For any countable transitive complete theory T with infinite models and the finite model property, we construct a minimal structure M such that the theory of M is small if and only if T is small, and is λ-stable if and only if T is λ-stable. This gives a series of new examples of minimal structures.
A structure (M, $ ,...) is called quasi-o-minimal if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal; one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use it to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any quasi-o-minimal (...) ordered ring is a real closed field, or has zero multiplication; every quasi-o-minimal divisible ordered group is o-minimal; every quasi-o-minimal archimedian densely ordered group is divisible. We show that a counterpart of quasi-o-minimality in stability theory is the notion of theory of U-rank 1. (shrink)
A relation on a linearly ordered structure is called semi-bounded if it is definable in an expansion of the structure by bounded relations. We study ultimate behavior of semi-bounded relations in an ordered module M over an ordered commutative ring R such that M/rM is finite for all nonzero r $\epsilon$ R. We consider M as a structure in the language of ordered R-modules augmented by relation symbols for the submodules rM, and prove several quantifier elimination results for semi-bounded relations (...) and functions in M. We show that these quantifier elimination results essentially characterize the ordered modules M with finite indices of the submodules rM. It is proven that (1) any semi-bounded k-ary relation on M is equal, outside a finite union of k-strips, to a k-ary relation quantifier-free definable in M, (2) any semibounded function from $M^{k}$ to M is equal, outside a finite union of k-strips, to a piecewise linear function, and (3) any semi-bounded in M endomorphism of the additive group of M is of the form x $\mapsto \sigmax$ , for some $\mapsto \sigma$ from the field of fractions of R. (shrink)
The ability to predict is the most importantability of the brain. Somehow, the cortex isable to extract regularities from theenvironment and use those regularities as abasis for prediction. This is a most remarkableskill, considering that behaviourallysignificant environmental regularities are noteasy to discern: they operate not only betweenpairs of simple environmental conditions, astraditional associationism has assumed, butamong complex functions of conditions that areorders of complexity removed from raw sensoryinputs. We propose that the brain's basicmechanism for discovering such complexregularities is implemented in (...) the dendritictrees of individual pyramidal cells in thecerebral cortex. Pyramidal cells have 5–8principal dendrites, each of which is capableof learning nonlinear input-to-outputtransfer functions. We propose that eachdendrite is trained, in learning its transferfunction, by all the other principal dendritesof the same cell. These dendrites teach eachother to respond to their separate inputs with matching outputs. Exposed to differentbut related information about the sensoryenvironment, principal dendrites of the samecell tune to functions over environmentalconditions that, while different, are correlated . As a result, the cell as awhole tunes to the source of the regularitiesdiscovered by the cooperating dendrites,creating a new representation. When organizedinto feed-forward/feedback layers, pyramidalcells can build their discoveries on thediscoveries of other cells, graduallyuncovering nature's hidden order. Theresulting associative network is powerfulenough to meet a troubling traditionalobjection to associationism: that it is toosimple an architecture to implement rationalprocesses. (shrink)
Oleg Grabar has argued that there was not a system of visual symbols in Islamic culture; consequently it is difflcult to hold that an Islamic architecture exists; that is, if we were to stand before a mosque and try to experience it aesthetically or see what kind of building it is we would not be able to say that it is a mosque. In this paper we argue against this proposition. We, first, present a brief analysis of Grabar's view. (...) Second, we critically evaluate this view. Third, we explicate how the mosque as an architectural type embodies uniquely Islamic symbols. We shall illustrate this point by an analysis of one basic Islamic symbol: the Mihrab. The thesis we defend is that there are basic Islamic symbols and that these symbols inhere in the mosque. It is this fact that lends credibility to the claim that an Islamic architecture exists. /// Oleg Grabar defendeu a tese de que não existe um sistema de símbolos visuais na cultura islâmica; consequentemente, é difícil defender a existência de uma arquitectura islâmica; ou seja, se estivéssemos diante de uma mesquita e tentássemos fazer uma experiência estética da mesma ou analisar que tipo de edifício se trata, não seríamos capazes de dizer que se trata de uma mesquita. No presente artigo, os autores argumentam contra esta proposição. Em primeiro lugar, os autores começam por apresentar uma breve análise do ponto de vista de Grabar. Em segundo lugar, avaliam criticamente esta posição. Em terceiro lugar tentam explicar até que ponto a mesquita como tipo arquitectónico apenas incorpora símbolos islâmicos. Os autores exemplificam este ponto mediante a análise de um dos símbolos básicos do Islamismo: o Mihrab. O artigo defende, portanto, a tese de que existem símbolos islâmicos básicos e de que estes símbolos estão presentes na mesquita. Ora é precisamente este facto que dá credibilidade à afirmação de que existe uma arquitectura islâmica propriamente dita. (shrink)
We propose that a top priority of the cerebral cortex must be the discovery and explicit representation of the environmental variables that contribute as major factors to environmental regularities. Any neural representation in which such variables are represented only implicitly (thus requiring extra computing to use them) will make the regularities more complex and therefore more difficult, if not impossible, to learn. The task of discovering such important environmental variables is not an easy one, since their existence is only indirectly (...) suggested by the sensory input patterns the cortex receives – these variables are “hidden.” We present a candidate computational strategy for (1) discovering regularity-simplifying environmental variables, (2) learning the regularities, and (3) using regularities in perceptual and decision-making tasks. The SINBAD computational model discovers useful environmental variables through a search for different, but nevertheless highly correlated functions of any kind over non-overlapping subsets of the known variables, this being indicative of some important environmental variable that is responsible for the correlation. We suggest that such a search is performed in the neocortex by the dendritic trees of individual pyramidal cells. According to the SINBAD model, the basic function of each pyramidal cell is (1) to discover and represent one of the regularity-simplifying environmental variables, and (2) to learn to infer the state of its variable from the states of other variables, represented by other pyramidal cells. A network of such cells – each cell just attending to representation of its variable – can function as a sophisticated and useful inferential model of the outside world. (shrink)
At first, Bloom's theory appears inimical to empiricism, since he credits very young children with highly sophisticated cognitive resources (e.g., a theory of mind and a belief that real kinds have essences), and he also attacks the empiricist's favoured learning theory, namely, associationism. We suggest that, on the contrary, the empiricist can embrace much of what Bloom says.
