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)

Complex Systems Biology approaches are here considered from the viewpoint of Robert Rosen’s (M,R)-systems, Relational Biology and Quantum theory, as well as from the standpoint of computer modeling. Realizability and Entailment of (M,R)-systems are two key aspects that relate the abstract, mathematical world of organizational structure introduced by Rosen to the various physicochemical structures of complex biological systems. Their importance for understanding biological function and life itself, as well as for designing new strategies for treating diseases such as cancers, is (...) pointed out. The roles played by multiple metastable states in the “continuous uphill flow of Life” supported through internal bioenergetic processes that are coupled to essential inflows are also discussed in relation to dynamic realizations of (M,R)-systems. Furthermore, the roles played by the underlying, many-valued, quantum logics and symbolic computations for ultra-complex biological systems are also briefly discussed. (shrink)

Colour word usage within languages follows the same ordering as that proposed by Berlin and Kay between languages. This provides additional validation and support for Berlin and Kay's schema.

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)

In his lucid paper “The Objectivity of History” Professor Pass more poses the problem of history's objectivity and seeks to find out in what the objectivity of history might consist. In this note I wish only to criticize his presentation of Popper's views . I think Pass more's failure to report Popper's views correctly causes him to overlook the striking similarity between Popper's conclusion and his own.

Feeling out of place because he is the only elephant who sings, Little Elephant sets off a journey to find a home where he belongs.

In our papers on the rationality of magic, we distinghuished, for purposes of analysis, three levels of rationality. First and lowest (rationalitYl) the goal directed action of an agent with given aims and circumstances, where among his circumstances we included his knowledge and opinions. On this level the magician's treatment of illness by incantation is as rational as any traditional doctor's blood-letting or any modern one's use of anti-biotics. At the second level (rationalitY2) we add the element of rational thinking (...) or thinking which obeys some set of explicit rules, a level which is not found in magic in general, though it is sometimes given to specific details of magical thinking within the magical thought-system. It was the late Sir Edward E. Evans-Pritchard who observed that when considering magic in detail the magician may be as consistent or critical as anyone else; but when considering magic in general, or any system of thought in general, the magician could not be critical or even comprehend the criticism. Evans-Pritchard went even further: he was sceptical as to whether it could be done in a truly consistent manner: one cannot be critical of one's own system, he thought. On this level (rationalitY2) of discussion we have explained (earlier) why we prefer to wed Evans Pritchard's view of the magician's capacity for piece-meal rationality to Sir James Frazer's view that magic in general is pseudo-rational because it lacks standards of rational thinking. (shrink)

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)

Popper holds to the unity of scientific method: any differences between natural and social science are a product of theory, not a pretheoretical premise. Distin guishing instead pure and applied generalizing sciences, Popper focuses on the different role of laws in each. In generalizing social science, our tools are the logic of the situation, including the rationality principle, and unintended conse quences. Situations contain individuals, but also social entities not reducible to individuals: conspiracy theory is the extreme form of individualism. (...) Action in situations has unintended consequences. Both social and natural laws may be required to explain outcomes. The fate of Popper's ideas is a case study in the logic of the situation. Professional philosophers of social science lean toward individualism and a priorism (either intuitionist or rational choice). There are social and political explanations of this outcome, but little critical engagement with Popper's ideas. (shrink)

Wall, G. Locke's attack on innate knowledge.--Harris, J. Leibniz and Locke on innate ideas.--Greenlee, D. Locke's idea of idea.--Aspelin, G. Idea and perception in Locke's essay.--Greenlee, D. Idea and object in the essay.--Mathews, H. E. Locke, Malebranche and the representative theory.--Alexander, P. Boyle and Locke on primary and secondary qualities.--Ayers, M. R. The ideas of power and substance in Locke's philosophy.--Allison, H. E. Locke's theory of personal identity.--Kretzmann, N. The main thesis of Locke's semantic theory.--Woozley, A. D. Some remarks on (...) Locke's account of knowledge.--Laudan, L. The nature and sources of Locke's views on hypotheses. (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)