Let κ be a cardinal which is measurable after generically adding ${\beth_{\kappa+\omega}}$ many Cohen subsets to κ and let ${\mathcal G= ( \kappa,E )}$ be the κ-Rado graph. We prove, for 2 ≤ m < ω, that there is a finite value ${r_m^+}$ such that the set [κ] m can be partitioned into classes ${\langle{C_i:i (...) of ${\mathcal G}$ in ${\mathcal G}$ such that ${[\mathcal{G} ^\ast ] ^m\cap C_i}$ is monochromatic. It follows that ${\mathcal{G}\rightarrow (\mathcal{G} ) ^m_{<\kappa/r_m^+}}$ , that is, for any coloring of ${[ \mathcal {G} ] ^m}$ with fewer than κ colors there is a copy ${\mathcal{G} ^{\prime}}$ of ${\mathcal{G}}$ such that ${[\mathcal{G} ^{\prime} ] ^{m}}$ has at most ${r_m^+}$ colors. On the other hand, we show that there are colorings of ${\mathcal{G}}$ such that if ${\mathcal{G} ^{\prime}}$ is any copy of ${\mathcal{G}}$ then ${C_i\cap [\mathcal{G} ^{\prime} ] ^m\not=\emptyset}$ for all ${i 2 we have ${r_m^+ > r_m}$ where r m is the corresponding number of types for the countable Rado graph. (shrink)

Every set can been thought of as a directed graph whose edge relation is ∈. We show that many natural examples of directed graphs of this kind are indivisible: for every infinite κ, for every indecomposable λ, and every countable model of set theory. All of the countable digraphs we consider are orientations of the countable random graph. In this way we find indivisible well‐founded orientations of the random graph that are distinct up to isomorphism, and ℵ1 (...) that are distinct up to siblinghood. (shrink)

Analogues of Ramsey’s Theorem for infinite structures such as the rationals or the Rado graph have been known for some time. In this context, one looks for optimal bounds, called degrees, for the number of colors in an isomorphic substructure rather than one color, as that is often impossible. Such theorems for Henson graphs however remained elusive, due to lack of techniques for handling forbidden cliques. Building on the author’s recent result for the triangle-free Henson graph, we (...) prove that for each [Formula: see text], the k-clique-free Henson graph has finite big Ramsey degrees, the appropriate analogue of Ramsey’s Theorem. We develop a method for coding copies of Henson graphs into a new class of trees, called strong coding trees, and prove Ramsey theorems for these trees which are applied to deduce finite big Ramsey degrees. The approach here provides a general methodology opening further study of big Ramsey degrees for ultrahomogeneous structures. The results have bearing on topological dynamics via work of Kechris, Pestov, and Todorcevic and of Zucker. (shrink)

The universal homogeneous triangle-free graph, constructed by Henson [A family of countable homogeneous graphs, Pacific J. Math.38(1) (1971) 69–83] and denoted H3, is the triangle-free analogue of the Rado graph. While the Ramsey theory of the Rado graph has been completely established, beginning with Erdős–Hajnal–Posá [Strong embeddings of graphs into coloured graphs, in Infinite and Finite Sets. Vol.I, eds. A. Hajnal, R. Rado and V. Sós, Colloquia Mathematica Societatis János Bolyai, Vol. 10 (North-Holland, 1973), (...) pp. 585–595] and culminating in work of Sauer [Coloring subgraphs of the Rado graph, Combinatorica26(2) (2006) 231–253] and Laflamme–Sauer–Vuksanovic [Canonical partitions of universal structures, Combinatorica26(2) (2006) 183–205], the Ramsey theory of H3 had only progressed to bounds for vertex colorings [P. Komjáth and V. Rödl, Coloring of universal graphs, Graphs Combin.2(1) (1986) 55–60] and edge colorings [N. Sauer, Edge partitions of the countable triangle free homogenous graph, Discrete Math.185(1–3) (1998) 137–181]. This was due to a lack of broadscale techniques. We solve this problem in general: For each finite triangle-free graph G, there is a finite number T(G) such that for any coloring of all copies of G in H3 into finitely many colors, there is a subgraph of H3 which is again universal homogeneous triangle-free in which the coloring takes no more than T(G) colors. This is the first such result for a homogeneous structure omitting copies of some nontrivial finite structure. The proof entails developments of new broadscale techniques, including a flexible method for constructing trees which code H3 and the development of their Ramsey theory. (shrink)

