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)

The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly concur with (...) systems of relevance logic and paraconsistent logic. In this paper it will be argued that McCall’s historical analysis is fundamentally mistaken since it doesn’t take into account two versions of connexivism. While “humble” connexivism maintains that connexive properties only apply to “normal” antecedents, “hardcore” connexivism insists that they also hold for “abnormal” propositions. It is shown that the overwhelming majority of the forerunners of connexive logic were only “humble” connexivists. Their ideas concerning connexive implication don’t give rise, however, to anything like a non-classical logic. (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)

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)

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)

The old division of all sciences into the two equally important classes of theoretical and practical disciplines is hardly ever applied today. However, the proprium of a practical science that is aimed at what should be, can be elucidated using medicine as an example. The efforts of medicine are not limited to a mere `application' of methods and results of theoretical disciplines. Even the concepts of `illness' and `diagnosis', which are central to medicine, are defined in a normative-deontological manner. They (...) are supposed not only to help formulating and justifying assertions on facts, but also to be a means to enable and standardise action. Since every action takes place in a concrete situation, a practical science must always bridge the hiatus between the general and the particular. This requires judgement, a personal, individual capacity that cannot be operationalised without residue. In contrast to the theoretical disciplines, such a science is not the master of its own questions and problems; and is subject to the dictate of time, since all action is final and irrevocable. (shrink)

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)

The Dialectica-style functional interpretation of Kripke-Platek set theory with infinity ( $\hbox{\sf KP} \omega$ ) given in [1] uses a choice functional (which is not a definable set function of ( $hbox{\sf KP} \omega$ ). By means of a Diller-Nahm-style interpretation (cf. [4]) it is possible to eliminate the choice functional and give an interpretation by set functionals primitive recursive in $x\mapsto\omega$ . This yields the following characterization: The class of $\Sigma$ -definable set functions of $\hbox{\sf KP} \omega$ coincides with (...) the collection of set functionals of type 1 primitive recursive in $x\mapsto \omega$. (shrink)

This paper argues that social representations cannot be used as independent variables in causal explanations of social behaviour. It is shown that the structure of investigations often follows a causally explanatory design despite explicit statements to the contrary by the researchers. This fact is analyzed with three investigations. It is argued that verbal data used to assess the contents of a representation as independent variable are logically equivalent to data obtained from the “dependent” overt behaviour. Therefore these two kinds of (...) data must be seen as two illustrations of the same representational contents. The researchers’preference for using verbal data to assess the independent variable and the tendency to introduce a causal relationship between representation and behaviour is shown to result from misplacing folk-beliefs. Folk-beliefs about intentional causality, it is shown, pertain to the same level as other beliefs about the world on the part of the subjects. Hence they are part of the folk-representation itself and must be treated as such; their use in scientific accounts of the belief-action relationship is not implied by data on rational belief systems. It is suggested to conceptualize social representations as integral units of beliefs and action which may be used to explain causally subsequent contingent social events. The function of folk-beliefs in intentional causality for the self-concept of rational people and for social accountability is discussed. (shrink)

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.

The paper focuses on interpreting ceteris paribus conditions as normal conditions. After discussing six basic problems for the explication of normal conditions and seven interpretations that do not well solve those problems I turn to what I call the epistemic account. According to it the normal is, roughly, the not unexpected. This is developed into a rigorous constructive account of normal conditions, which makes essential use of ranking theory and in particular allows to explain the phenomenon of multiply exceptional conditions. (...) Finally, this static account is extended to a schematic dynamic model of how we may learn about those normal and exceptional conditions. (shrink)

ZUSAMMENFASSUNGEs werden aus der Theologiegeschichte vier Typen von Willensfreiheit erhoben: der Typus liberum arbitrium , der Typus des nominalistischen Willensbegriffs , der Typus des mystischen Willensbegriffs und der Typus der Rechtfertigungslehre. Die ersten drei Typen werden psychologisch interpretiert im Sinne der Ichentwicklung als präautonom, autonom und transautonom. Nach der Darstellung und Diskussion der gegenwärtigen neurowissenschaftlichen Debatte um die Willensfreiheit wird ein systemisch verstandener Personbegriff als Brückenkonzept vorgeschlagen.SUMMARYFour types of free will are identified from the history of theology: The type of (...) the liberum arbitrium, the type of nominalism, the type of mysticism and the type of justification. For the first three types a psychological interpretation in terms of pre-autonomy, autonomy, and trans-autonomy is offered, based on self-transcendence as a religious feature. Two basically opposing interpretations of the same empirical data favoring free will and favoring a non-free will are discussed and compared with the theological tradition. A new notion of the person, based on the system theory, is suggested as a bridging concept to link the theological and neuro-scientific ideas of free will. (shrink)