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.

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 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)

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)

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)

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)