Andrej Ule

Der Autor setzt sich mit Gödels kosmologischem Ansatz auseinander, der scheinbar Zeitschleifen und Zeitreisen erlaubt, sowie insbesondere mit seiner These, dass die Objektivität des Zeitablaufs nicht a priori gegeben ist, sondern von physikalischen Bedingungen im All abhängt. Wir könnten keine einheitliche Weltzeitlinie in Bezug zum mittleren Bewegungsstatus der Dinge „definieren”, sondern nur einige relative und partielle Zeitabläufe, die den Betrachtern als gleichzeitig verlaufend vorkommen würden. Der Autor hinterfragt die Möglichkeit verschiedener „Zeitwahrnehmungen“ für denselben Betrachter: einmal da, wo der Zeitverlauf eine gewöhnliche „Bewegung” wäre und die Vergangenheit der Gegenwart vorausgeht , und wiederum dort, wo dieser Verlauf gewissermaßen simultan wäre. Er vertritt die Meinung, dass das Bewusstsein viele Zeitmodalitäten besitzen kann und dass die „Annihilierung des Zeitablaufs” eine davon wäre. Vielleicht deutet gerade die momentane Besinnung auf vergangene Ereignisse in unserem Geist auf diese Möglichkeit hin. Allerdings bleibt die Frage offen, was diese Möglichkeit für die physikalische Realität oder für den „Kosmos selbst” bedeutet

The Carssirer's conceptions of aprioricity, especially of synthetic a priori principles in exact sciences, is analysed. I consider his 'Marburg's' period, first of all his paper on Kant and modern mathematics. Cassirer defends the thesis on invariance principles as the modern variant of synthetic principles a priori. I analyze his arguments on the existence of apriori principles of science and compare his concept of aprioricity with holistic accounts of theories, 'semantic view of theories' and structural realism.

I analyze some classical solutions of the skeptical argument and some of their week points (especially the contextualist solution). First I have proposed some possible improvement of the contextualist solution (the introduction of the explicit-implicit belief and knowledge distinction beside the differences in the relevance of some counter-factual alternatives). However, this solution does not block too fast jumps of the everyday context (where empirical knowledge is possible) into skeptical context (where empirical knowledge is impossible). Then I analyze some formal analogies between some modal arguments on the contingency of empirical facts (and the world as whole) and the skeptical arguments against empirical knowledge. I try to show that the skeptical conclusion “Empirical knowledge does not exist” is logically coherent with the thesis that they are empirical facts and that we have true belief on them. In order to do that without contradictions I have to accept a non-classical definition of knowledge: S knows that p:= S is not justified to allow that non-p. Knowledge and justified allowance function here as some pseudo-theoretical concepts which allow only some partial and conditional definitions by some “empirical” terms and logical conditions.

In the article are presented the main philosophical explanations of the application of mathematics on the real world (Plato, Aristotle, rationalists, empiricists, Kant, Frege, Husserl, Carnap etc.). They indicate some typical triangular structure of relationships where the mathematical structures somehow correspond to the forms of reality, and thus are possible though something third what bound them. The attempts to solve the question of the application of mathematics by the dispensability of mathematics (e.g. Field) do not success because they do not explain the big success of mathematics in science. However they call our attention to the meaning of transpositions of some empirical contents on the level of theirs mathematical representations. That is neither an abstraction nor an idealisation but is the mapping from the empirical into a formal language. The opposite attempts to identify mathematics and the fundamental structure of reality also do not explain the success of mathematics because of the obvious ontological differences between the mathematical and the real objects. I return finally to Plato and show how he denies the reduction of numbers to some sets. We have to distinguish the idea of numbers and the various aspects of it, for example the cardinal and the ordinal numbers. According to this platonic insight only the idea of numbers exists. Its aspects are only some partial reflections of this idea in our mathematical theories and in the application of mathematics.

The book presents the most relevant theories of truth (correspondence, semantic, deflational, pragmaticist, coherentist, constructivist, evidential), with the emphasis of analytical approaches. The author develops a version of the realist correspondence concept of truth while distinguishing various criteria of truth. He is skeptical in regard of any, complete or certain truth but he does not accept epistemic skepticism either, but argues for a moderate realism where objective orientation towards truth suffices as catching (ever) more truth than falsity