We show that one can solve Post's Problem by constructing generic sets in the usual set theoretic framework applied to tiny universes. This method leads to a new class of recursively enumerable sets: r.e. generic sets. All r.e. generic sets are low and simple and therefore of Turing degree strictly between 0 and 0'. Further they supply the first example of a class of low recursively enumerable sets which are automorphic in the lattice E of recursively enumerable sets with inclusion. (...) We introduce the notion of a promptly simple set. This describes the essential feature of r.e. generic sets with respect to automorphism constructions. (shrink)
We prove optimal lower bounds on the computation time for several well-known test problems on a quite realistic computational model: the random access machine. These lower bound arguments may be of special interest for logicians because they rely on finitary analogues of two important concepts from mathematical logic: inaccessible numbers and order indiscernibles.
This paper contributes to the question of under which conditions recursively enumerable sets with isomorphic lattices of recursively enumerable supersets are automorphic in the lattice of all recursively enumerable sets. We show that hyperhypersimple sets (i.e. sets where the recursively enumerable supersets form a Boolean algebra) are automorphic if there is a Σ 0 3 -definable isomorphism between their lattices of supersets. Lerman, Shore and Soare have shown that this is not true if one replaces Σ 0 3 by Σ (...) 0 4. (shrink)
Stability properties of kinetic model equations (including discrete versions of the master equation and Boltzmann's equation) are derived by means of Lyapunov's direct method. The construction of suitable Lyapunov functions leads to results about the structural stability of the dynamical systems and makes it possible to compose more complicated systems from the given ones, preserving automatically some form of stability.
What does quantum ﬁeld theory (QFT) tell us about the furniture of the world? Seventeen essays gathered in the four parts of Ontological Aspects of Quantum Field Theory address this question from different angles and with different objectives. Together, they form a wide-ranging and up-to-date volume that makes a valuable contribution to an ongoing discussion, which, due to the comprehensive introduction by the editors, can be of interest to experts and novices alike.
Summary: This book is the first serious attempt to compare the major trends of this school of thought and to discuss their similarities and differences from a non-belligerent position… Lindemann’s book is a competent and very valuable introduction to the ideas of constructivism and their application to pedagogy.
Whether meaning is compositional has been a major issue in linguistics and formal philosophy of language for the last 2 decades. Semantic holism is widely and plausibly considered as an objection to the principle of semantic compositionality therein. It comes as a surprise that the holistic peculiarities of scientific language have been rarely addressed in formal accounts so far, given that semantic holism has its roots in the philosophy of science. For this reason, a model-theoretic approach to semantic holism in (...) the language of science is presented here. This approach preserves compositionality to a large extent. *Received September 2009; revised February 2010. †To contact the author, please write to: Seminar for Philosophy, Logic, and Theory of Science, Hauspostfach 49, Ludwig-Maximilians-Universität, Munich 80539, Germany; e-mail: firstname.lastname@example.org. (shrink)
The German philosopher Robert Spaemann provides an important contribution to a number of contemporary debates in philosophy and theology, opening up possibilities for conversation between these disciplines. He engages in a dialogue with classical and contemporary positions and often formulates important and original insights which lie beyond common alternatives. In this study Holger Zaborowski provides an analysis of the most important features of Spaemann's philosophy and shows the unity of his thought. The question 'Who is a person?' is of (...) increasing significance: Are all human beings persons? Are there animals that can be considered persons? What does it mean to speak of personal identity and of the dignity of the person? Spaemann provides an answer to these questions: Every human being, he argues, is a person and, therefore, 'has' his nature in freedom. In order to understand the person, Spaemann explains, we have to think about the relation between nature and freedom and avoid the reductive accounts of this relation prevalent in important strands of modern thought. Spaemann develops a challenging critique of modernity, incorporating analysis of modern anti-modernisms and showing that these are also subject to a dialectical development, perpetuating the problematic shortcomings of many features of modern reasoning. If we do not want to abolish ourselves as persons, Spaemann reasons, we need to find a way of understanding ourselves that evades the dialectic of modernity. Thus, he reminds his readers of 'self-evident' knowledge: insights that we have once already known, but tend to forget. (shrink)
Recent developments under the keywords dynamicism, embodiment and situated cognition suggest the view that cognitive systems are not confined to the neural sys‐tem but leak into the world beyond the traditional system boundaries. This is the thesis of extended cognition. Such an extension of the cognitive vehicles leads to a new kind of content externalism, known as active externalism. The essay pursues three objectives: firstly, to distinguish the theses of extended cognitive and active externalism. Secondly, to delineate active externalism from (...) its various passive-externalist precursors in the form of physical, historical and social externalism and to scrutinize its special position, which amounts to a comprehensive discussion and analysis of all variants of mental externalism. And thirdly, to show that social externalism as opposed to physical and historical externalism allows for a gradual transition from passive to active mental externalism. (shrink)