The article presents results of an ongoing study of centers of intellectual innovations in post-Soviet Russia. Using the European University at St. Petersburg as the main object of their analysis, the authors demonstrate how new models of academic careers, which became available in the 1980s and 1990s, were eventually institutionalized as new models of knowledge production and educational practices. Supported by American foundations, this private university had to invent a new institutional structure and to position itself within the field of (...) higher education, still mostly dominated by the state. (shrink)
Primatological and archaeological evidence along with anthropological accounts of hunter-gatherer societies indicate that lethal between-group violence may have been sufficiently frequent during our ancestral past to have shaped our evolved behavioral repertoire. Two simulations explore the possibility that heroism (risking one's life fighting for the group) evolved as a specialized form of altruism in response to war. We show that war selects strongly for heroism but only weakly for a domain-general altruistic propensity that promotes both heroism and other privately costly, (...) group-benefiting behaviors. A complementary analytical model shows that domain-specific heroism should evolve more readily when groups are small and mortality in defeated groups is high, features that are plausibly characteristic of our collective ancestral past. (shrink)
We say that a first order formula ϕ distinguishes a structure M over a vocabulary L from another structure M′ over the same vocabulary if ϕ is true on M but false on M′. A formula ϕ defines an L-structure M if ϕ distinguishes M from any other non-isomorphic L-structure M′. A formula ϕ identifies an n-element L-structure M if ϕ distinguishes M from any other non-isomorphic n-element L-structure M′. We prove that every n-element structure M is identifiable by a (...) formula with quantifier rank less than (1 − 1/2k)n + k2 − k + 4 and at most one quantifier alternation, where k is the maximum relation arity of M. Moreover, if the automorphism group of M contains no transposition of two elements, the same result holds for definability rather than identification. The Bernays-Schönfinkel class consists of prenex formulas in which the existential quantifiers all precede the universal quantifiers. We prove that every n-element structure M is identifiable by a formula in the Bernays-Schönfinkel class with less than $(1-\frac{1}{2k})n+k^{2}-k+4$ quantifiers. If in this class of identifying formulas we restrict the number of universal quantifiers to k, then less than $n-\sqrt{n}+k^{2}+k$ quantifiers suffice to identify M and, as long as we keep the number of universal quantifiers bounded by a constant, at total $n-O(\sqrt{n})$ quantifiers are necessary. (shrink)
Oleg B. Zaslavskii. The little in a non-Euclidean world: On the artistic space in Tom Stoppard's film and play “Rosencrantz and Guildenstern are dead”. It is shown that quite different aspects of Tom Stoppard’s work — spatial organization, relationship between reality and the conditional character of events, causality and narrative links, the problems of choice and personality — are united by the spatial one-sided model like the Möbius strip or Klein bottle. The artistic space turns out to be not (...) orientable, the time being cyclic. This enables us to explain the mutual exchange of names between Rosencrantz and Guildenstern and a number of other paradoxical features in the plot and composition. The model like the Möbius strip embodies the absence of a free choice: there is no other side in the world and there is no chance to escape from the fate indicated in the title of Tom Stoppard’s work. The relevance of topology, e.g. the property of a globalnature, is connected with the fact that a bearer of danger is the world as a whole. Apart from this, it points to the fact that such a structure of the world is essentially “non-Euclidean” and cannot be understood on the basis of observations from every-day life or “obvious” experiments like those carried out by Rosencrantz. (shrink)
Oleg B. Zaslavskii. Structural paradoxes of Russian literature and poetics of pseudobroken text. Traditionally, the Pushkin’s work “My provodili vecher na dache…” is considered to be uncompleted. However, on the basis of structural arguments, we show that, in fact, it is completed as an artistic whole. Taking also into account the results of previous analysis of works by Pushkin, Lermontov and Gogol’, we introduce a new notion of “pseudobroken texts”. Their distinctive feature consists in the structural correspondence between the (...) break of a plot and a break as the theme of the text — such, that it is the break of a text which confirms that the text is finished. From the general viewpoint, such a paradoxical phenomenon can be viewed as modeling the impossibility to destroy art and culture. (shrink)