Nous ne pouvons pas laisser l'avenir de l'humanité et les questions écologiques à l'appréciation de quelques-uns. Ce problème mérite un véritable débat scientifique, philosophique et politique. Au milieu des incertitudes grandissantes, cet ouvrage se propose comme une lecture critique d'une culture dominée par la raison technoscientifique et la puissance capitaliste. Si l'humanité doit continuer à exister, comme le pense Hans Jonas, comment la vulnérabilité peut-elle devenir une force, un levier pour sa préservation? Le devoir-être des générations futures implique un devoir-agir (...) urgent de la part des générations actuelles. Lorsque cette exigence est menacée, la responsabilité s'impose comme un devoir de type kantien. L'humanité doit redécouvrir un nouveau rapport au monde : elle doit reconnaître que la nature est limitée et qu'elle n'est pas disponible à volonté. L'amour de la nature, la sobriété, la justice semblent incontournables dans l'exercice de cet impératif: 'Agis de façon que les effets de ton action soient compatibles avec la permanence d'une vie authentiquement humaine sur terre'"--Page 4 of cover. (shrink)

Prispevek obravnava nekatere pojme politične filozofije Clauda Leforta. Pokazati želi, da za rekonstrukcijo politične filozofije, ki se je loteva Lefort, ni toliko konstitutiven njen prelom z znanstvenim diskurzom, ampak vse prej pojem simbolnega, ime za družbeno, ki je zavezano razliki in delitvi.

The objective of the present essay is to show that the traditional dilemma of philosophy, namely, does science think or does not think, has today become the problem that science itself has to solve. To assert that science thinks means first that science, when it thinks, constructs its object in an always specific manner; second, in construing its object, it adds to it the real, i.e., a reference, external to the scientific construction itself, which science then discovers as the basis (...) and source of its construction. This article argues that it is for strictly scientific reasons that science is today faced with the task of affirming itself as a domain of thought in both aforementioned meanings. Affirming the view that science thinks is a scientific struggle for the existence of politics of emancipation. (shrink)

Der Beitrag geht, sich auf die Grundlegung zur Metaphysik der Sitten und die Kritik der praktischen Vernunft beziehend, der Frage nach, ob es möglich ist, Kants praktische Philosophie, jenseits des Dilemmas abstrakter moralischer Universalismus vs. Rechte des Partikulären als Ansatz einer Theorie des subjektivierten Handelns zu begreifen. Das heisst eines Handelns, in dem das Individuum nicht nur im "Dienste der Güter" bzw. seiner empirisch-pathologischen Interessen und Neigungen steht. In der Beantwortung dieser Frage wird die Aussage des kategorischen Imperativs "ich soll (...) so oder so handeln, ob ich gleich nichts anderes wollte" im ersten Schritt als eine Forderung verstanden, die nicht einfach nichts Empirisches zu wollen verlangt, sondern das Wollen an ein Nichts als Etwas bindet. Im zweiten Schritt wird dann gezeigt, dass am Ort dieses Nichts als Etwas das Vernunftfaktum als abgründiger Grund eines Handelns steht, das mit dem Anspruch auftritt, für niemanden zu gelten, wenn es nicht bedingungslos für alle geltend gemacht werden kann. (shrink)

A partir la thèse avancée par Monique David-Ménard, selon laquelle l’entendement réussi là où la raison échoue, il s’agit d’examiner la révolution kantienne dans la manière de penser. Pour tirer les conséquences du renversement dans la pensée mis en oeuvre par la philosophie kantienne, l’auteur interroge la constitution de la réalité dans la perspective transcendantale comme double opération avec le non-savoir portant respectivement sur le sujet et le noumène. Sur le fond de cette interrogation, il montre que la réalité à (...) laquelle a affaire la philosophie kantienne n’est ni la réalité objective constituée, ni la réalité hallucinée du désir de la raison transgressant les limites de la connaissance, mais à une réalité subjectivée, constituée par la mise en scène de la double destitution : celle de la réalité phénoménale et celle de la raison. C’est sur ce point que peut s’établir une alliance militante entre la philosophie et la psychanalyse, alliance dont l’enjeu principal, pour l’une comme pour l’autre, consiste justement en ceci que chacune, pour son propre compte, pense la réalité comme une telle scène du Deux. (shrink)

