Leibniz was an outstanding mathematician of the 17th century and one of the most original philosophers of European history. Against this background it is astonishing that the ideas of Leibniz concerning probability have to date not been appreciated by mathematicians and philosophers. In this article the most important work of Leibniz with respect to probability theory, his De incerti aestimatione , is analysed. Here Leibniz deals with the 'problem of points', the then famous problem as to how to divide justly (...) the stake when two players have to break off a number of prearranged games. The correspondence between Fermat and Pascal about this problem is regarded as the birth of probability theory. Yet, Leibniz favoured another solution to both of these. We reconstruct the underlying normative ideas of Leibniz and of Fermat and Pascal and show that they are equally sound and justifiable. (shrink)

The following article is a response to K. Mainzer's ‘Knowledge-Based Systems; Remarks on the Philosophy of Technology and Artificial Intelligence’. We show, that Mainzer does not reach any of his aimsto analyse the possibilities and limits of AI-technology.to reduce anxiousness and hostility against AI, which is motivated by phantastic speculations.to evaluate the factual impact of AI on our lives and on society.His article contributes on the contrary to phantastic speculations, which are not technologically justified in any way. There are two (...) main reasons for his misleading view: (a) the state of the art of knowledge-based systems is incorrectly described; (b) the roots, paradigms and alternatives to AI are not in the least sufficiently analysed. We examine issues (a) and (b) in Chapter 1 and Chapter 2. In Chapter 3 we discuss, how the conclusions, which Mainzer draws, have to be modified. In analysing the lines of argumentation of Mainzer we try to clarify the methodological errors and the philosophical attitude of Mainzer, which is in many respects not adequate to the subject of the article. (shrink)

Knowledge-based systems - Utopia and Reality. The following article is a response to K. Mainzer's 'Knowledge-Based Systems; Remarks on the Philosophy of Technology and Artificial Intelligence'. We show, that Mainzer does not reach any of his aims - to analyse the possibilities and limits of AI-technology, - to reduce anxiousness and hostility against AI, which is motivated by phantastic speculations, - to evaluate the factual impact of AI on our lives and on society. His article contributes on the contrary to (...) phantastic speculations, which are not technologically justified in any way. There are two main reasons for his misleading view: (a) the state of the art of knowledge-based systems is incorrectly described; (b) the roots, paradigms and alternatives to AI are not in the least sufficiently analysed. We examine issues (a) and (b) in Chapter 1 and Chapter 2. In Chapter 3 we discuss, how the conclusions, which Mainzer draws, have to be modified. In analysing the lines of argumentation of Mainzer we try to clarify the methodological errors and the philosophical attitude of Mainzer, which is in many respects not adequate to the subject of the article. (shrink)