Modern cognitive approach represents the interdisciplinary branch of scientific reflection uniting researchers of knowledge, studying laws of purchase, transformation, representation, storages and reproduction of the information. People react to own experience, instead of "objective" reality. Cognitive map of the world according to which we operate, our feelings, belief and life experience create. We have no direct access to a "objective" reality, therefore our cognitive map is for us this unique "real" reality. Cognitive science widely uses methodology of synergetic approach successfully (...) describing processes of self‐organizing. On the other hand, the synergetic addresses to modelling cognitive systems both the separate individual and collective cognitive processes. Therefore there are bases tospeak about formation cognitive‐synergetic scientific program ‐ the approach which is under construction on principles of modern nonlinear thinking. (shrink)
Machine generated contents note: -- Introduction to the OneThe Concept of One: From Philosophy to Politics -Artemy Magun Part I. Metaphysics of the One and the Multiple1. More than One -Jean Luc Nancy 2. Condivision, or Towards a Non- communitarian Concatenation of Singularities -Gerald Raunig 3. Unity and Solitude -Artemy Magun 4. The Fragility of the One -Maria Calvacante 5. The One: Construction or Event? For a Politics of Becoming -Boyan Mancher Part II. 20th-Century Thinkers of Unity and Multiplicity 6. (...) Truth and Infinity in Badiou and Heidegger -Alexey Chernyakov 7. Complicated Presence: The Unity of Being in Parmenides and Heidegger -Jussi Bachman 8. The Universal, the General, the Multiple in the Perspective of a Political Utopia: Deleuze and Badiou on the Event -Keti Chukhrov 9. Humanity, Unity and the One -Nina Power Part III. Unity and Multiplicity in Nature 10. Elemental Nature as the Ultimate Common Ground of the World Community -Susanna Lindberg 11. Vegetative Democracy, or the Post-metaphysics of Plants -Michael Marder Part IV. Unity in Action: Forms of Political Consolidation in the Case of Contemporary Russia12. Collectivity in Post-revolutionary Russia -Igor Tchubarov13. Street University: Production of Collective Time and Public Space -Pavel Arsenyev 14. Fighting Together: the Problem of Solidarity -Carine Cle;ment Part V. E Pluribus Unum: Res Publica and Community 5. How Does One Constitute the One? Theology of the Icon, Theory of Non-representative Art and of Non-representative Politics -Oleg Kharkhodin 12. Drawing Lots in Politics: Unity and Totality -Yves Sintomer. (shrink)
Machine generated contents note: -- Introduction to the OneThe Concept of One: From Philosophy to Politics -Artemy Magun Part I. Metaphysics of the One and the Multiple1. More than One -Jean Luc Nancy 2. Condivision, or Towards a Non- communitarian Concatenation of Singularities -Gerald Raunig 3. Unity and Solitude -Artemy Magun 4. The Fragility of the One -Maria Calvacante 5. The One: Construction or Event? For a Politics of Becoming -Boyan Mancher Part II. 20th-Century Thinkers of Unity and Multiplicity 6. (...) Truth and Infinity in Badiou and Heidegger -Alexey Chernyakov 7. Complicated Presence: The Unity of Being in Parmenides and Heidegger -Jussi Bachman 8. The Universal, the General, the Multiple in the Perspective of a Political Utopia: Deleuze and Badiou on the Event -Keti Chukhrov 9. Humanity, Unity and the One -Nina Power Part III. Unity and Multiplicity in Nature 10. Elemental Nature as the Ultimate Common Ground of the World Community -Susanna Lindberg 11. Vegetative Democracy, or the Post-metaphysics of Plants -Michael Marder Part IV. Unity in Action: Forms of Political Consolidation in the Case of Contemporary Russia12. Collectivity in Post-revolutionary Russia -Igor Tchubarov13. Street University: Production of Collective Time and Public Space -Pavel Arsenyev 14. Fighting Together: the Problem of Solidarity -Carine Cle;ment Part V. E Pluribus Unum: Res Publica and Community 5. How Does One Constitute the One? Theology of the Icon, Theory of Non-representative Art and of Non-representative Politics -Oleg Kharkhodin12. Drawing Lots in Politics: Unity and Totality -Yves Sintomer. (shrink)
