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)

Dieses Buch geht davon aus, dass eine moderne Hermeneutik als Theorie des Verstehens im begrifflichen Rahmen der gegenwärtigen Theorie des Geistes und der Semantik rekonstruiert werden sollte. Vor diesem theoretischen Hintergrund, der in einem eigenen Kapitel näher umrissen wird, soll die Geschichte der Hermeneutik neu gelesen werden. Dabei wird deutlich, dass diese Lesart vielfach neue historische Interpretationen zu entwickeln und die wichtigsten Stationen der Geschichte der Hermeneutik theoretisch auf neue Weise zu integrieren vermag. Über die hermeneutischen Positionen hinaus, die in (...) den bisherigen Gesamtdarstellungen auftauchen, werden auch Entwürfe diskutiert, die besonders unter geist-theoretischen Aspekten interessant sind, zum Beispiel die antike Hermeneutik, die Hermeneutik Max Webers, die Hermeneutik der logischen Empiristen und die naturalistische Hermeneutik. Vor allem aber wird belegt, dass die Geschichte der Hermeneutik teilweise zu großen Einsichten gelangt ist, an die eine moderne Hermeneutik anknüpfen kann. Das Buch wendet sich nicht nur an Spezialisten der Hermeneutik-Geschichte, sondern an alle Interessierten, denen das Schicksal der verstehenden Wissenschaften am Herzen liegt, und möchte ihnen eine Perspektive empfehlen, unter der sich der Status und die Autonomie der Geisteswissenschaften sowie ihr Bezug auf das Humane unter Heranziehung substantieller Theorien auf neue Weise würdigen lassen. (shrink)

We shall investigate certain statements concerning the rigidity of unary functions which have connections with forms of the axiom of choice.

The geometro-stochastic quantization of a gauge theory based on the (4,1)-de Sitter group is presented. The theory contains an intrinsic elementary length parameter R of geometric origin taken to be of a size typical for hadron physics. Use is made of a soldered Hilbert bundle ℋ over curved spacetime carrying a phase space representation of SO(4, 1) with the Lorentz subgroup related to a vierbein formulation of gravitation. The typical fiber of ℋ is a resolution kernel Hilbert space ℋ $_{\bar (...) \eta }^{(\rho )} $ constructed in terms of generalized coherent states $\bar \eta $ ρ related to the principal series of unitary irreducible representations of SO(4, 1), namely de Sitter horospherical waves for spinless particles characterized by the parameter ρ. The framework is, finally, extended to a quantum field-theoretical formalism by using bundles with Fock space fibers constructed from ℋ $_{\bar \eta }^{(\rho )} $. (shrink)

It is argued that the narrow concept of selection used since the time ofDarwin is only concerned with the relation between organism and its environment . It did not include the organism itself, which was the object of the pre-phylogenetic idealistic morphology. An adequate understanding of the mechanism of evolution dispenses with the concept of morphology as the basis of phylogeny.Es wird aufgezeigt, da\ der aufDarwin selbst zurückgehende eingeengte Gebrauch des Selektionskonzeptes auf die Beziehung zwischen Organismus und Umwelt die biologische (...) Konstruktion der vorphylogenetischen idealistischen Morphologie überlassen hat. Ein zutreffendes VerstÄndnis des Evolutionsmechanismus begreift aber die biologische Apparatur ein, entzieht der Morphologie, soweit sie sich als Vorbedingung phylogenetischen Arbeitens versteht, den Boden. (shrink)

The article discusses principles that form part of evolutionary systems thinking in social sciences and humanities. It is argued that introducing the concept of self-organization relates agency and structures in a way that makes it possible to take up certain features of Critical Theory by which it can meet the demands for a critical social science. These principles are applied to the question of whether there is convergence or divergence in and by means of the Internet. It will be clarified (...) that the Internet is basically a social system and that it is a subsystem of the larger and overarching system of the whole society. It will be shown how the Internet can be perceived as a possible trigger for societal developments bringing about fundamental change in the nature of society. Thus the article cuts across philosophical, system theoretical, social theoretical, sociology of technology, and information society theory considerations. Key Words: dynamic • "mechanism" • self-organizaton • revolution • evolution • Critical Theory • information society • Internet. (shrink)

Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through information or experience; induction and belief change are one and same topic, after all. The most basic of these rules is simply to conditionalize with respect to the information received; and there are similar and more general rules. 1 Hence, a fundamental reason for the epistemological success of (...) probability theory is that there at all exists a well-behaved concept of conditional probability. Still, people have, and have reasons for, various concerns over probability theory. One of these is my starting point: Intuitively, we have the notion of plain belief; we believe propositions2 to be true (or to be false or neither). Probability theory, however, offers no formal counterpart to this notion. Believing A is not the same as having probability 1 for A, because probability 1 is incorrigible3; but plain belief is clearly corrigible. And believing A is not the same as giving A a probability larger than some 1 - c, because believing A and believing B is usually taken to be equivalent to believing A & B.4 Thus, it seems that the formal representation of plain belief has to take a non-probabilistic route. Indeed, representing plain belief seems easy enough: simply represent an epistemic state by the set of all propositions believed true in it or, since I make the common assumption that plain belief is deductively closed, by the conjunction of all propositions believed true in it. But this does not yet provide a theory of induction, i.e. an answer to the question how epistemic states so represented are changed tbrough information or experience. There is a convincing partial answer: if the new information is compatible with the old epistemic state, then the new epistemic state is simply represented by the conjunction of the new information and the old beliefs. This answer is partial because it does not cover the quite common case where the new information is incompatible with the old beliefs. It is, however, important to complete the answer and to cover this case, too; otherwise, we would not represent plain belief as conigible. The crucial problem is that there is no good completion. When epistemic states are represented simply by the conjunction of all propositions believed true in it, the answer cannot be completed; and though there is a lot of fruitful work, no other representation of epistemic states has been proposed, as far as I know, which provides a complete solution to this problem. In this paper, I want to suggest such a solution. In [4], I have more fully argued that this is the only solution, if certain plausible desiderata are to be satisfied. Here, in section 2, I will be content with formally defining and intuitively explaining my proposal. I will compare my proposal with probability theory in section 3. It will turn out that the theory I am proposing is structurally homomorphic to probability theory in important respects and that it is thus equally easily implementable, but moreover computationally simpler. Section 4 contains a very brief comparison with various kinds of logics, in particular conditional logic, with Shackle's functions of potential surprise and related theories, and with the Dempster - Shafer theory of belief functions. (shrink)

This article investigates three technological developments that are related to spatial determinations and that influence behavior in both the public and the private spheres of life. Examined are the changing relative size of movie screens and their venues, the seeming conflicting dynamic of entertainment and communication screens in the private sphere both increasing and decreasing in size, and the influence of action-at-a-distance technology.

Is Einstein's metric theory of gravitation to be quantized to yield a complete and logically consistent picture of the geometry of the real world in the presence of quantized material sources? To answer this question, we give arguments that there is a consistent way to extend general relativity to small distances by incorporating further geometric quantities at the level of the connection into the theory and introducing corresponding field equations for their determination, allowing thereby the metric and the Levi-Civita connection (...) to remain classical quantities. The dualism between matter and geometry is extended to quantized fields with the help of a Hibert bundle ℋ raised over a Riemann-Cartan spacetime. Quantized subnuclear matter fields (generalized quantum mechanical wave functions) are sections on ℋ which determine generalized bilinear currents acting as sourc currents for the bundle geometry at small distances. The established dualism between matter and the underlying bundle geometry contains general relativity as a classical part. (shrink)

Summary The philosophical implications associated with the choice of a particular geometry required for the formulation of a dynamics at subnuclear distances are discussed. A dualism between geometry and matter — the former identified with a fiber bundle of Cartan type raised over space-time, the latter represented by a generalized quantum mechanical wave function — is presented as a possible framework for the dynamics of strongly interacting particles at distances of 10-13 cm.

If it is the tendency of technology, and especially of information and communication technology, particularly in the context of the smart city, not to empower the human person but rather to disenfranchise them by curtailing their capability to judge and choose, how can one counter this dynamic? Code, make, talk, and pray are suggested as possible modes of resistance.

ls it possible to understand not only linguistic expressions and actions but also persons? According to common sense it surely is. Here it is argued that to understand a person a fourfold knowledge is required, although this knowledge is not identical with the understanding of a person. The understanding of a person is cognitive, but neither complete nor scientific.

A concept for a primitive angiospermous branch system is given in order to have a starting point for the derivation of the diverse and highly differentiated branch systems observed in contemporary angiosperms. Hitherto Troll's (1964, 1969) comparative study of the synflorescences in this plant group — developed out predominantly on herbaceous plants — was the most comprehensive and sophisticated treatment dealing with branch systems. Unfortunately, the work on tropical tree architecture by Hallé et al. (1978) has no reference to the (...) classical studies of Troll and his pupils. Thus Müller-Doblies and Weberling (1984) emphasized the high degree of terminological incompatibility between the two works. Angiosperms are seen as a monophyletic plant division. Consequently, the branch system of the first primitive angiosperms must be the starting point in the evolution of the abundant diversity of branch systems and growth forms of modern angiosperms. If it is accepted that primitive angiospermous shoots were terminated by a large flower, one may assume, that the reproductive end of the shoot was enriched by paracladia early in evolution, thereby developing a terminal inflorescence instead of a single flower. Thus the primitive shoot unit was divided into a basal vegetative region — the trophotagma, branching retardively — and the reproductive terminal region, the anthotagma, branching simultaneously. It is demonstrated through a selection of different examples, that the construction of such a system possesses the options for several modifications, enabling the evolution of the abundant diversity of branch systems which characterizes contemporary angiosperms. (shrink)