Muslimische Theologen und Philosophen im Wett- und Widerstreit um die Ratio - Ein Thesenpapier zum Diktum der 'Vernunftreligion' Islam im 11.-14. Jahrhundert

In this paper I investigate the vivid discussions among Muslim theologians and philosophers about the relationship of reason and religion from the 11th to the 14th centuries – which continue to be used as points of reference today. I argue that the idea of Islam as a religion which is in harmony with reason was one of the key postulates of the dominant thinkers of that period, regardless of their school of thought or their attitude towards literal or allegorical ways of understanding the Coran. In consequence, religion has been rationalized or even intellectualized to a high degree while philosophy in turn has been deeply coloured by religious images and concepts. Yet the understanding of religion as well as of reason and its instruments has been so heterogeneous that rationalization could bear very different, even conflicting meanings, thereby undermining the postulated harmony. In seven theses I foreground several striking similarities and differences between theologians and philosophers who diverge in their usage and understanding of reason as well as of the nature of religion.

Admissibility in Finitely Generated Quasivarieties

Checking the admissibility of quasiequations in a finitely generated (i.e., generated by a finite set of finite algebras) quasivariety Q amounts to checking validity in a suitable finite free algebra of the quasivariety, and is therefore decidable. However, since free algebras may be large even for small sets of small algebras and very few generators, this naive method for checking admissibility in Q is not computationally feasible. In this paper, algorithms are introduced that generate a minimal (with respect to a multiset well-ordering on their cardinalities) finite set of algebras such that the validity of a quasiequation in this set corresponds to admissibility of the quasiequation in Q. In particular, structural completeness (validity and admissibility coincide) and almost structural completeness (validity and admissibility coincide for quasiequations with unifiable premises) can be checked. The algorithms are illustrated with a selection of well-known finitely generated quasivarieties, and adapted to handle also admissibility of rules in finite-valued logics.

Textanalyse in den Wissenschaften. Inhalte und Argumente analysieren und verstehen. 2. überarb. Auflage

Das Buch vermittelt methodische Grundlagen für die Arbeit mit Texten in den Wissenschaften, besonders die Fähigkeit, Inhalt und Argumentation komplexer Texte zu erfassen, wiederzugeben und zu beurteilen. Die Einführung entspricht den fachlichen Standards der Philosophie und Geisteswissenschaften, ist fachübergreifend konzipiert und setzt kein spezifisches Wissen voraus. Der Band richtet sich an Studierende verschiedener Fachrichtungen sowie an Personen, die sich mit dem Wissen anderer Fachrichtungen auseinandersetzen oder im Dialog mit der Öffentlichkeit stehen. Mit Fallbeispielen aus verschiedenen Wissensbereichen und kommentierten Literaturhinweisen.

Reconstructing Arguments: Formalization and Reflective Equilibrium

Traditional logical reconstruction of arguments aims at assessing the validity of ordinary language arguments. It involves several tasks: extracting argumentations from texts, breaking up complex argumentations into individual arguments, framing arguments in standard form, as well as formalizing arguments and showing their validity with the help of a logical formalism. These tasks are guided by a multitude of partly antagonistic goals, they interact in various feedback loops, and they are intertwined with the development of theories of valid inference and adequate formalization. This paper explores how the method of reflective equilibrium can be used for modelling the complexity of such reconstructions and for justifying the various steps involved. The proposed approach is illustrated and tested in a detailed reconstruction of the beginning of Anselm’s De casu diaboli.

Mind change complexity of learning logic programs

The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts. Building on Angluin’s notion of finite thickness and Wright’s work on finite elasticity, Shinohara defined the property of bounded finite thickness to give a sufficient condition for learnability of indexed families of computable languages from positive data. This paper shows that an effective version of Shinohara’s notion of bounded finite thickness gives sufficient conditions for learnability with ordinal mind change bound, both in the context of learnability from positive data and for learnability from complete (both positive and negative) data. Let Omega be a notation for the first limit ordinal. Then, it is shown that if a language defining framework yields a uniformly decidable family of languages and has effective bounded finite thickness, then for each natural number m >0, the class of languages defined by formal systems of length <= m: • is identifiable in the limit from positive data with a mind change bound of Omega (power)m; • is identifiable in the limit from both positive and negative data with an ordinal mind change bound of Omega × m. The above sufficient conditions are employed to give an ordinal mind change bound for learnability of minimal models of various classes of length-bounded Prolog programs, including Shapiro’s linear programs, Arimura and Shinohara’s depth-bounded linearly covering programs, and Krishna Rao’s depth-bounded linearly moded programs. It is also noted that the bound for learning from positive data is tight for the example classes considered.

The logic of ADHD : a brief review of fallacious reasoning

This paper has two central purposes: the first is to survey some of the more important examples of fallacious argument, and the second is to examine the frequent use of these fallacies in support of the psychological construct: Attention Deficit Hyperactivity Disorder (ADHD). The paper divides 12 familiar fallacies into three different categories—material, psychological and logical—and contends that advocates of ADHD often seem to employ these fallacies to support their position. It is suggested that all researchers, whether into ADHD or otherwise, need to pay much closer attention to the construction of their arguments if they are not to make truth claims unsupported by satisfactory evidence, form or logic.