)

This collection of essays delineates the history of the rather disparate intellectual tradition usually labeled as "Platonic" or "Neoplatonic". In chronological order, the book covers the most eminent philosophic schools of thought within that tradition. The most important terms of the Platonic tradition are studied together with a discussion of their semantic implications, the philosophical and theological claims associated with the terms, the sources that furnish the terms, and the intellectual traditions aligned with or opposed to them. The contributors thereby (...) provide a vivid intellectual map of the Middle Ages and the Early Modern period. Contributions are written in English or German. (shrink)