A main subject of philosophy of science is the reconstruction of scientific theories. Not only scientists are holding theories but everybody else, namely theories about everyday knowledge. In this article two geometric theories of this kind are reconstructed. The reconstruction is performed under the structuralist view of theories. It turns out that there are important differences between scientific theories and everyday theories, concerning the intended applications as well as the logical status of the concepts.

Leibniz is one of the founders of calculus, a starting point of modern mathematics. A crucial point in the understanding of Leibniz' calculus is the concept of differential, especially differential of higher order. In this article we discuss the first successful application of differentials of higher order, namely the determination of the radius of curvature. 1692 Jakob Bernoulli determined three formulas for this radius. Leibniz was not satisfied with the proofs of Bernoulli and published two years later a new elegant (...) deduction. The article is a reconstruction of Bernoulli's and Leibniz' approaches showing the ingenious work of Leibniz in this field. (shrink)

Homo Mysticus presents three renowned lectures delivered by Wolfgang Struve from 1974 to 1984, translated into English in this volume. Philosophical and mystical experiences are finally given expression in this remarkable collection.

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)

One of the most famous critiques of the Leibnitian calculus is contained in the essay “The Analyst” written by George Berkeley in 1734. His key argument is those on compensating errors. In this article, we reconstruct Berkeley's argument from a systematical point of view showing that the argument is neither circular nor trivial, as some modern historians think. In spite of this well-founded argument, the critique of Berkeley is with respect to the calculus not a fundamental one. Nevertheless, it highlights (...) central aspects of the calculus that are characteristic of modern scientific theories. (shrink)

The species concept is one of the oldest and most fundamental in biology. And yet it is almost universally conceded that no satisfactory definition of what constitutes a species has ever been proposed. The present article is devoted to an attempt to review the status of the problem from a methodological point of view. Since the species is one of the many taxonomic categories, the question of the nature of these categories in general needs to be entered into.

Are empirical theories empirically testable? In this article Theoretische Begriffe und die Prüfbarkeit von Theorien V. Gadenne comes to the conclusion that theories are testable. On this basis he criticizes the non-statement view which asserts the contrary. It is shown that this criticism, however, is erroneous.

In the history of mathematics Leibniz as one of the scientists who developed the calculus of differentials has an outstanding position. However, it is difficult to reconstruct his theory in a consistent way. The main problem is the concept of differential. For an adequate understanding of this concept it is necessary to analyze how it is used. In this article we deal with the first systematic formulation of Leibniz' calculus, the Lectiones de calculo differentialium of Johann Bernoulli from 1691/92. It (...) will be proved that Leibniz's theory is consistent and can be reconstructed as an empirical theory - concerning physical curves - within the structuralist metatheory. The concept of differential is a theoretical one in respect to this theory. (shrink)

For an appropriate understanding of Leibniz's calculus the concept of differential is a crucial one. In Die Differentialrechnung nach Leibniz -eine Rekonstruktion (published in this journal in 2001) the calculus differentialis of Leibniz was analysed. In this paper we deal with the first systematic formulation of the calculus integralis, the Lectiones mathematicae de methodo integralium aliisque of Johann Bernoulli from 1691/92. It will be pointed out that Leibniz's theory is consistent and can be reconstructed as an empirical theory within the (...) structuralist metatheory. (shrink)