Wolfgang Malzkorn

"Foundations of the Formal Sciences" is a series of interdisciplinary conferences in mathematics, philosophy, computer science and linguistics. The main goal is to reestablish the traditionally strong links between these areas of research that have been lost in the past decades. The second conference in the series had the subtitle "Applications of Mathematical Logic in Philosophy and Linguistics" and brought speakers from all parts of the Formal Sciences together to give a holistic view of how mathematical methods can improve our philosophical and technical understanding of language and scientific discourse, ranging from the theoretical level up to applications in language recognition software. Audience: This volume is of interest to all formal philosophers and theoretical linguists. In addition to that, logicians interested in the applications of their field and logic students in mathematics, computer science, philosophy and linguistics can use the volume to broaden their knowledge of applications of logic.

It is well known that a central issue in the famous debate between Gottfried Wilhelm Leibniz and Samuel Clarke is the nature of space. They disagreed on the ontological status of space rather than on its geometrical or physical structure. Closely related is the disagreement on the existence of vacuums in nature: while Leibniz denies it, Clarke asserts it. In this paper, I shall focus on Leibniz's position in this debate. In part one, I shall reconstruct the theory of physical space which Leibniz presents in his letters to Clarke. This theory differs from Leibniz's ultimate metaphysics of space, but it is particularly interesting for systematic reasons, and it also gave rise to a lively discussion in modern philosophy of science. In part two, I shall examine whether the existence of vacuums is ruled out by that theory of space, as Leibniz seems to imply in one of his letters. I shall confirm the result of E. J. Khamara that Leibniz's theory of space rules out the existence of a certain kind of vacuum, namely extramundane vacuums, although it does not rule out vacuums within the world.

It is well known that a central issue of the famous debate between Gottfried Wilhelm Leibniz and Samuel Clarke is the nature of space. Leibniz and Clarke disagree on the ontological status of space rather than on its structure. Closely related to the disagreement on the ontological status of space is a further disagreement on the existence of vacuums in nature: While Leibniz denies their existence, Clarke asserts it. In this paper I shall focus on Leibniz’s position in the debate about these issues. The first part is an introduction. In the second part I shall try to reconstruct the theory of physical space which Leibniz presents in his letters to Clarke. This theory is particularly interesting for systematic reasons and gave rise to a lively discussion in modern philosophy of nature. In the third part I shall point out some major difficulties of the theory. In the fourth part I shall examine whether the existence of vacuums is ruled out by this theory of space, as Leibniz seems to imply in one of his letters. I shall confirm E. J. Khamara’s claim that Leibniz’s theory of space does not rule out the existence of vacuums in general. But, as I shall argue, this result can be refined: Leibniz’s theory of space rules out the existence of a certain kind of vacuum, namely extramundane vacuums; it does not, however, rule out vacuums within the world

In this paper it is argued that the _Physical Monadology of 1756 has to be seen as an attempt to evade the same paradox as the one given in the second antinomy of the _Critique of Pure Reason. Since this attempt presupposes the claim that space rests upon relations between substances, it contradicts the thesis that it is a mere form of intuition, presented by Kant in his dissertation of 1770. Therefore, at least since 1770 the paradox of the divisibility of matter rose up again so that Kant had to deal with it once again in his first _Critique. Remarkably, his key to solve the second antinomy is the same which ruled out his earlier solution of 1756 and gave rise to the paradox again, i.e., the ideality of space and time. But, contrary to the dissertation, in the _Critique it is substituted by the doctrine that our knowledge of objects depends on and is restricted to intuitively given objects and this is crucial to the solution of the second antinomy. Finally, it will be shown how Kant deals with the problem of the divisibility of matter in the _Metaphysical Foundations of Natural Science

The aim of this paper is twofold. Firstly, I give a brief account of the history of the debate on the problem of defining disposition concepts from its beginning in the late 1920s until today. This account is divided into four parts, corresponding with 2, 3, 4 and 5 of the paper, each of which deals with a major period of the debate. Section 2 reports up to the mid-1950s. Section 3 deals with important contributions to the discussion between 1955 and 1958. However, the progress made around that time was far ahead of the logical theory and techniques which were needed for foundational reasons and for a better understanding of the basic notions. Some logical techniques appropriate for that aim were developed in the late 1960s and early 1970s. Though not uncontroversial, those logical techniques resulted in improvements of the insights gained in the mid-1950s; I shall report on those logical techniques and their application to the problem of defining disposition concepts in Section 4. In the early 1990s, however, the whole tradition of defining disposition concepts in terms of conditionals has been challenged by some strong counter-examples which are treated in Section 5. Finally, the second of the aims of this paper is explored in Section 6, in which I sketch very briefly the current stage of the debate by discussing and evaluating the most recent approaches to the subject.