Članek utemeljuje trditev, da za transcendentalno teorijo objektivnosti nista značilni le občost in nujnost, ampak tudi refleksivnost. Teorija objektivnosti se vselej tudi že obrača nazaj nase in določa pomen lastne določitve objektivnega spoznanja. Samonanašalnost spoznavne konstitucije objekta pa se izraža v nujnosti zveze med realnim nasprotjem in dialektičnim nasprotjem. Skozi to razmerje spoznanje ni le določeno kot objektivno, ampak je vselej tudi že naddoločeno kot uspeh. Pomen konstitucije spoznavnega objekta je uspeh, analiza Kantove fasciniranosti z nevarno bližino uma in norosti (...) pa pokaže, da misli njegova filozofija uspeh kot dejanje, s katerim se uspe um razmejiti od lastne norosti. (shrink)

This article aims at clarifying the status of the Idea in two of Badiou's recent works: Second manifeste pour la philosophie and L'hypothèse communiste. Badiou sets out from the assumption that the operation with the Idea implies an affirmation of the materialism of a philosophy that is under the conditon of four generic procedures. In his attempt to elaborate Badiou's materialism of the Idea, the author does not turn to Plato, as one would expect, but, rather, to Kant's theory of (...) ideas such as it is presented in the Transcendental Dialectics of the first Critique. In so doing, the author seeks to develop Kant's idea in terms of the act. Posing the question of the Idea in terms of the act has at least two advantages: it shows how the pure reason separates itself from the Thing in itself that affects it while allowing for its appearance in the world. (shrink)

Analysing the role of Kant’s third and final Critique, the _Critique of Judgement_, in the system of Kant’s three Critiques (_Critique of Pure Reason_, _Critique of Practical Reason_, _Critique of Judgement_), the paper posits that with the conclusion of the system of critiques in the third _Critique_, Kant succeeds in presenting it as a point of a transfinitisation of knowledge within the critiques’ system.

This study evaluated the effects of an exergame program combined with traditional tennis training on autonomic regulation, tennis technique, gross motor skills, clinical reaction time, and cognitive inhibitory control in children. Sixty-three children were randomized into four groups and compared at baseline, 6-month immediately post intervention and at 1-year follow-up post intervention. At 6-month post intervention the combined exergame and regular training sessions revealed: higher breathing frequency, heart rate and lower skin conductance levels during exergaming; additional benefits in the point (...) of contact and kinetic chain elements of the tennis forehand and backhand technique ; negative impact on the shot preparation and the follow-through elements ; higher ball skills ; higher percentages of clinical reaction time improvement and cognitive inhibitory control improvement in both congruent and incongruent trials. The 1-year follow-up test showed no differences in the tennis technique, clinical reaction time and cognitive inhibitory control improvement between groups with the same number of trainings per week. The findings support exergaming as an additional training tool, aimed to improve important cognitive-motor tennis skills by adding dynamics to the standardized training process. Caution should be placed to planning this training, e.g., in a mesocycle, since exergaming might decrease the improvement of specific tennis technique parts of the trainees.. (shrink)

Countable homogeneous relational structures have been studied by many people. One area of focus is the Ramsey theory of such structures. After a review of background material, a partition theorem of Laflamme, Sauer, and Vuksanovic for countable homogeneous binary relational structures is discussed with a focus on the size of the set of unavoidable colors.

Reviewed Works:Edwin W. Miller, On a Property of Families of Sets.Ben Dushnik, E. W. Miller, Partially Ordered Sets.P. Erdos, Some Set-theoretical Properties of Graphs.G. Fodor, Proof of a Conjecture of P. Erdos.P. Erdos, R. Rado, A Partition Calculus in Set Theory.P. Erdos, R. Rado, Intersection Theorems for Systems of Sets.A. Hajnal, Some Results and Problems on Set Theory.P. Erdos, A. Hajnal, On a Property of Families of Sets.A. Hajnal, Proof of a Conjecture of S. Ruziewicz.P. Erdos, A. Hajnal, (...) R. Rado, Partition Relations for Cardinal Numbers.P. Erdos, A. Hajnal, On a Problem of B. Jonsson.P. Erdos, A. Hajnal, On Chromatic Number of Graphs and Set-Systems. (shrink)

Suppose that α = γ + δ where $\gamma \geq \delta > 0$ . Then there is a graph G = (ω ω α ,E) which has no independent set of order type ω ω α and has no pentagram (a pentagram is a set of five points with all pairs joined by edges). In the notation of Erdos and Rado, who generalized Ramsey's Theorem to this setting, $\omega^{\omega^\alpha} \nrightarrow (\omega^{\omega^\alpha},5)^2.$.

