Various forms of mathematical induction are applicable to domains with some kinds of order. This naturally leads to the questions about the possibility of unification of different inductions and their generalization to wider classes of ordered domains. In the paper we propose a common framework for formulating induction proof principles in various structures and apply it to partially ordered sets. In this framework we propose a fixed induction principle which is indirectly applicable to the class of all posets. In a (...) certain sense, this result provides a solution to the problem of formulating a common generalization of a number of well-known induction principles for discrete and continuous ordered structures. (shrink)

It is shown that for every Turing degree d there is an ω-categorical group G such that the isomorphism type of G is of degree d. We also find an ω-categorical group G such that the isomorphism type of G has no degree.

The study provides an insight into the structural features of the famous VIII century Buddhist treatise Tattvasaṅgrāha by Śāntarakṣita with regard to the text’s main purpose ( prayojana ) as it is treated in Kamalaśīla’s commentary Pañjikā. Any text along with its referential (representational) function of conveying message - meaning to the addressee, or its expressive function, reflecting the author's attitude to what is communicated, also performs the ‘appellative’ function, encouraging the recipient of the message to act. This function which (...) could also be called praxiological was always significant in Indian text culture, since from the times of Veda-s it was embedded in its very core. This function is of paramount importance in the case of Indian religious and philosophical texts, whose main aim is to convince and transform the consciousness of their percipients. Along with linear models of message transfer, Sanskrit texts could demonstrate non-linear semantic structures, transmitting the main idea of the text indirectly. It is exactly how one should perceive the message of Śāntarakṣita’s Tattvasaṅgrāha according to the suggested by Śāntarakṣita’s prominent student Kamalaśīla in his Pañjikā -commentary to the treatise. He proposes to consider Tattvasaṅgrāha not as a thematically heterogeneous encyclopaedic or doxographic work, whose main objective is to refute different non-Buddhist views (as it is often treated by scholars now), but as a text, which by its very design exposes one of the most important Buddhist principles - the law of the dependent origination ( pratītyasamutpāda ). The themes, discussed in a number of the chapters of Tattvasaṅgrāha, indeed, appear to have direct correlation with the characteristics of pratītyasamutpāda given to it in Śālistamba-sūtra - an early Mahāyāna text, which explains this universal law. Kamalaśīla suggests looking at Tattvasaṅgrāha as at one big unit-sentence - mahāvākya, with the exposition of pratītyasamutpāda as its unitary purpose-meaning ( abhidheya ). In this context, the treatise functions as a praxiological tool for the ‘installing’ into the consciousness of the text’s addressee the knowledge of ‘true principles’ (tattva-s) of pratītyasamutpāda. This interpretation of the main message of the text raises also a question of the adequate translation of the name of the treatise into other languages, because, according to Kamalaśīla, ‘ Tattvasaṅgrāha’ means the ‘Assembly of Principles-(tattva’-s)’ which specify precisely pratītyasamutpāda (pratītyasamutpāda-viśeṣaṇāni tattvāni). (shrink)

In this paper we discuss the two-system framework, examine its strengths, point out a fundamental weakness concerning the unity of conscious experience, and then propose a new hypothesis that avoids that weakness and other related concerns. According to our strong emergence hypothesis, what emerges are not merely mental properties in specialized, distributed neural areas, but also a new, irreducibly singular entity that functions in a recurrent manner to integrate its mental properties and to rewire its brain. We argue that the (...) former function is suggested, in part, by the effects of anesthetics on sensory integration, and that the latter function is suggested by evidence garnered from the neuroscience of mindfulness, constraint-induced movement therapy for stroke, and neuroimaging data surrounding mental illness. We then discuss how our strong emergence hypothesis relates to the description and treatment of neuropsychiatric disorders. Finally, potential objections are addressed. (shrink)

We give an example of a simple ω-categorical theory such that for any finite set of parameters the corresponding constant expansion does not satisfy the PAPA. We describe a wide class of homogeneous structures with generic automorphisms and show that some natural reducts of our example belong to this class.

The age of a structure M is the set of all isomorphism types of finite substructures of M. We study ages of generic expansions of ω-stable ω-categorical structures.

1. ptie. Science de la philosophie synthétique du droit et des sciences juridiques--2. ptie. Philosophie synthétique du droit et des sciences juridiques.--3. ptie. Philosophie synthétique des sciences juridiques. Logique et théorie de la connaissance juridique.

In the present inquiry I explore the concept of conceptual analysis, looking for ways for it to be improved, and I come to the following conclusions. Conceptual analysis as ordinarily understood in analytic philosophy is a method which consists in drawing a conclusion about what the definition of a predicate is on the basis of an armchair investigation into whether the predicate is semantically applicable in different possible cases; but, the concept of conceptual analysis can be improved by making two (...) changes to it: 1) the investigation into whether the predicate is semantically applicable in different possible cases is not to serve as a basis for a conclusion about what the definition of the predicate is, but as a basis for a conclusion about whether this-and-this is an only necessary, only sufficient, both necessary and sufficient, or neither necessary nor sufficient condition for the predicate’s semantic application; 2) the investigation into whether the predicate is semantically applicable in different possible cases is done not only from the armchair, but also empirically. (shrink)

Various threshold Boolean networks, a formalism used to model different types of biological networks, can produce similar dynamics, i.e. share same behaviors. Among them, some are complex, others not. By computing both structural and behavioral complexities, we show that most TBNs are structurally complex, even those having simple behaviors. For this purpose, we developed a new method to compute the structural complexity of a TBN based on estimates of the sizes of equivalence classes of the threshold Boolean functions composing the (...) TBN. (shrink)

The article comprises three parts. Part I contains an overview of the areas in the analysis of modern French philosophy that have been of the greatest relevance to Russian researchers over the last years. We conclude that numerous aspects of the French philosophical thought of the twentieth century are well represented in the research of Russian authors, who also point out the emerging trends in its development. Part II deals with the development of analytic philosophy in Russia within the framework (...) of such areas as “critique of bourgeois philosophy”, a purely ideological stand only nominally related to philosophy, logic, and the history of philosophy and theoretical research. Part III contains a periodization of the history of phenomenology in Russia, pointing out the most important achievements of the contemporary Russian scholars of phenomenology as well as their understanding of the essence, the problems, and the aims of phenomenological philosophy. We also indicate the tendencies within the development of the discipline in the Russian Federation. (shrink)

The main result of the paper states that there is a finitely presented group _G_ with decidable word problem where detection of finite subsets of _G_ which generate amenable subgroups is not decidable.

Is property-awareness constituted by representation or not? If it were, merely being aware of the qualities of physical objects would involve being in a representational state. This would have considerable implications for a prominent view of the nature of successful perceptual experiences. According to naïve realism, any such experience—or more specifically its character—is fundamentally a relation of awareness to concrete items in the environment. Naïve realists take their view to be a genuine alternative to representationalism, the view on which the (...) character of such experiences is constituted by representation. But naïve realists must admit qualities or property instances as items of awareness if they are to remain wedded to common sense, and the nature of property-awareness may smuggle constitutive representation into the naïve realist account of character. I argue that whether property-awareness involves representation, and consequently whether naïve realism is distinct from representationalism or not, depends on what qualities are fundamentally. On universalist and nominalist accounts, property-awareness turns out to involve representation. Not so under tropism. (shrink)