A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil (...) Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)

Some factors affecting marital distances have been studied in two Outer Hebridean islands, Harris (843 marriages) and Barra (444 marriages), over the period 1855-1990. In each island marital distances fell before 1900, but then rose to their greatest values after the 1950s. Fishermen generally married at the shortest distances and men in land-based occupations at the longest. The depression in the fishing industry during the 1880s and early 1890s was associated with reductions in marital distances, especially among fishermen. In the (...) different regions of Harris, marital distances were least in the south-east, where settlement was most dense, and greatest in the south-west where it was most sparse. (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)

L'influence decisive de Christian Wolff sur la pensee du XVIIIe siecle ne saurait plus etre mise en question aujourd'hui. Toutefois, les commentateurs ont longtemps pris a la lettre la critique kantienne du wolffianisme, assimilant la doctrine de Wolff a celle de ses disciples et mettant l'accent presque exclusivement sur la rupture accomplie par l'oeuvre de Kant. Cela a contribue a sous-estimer le role considerable joue par Wolff dans la constitution du criticisme. Les etudes rassemblees dans ce volume se proposent d'interroger (...) les multiples formes sous lesquelles la conception wolffienne a determine le Denkweg kantien et de preciser comment la philosophie de Kant s'articule a celle de Wolff. Ni simple opposition, ni continuite sans heurt, le rapport de Kant a Wolff est complexe et passionnant, et demande, aujourd'hui encore, des analyses prenant en compte l'ensemble des disciplines philosophiques. (shrink)

Herein we examine the theory and practical limits of designing a voluntary incentive scheme to protect endangered species on private land. We consider both an ay-ante scheme, in which a contract to the landholder depends only on what the landholder reports, and an ay-post scheme, in which a contract to the landholder depends on reports from all landowners. Except in special cases, the ex-ante scheme never implements the full information allocation, and can actually set aside too much land. In contrast, (...) expected habitat size under the ex-post scheme is smaller than both the ex-ante and full information allocations. (C) 2001 Elsevier Science (USA). (shrink)

We study reducts of Peano arithmetic for which conditions of saturation imply the corresponding conditions for the whole model. It is shown that very weak reducts (like pure order) have such a property for κ-saturation in every κ ≥ ω 1 . In contrast, other reducts do the job for ω and not for $\kappa > \omega_1$ . This solves negatively a conjecture of Chang.

In a discussion-note in Mind, Father P. M. Farrell, O.P., gave an account, in what he admitted to be an embarrassingly brief compass, of the Thomist doctrine concerning evil. There is one sentence in this discussion which at first glance appears paradoxical. Father Farrell has been arguing that a universe containing ‘corruptible good’ as well as incorruptible is better than one containing ‘incorruptible good’ only. He continues: ‘If, however, they are to manifest this corruptible good, they must be corruptible and (...) they must sometimes corrupt.’ The final words, despite Father Farrell's italics, strike one as expressing, not a self-evident truth, but a non sequitur. The fact that I am capable of committing murder does not entail that I will at some time commit it. It is not immediately obvious that a similar entailment holds in the case of corruption and corruptibility. (shrink)

In the modal literature various notions of completeness have been studied for normal modal logics. Four of these are defined here, viz. (plain) completeness, first-order completeness, canonicity and possession of the finite model property — and their connections are studied. Up to one important exception, all possible inclusion relations are either proved or disproved. Hopefully, this helps to establish some order in the jungle of concepts concerning modal logics. In the course of the exposition, the interesting properties of first-order definability (...) and preservation under ultrafilter extensions are introduced and studied as well. (shrink)

Posidonivs was fortunate to be born in an age when the Romans had begun to recognize their own intellectual limitations, and had turned for guidance to a hitherto despised nation, admitted by themselves to be as much their superior in originality as it was inferior to them in practical matters. He was, moreover, the official exponent of a philosophical system which, destined as it was to exercise for hundreds of years the strongest moral influence over the world, had already taken (...) a firm hold on the more thoughtful minds at Rome. Probably any Greek teacher of ability had, in the time of Cicero, a good chance to make a name; Posidonius, who was a man of considerable intellectual gifts, great learning, and some originality, and who was, moreover, the accredited successor to Zeno and Chrysippus, obtained a reputation which lasted for some centuries. (shrink)

The posterior parietal cortex (PPC) is the most likely site where egocentric spatial relationships are represented in the brain. PPC cells receive visual, auditory, somaesthetic, and vestibular sensory inputs; oculomotor, head, limb, and body motor signals; and strong motivational projections from the limbic system. Their discharge increases not only when an animal moves towards a sensory target, but also when it directs its attention to it. PPC lesions have the opposite effect: sensory inattention and neglect. The PPC does not seem (...) to contain a “map” of the location of objects in space but a distributed neural network for transforming one set of sensory vectors into other sensory reference frames or into various motor coordinate systems. Which set of transformation rules is used probably depends on attention, which selectively enhances the synapses needed for making a particular sensory comparison or aiming a particular movement. (shrink)

John Locke:When we set before our eyes a round globe of uniform colour, v.g. gold, alabaster or jet, it is certain that the idea thereby imprinted in our mind is of a flat circle, variously shadowed, with several degrees of light and brightness coming to our eyes. But we having, by use, been accustomed to perceive what kind of appearance convex bodies are wont to make in us, what alterations are made in the reflections of light by the difference of (...) the sensible figures of bodies: the judgment presently, by an habitual custom, alters the appearances into their causes.H.H. Price:…. a distant hillside which is full of protuberances, and slopes upwards at quite a gentle angle, will appear flat and vertical….. This means that the sense-datum, the colour expanse which we sense, actually is flat and vertical. (shrink)