Rado’s Conjecture is a compactness/reflection principle that says any nonspecial tree of height ω1 has a nonspecial subtree of size ℵ1. Though incompatible with Martin’s Axiom, Rado’s Conjecture turns out to have many interesting consequences that are also implied by certain forcing axioms. In this paper, we obtain consistency results concerning Rado’s Conjecture and its Baire version. In particular, we show that a fragment of PFA, which is the forcing axiom for Baire Indestructibly Proper forcings, is compatible (...) with the Baire Rado’s Conjecture. As a corollary, the Baire Rado’s Conjecture does not imply Rado’s Conjecture. Then we discuss the strength and limitations of the Baire Rado’s Conjecture regarding its interaction with stationary reflection principles and some families of weak square principles. Finally, we investigate the influence of Rado’s Conjecture on some polarized partition relations. (shrink)

We prove that Rado's Conjecture implies that the nonstationary ideal on ω 1 is presaturated.

Todorčević showed that Rado's Conjecture implies CC*, a strengthening of Chang's Conjecture. We generalize this by showing that also CC**, a global version of CC*, follows from RC. As a corollary we obtain that RC implies Semistationary Reflection and, i.e. the statement that all forcings that preserve the stationarity of subsets of ω1 are semiproper.

A version of the Erdös-Rado theorem on partitions of the unordered n-tuples from uncountable sets is proved, without using the axiom of choice. The case with exponent 1 is just the Sierpinski-Hartogs' result that $\aleph (\alpha)\leq 2^{2^{2^{\alpha}}}$.

We introduce a framework for a graph-theoretic analysis of the semantic paradoxes. Similar frameworks have been recently developed for infinitary propositional languages by Cook and Rabern, Rabern, and Macauley. Our focus, however, will be on the language of first-order arithmetic augmented with a primitive truth predicate. Using Leitgeb’s notion of semantic dependence, we assign reference graphs (rfgs) to the sentences of this language and define a notion of paradoxicality in terms of acceptable decorations of rfgs with truth values. It (...) is shown that this notion of paradoxicality coincides with that of Kripke. In order to track down the structural components of an rfg that are responsible for paradoxicality, we show that any decoration can be obtained in a three-stage process: first, the rfg is unfolded into a tree, second, the tree is decorated with truth values (yielding a dependence tree in the sense of Yablo), and third, the decorated tree is re-collapsed onto the rfg. We show that paradoxicality enters the picture only at stage three. Due to this we can isolate two basic patterns necessary for paradoxicality. Moreover, we conjecture a solution to the characterization problem for dangerous rfgs that amounts to the claim that basically the Liar- and the Yablo graph are the only paradoxical rfgs. Furthermore, we develop signed rfgs that allow us to distinguish between ‘positive’ and ‘negative’ reference and obtain more fine-grained versions of our results for unsigned rfgs. (shrink)

This is a continuation of our paper where we show that Rado's Conjecture can trivialize ‐sequences in some cases when ϑ is not necessarily a successor cardinal.

We show that both Rado's Conjecture and strong Chang's Conjecture imply that there are no special ℵ2-Aronszajn trees if the Continuum Hypothesis fails. We give similar result for trees of higher heights and we also investigate the influence of Rado's Conjecture on square sequences.

We show that both Rado's Conjecture and strong Chang's Conjecture imply that there are no special ℵ2-Aronszajn trees if the Continuum Hypothesis fails. We give similar result for trees of higher heights and we also investigate the influence of Rado's Conjecture on square sequences.

Modeling mechanisms is central to the biological sciences – for purposes of explanation, prediction, extrapolation, and manipulation. A closer look at the philosophical literature reveals that mechanisms are predominantly modeled in a purely qualitative way. That is, mechanistic models are conceived of as representing how certain entities and activities are spatially and temporally organized so that they bring about the behavior of the mechanism in question. Although this adequately characterizes how mechanisms are represented in biology textbooks, contemporary biological research practice (...) shows the need for quantitative, probabilistic models of mechanisms, too. In this paper we argue that the formal framework of causal graph theory is well-suited to provide us with models of biological mechanisms that incorporate quantitative and probabilistic information. On the ba-sis of an example from contemporary biological practice, namely feedback regulation of fatty acid biosynthesis in Brassica napus, we show that causal graph theoretical models can account for feedback as well as for the multi-level character of mechanisms. However, we do not claim that causal graph theoretical representations of mechanisms are advantageous in all respects and should replace common qualitative models. Rather, we endorse the more balanced view that causal graph theoretical models of mechanisms are useful for some purposes, while being insufficient for others. (shrink)