A critique of algorithmic rationalisation offers at best some initial reasons and preliminary ideas. Critique is understood as a reflection on validity. It is limited to an “epistemological investigation” of the limits of the calculable or of what appears “knowable” in the mode of the algorithmic. The argumentation aims at the mathematical foundations of computer science and goes back to the so-called “foundational crisis of mathematics” at the beginning of the 20th century with the attempt to formalise concepts such as (...) calculability, decidability and provability. The Gödel theorems and Turing’s halting problem prove to be essential for any critical approach to “algorithmic rationalisation”. Both, however, do not provide unambiguous results, at best they run towards what later became known as “Gödel’s disjunction”. The chosen path here, however, suggests the opposite way, insofar as, on the one hand, the topos of creativity appear constitutive for what can be regarded as cognitive “algorithmic rationalisation” and which encounters systematic difficulties in the evaluation of non-trivial results. On the other hand, the investigations lead to a comparison between the “mediality” of formally generated structures, which have to distinguish between object-and metalanguages, and the “volatile” differentiality of human thought, which calls for syntactically non-simulatable sense structures. (shrink)

Previous efforts to bring the Hegelian dialectic closer to a clarification give reason for skepticism. The question: "What is dialectic", according to Dieter Henrich, "has remained without an answer so far". Hegel's objective-idealistic program is, however, so much linked to the possibility of a dialectical logic that it is an urgent desideratum to gain clarity about the stringency of dialectical argumentation. But this is only possible on the basis of a theory of dialectic. Hegel's own reflection on methods cannot be (...) considered sufficient in this respect. It does not enable us to defend the dialectical procedure against objections or to answer questions of method. In the following, a detailed reconstruction of the dialectic of 'being' and 'nothing' in Hegel's 'Science of Logic' will reveal basic structures of dialectical argumentation. As will be shown, antinomic structures play a key role. Such a 'reconstruction', however, will not be a simple confirmation of Hegelian texts, but will always have the character of a critique. In fact, it will turn out that in comparison with Hegel's development of categories, radical revisions are to be expected. ----- Bisherige Bemühungen, das Verfahren Hegelscher Dialektik einer Klärung näherzubringen, geben Anlass zur Skepsis. Die Frage: „Was ist Dialektik?“, so Dieter Henrich, sei „bisher ohne Antwort geblieben“. Das objektiv-idealistische Programm Hegels ist indes so sehr mit der Möglichkeit einer dialektischen Logik verknüpft, daß über die Stringenz dialektischer Argumentation Klarheit zu gewinnen ein dringliches Desiderat darstellt. Das aber ist nur auf der Grundlage einer Theorie der Dialektik möglich. Hegels eigene Methodenreflexion kann diesbezüglich nicht als zureichend erachtet werden. Sie versetzt uns nicht in die Lage, das dialektische Verfahren gegen Einwände zu verteidigen oder Methodenfragen zu beantworten. Im Folgenden sollen in einer detaillierten Rekonstruktion der Dialektik von ‘Sein’ und ‘Nichts’ in Hegels ‘Wissenschaft der Logik’ Grundstrukturen dialektischer Argumentation sichtbar gemacht werden. Wie gezeigt wird, kommt dabei antinomischen Strukturen eine Schlüsselfunktion zu. Eine solche 'Rekonstruktion' wird allerdings nicht eine umstandslose Bestätigung der Hegelschen Textvorlage sein können, sondern immer auch den Charakter einer Kritik haben. In der Tat wird sich ergeben, daß im Vergleich mit Hegels Kategorienentwicklung einschneidende Revisionen zu gewärtigen sind. (shrink)