Leibniz, the Young Kant, and Boscovich on the Relationality of Space

Leibniz’s main thesis regarding the nature of space is that space is relational. This means that space is not an independent object or existent in itself, but rather a set of relations between objects existing at the same time. The reality of space, therefore, is derived from objects and their relations. For Leibniz and his successors, this view of space was intimately connected with the understanding of the composite nature of material objects. The nature of the relation between space and matter was crucial to the conceptualization of both space and matter. In this paper, I discuss Leibniz’s account of relational space and examine its novel elaborations by two of his successors, namely, the young Immanuel Kant and the Croat natural philosopher Roger Boscovich. Kant’s and Boscovich’s studies of Leibniz’s account lead them to original versions of the relational view of space. Thus, Leibniz’s relational space proved to be a philosophically fruitful notion, as it yielded bold and intriguing attempts to decipher the nature of space and was a key part in innovative scientific ideas

Kant on the Peculiarity of the Human Understanding and the Antinomy of the Teleological Power of Judgment

Kant argues in the Critique of the Teleological Power of Judgment that the first stage in resolving the problem of teleology is conceiving it correctly. He explains that the conflict between mechanism and teleology, properly conceived, is an antinomy of the power of judgment in its reflective use regarding regulative maxims, and not an antinomy of the power of judgment in its determining use regarding constitutive principles. The matter in hand does not concern objective propositions regarding the possibility of objects or actual features of certain objects, namely, organisms. It is rather a methodological issue as to the appropriate way to explain the generation, development, and function of organisms. Taken in this manner as subjective maxims guiding the explanation and inquiry of organisms, the principles of mechanism and teleology need not necessarily be seen as contradictorily opposed but instead can be combined in the study of organisms. This, however, is not enough to complete the analysis of the antinomy of the teleological power of judgment. In order to show that there is an antinomy in this case, Kant has to establish that both seemingly conflicting maxims are necessary and natural to the human mind. He does it by grounding them in the ‘special character’ or peculiarity (Eigentümlichkeit) of the human understanding. However, it is not entirely clear just what exactly this peculiarity of the human understanding is. Paul Guyer argues that Kant suggests two different accounts of the peculiarity of the human intellect. According to one account, this peculiarity consists in the fact that our understanding forms general concepts and according to another, in its propensity to proceed from the parts to the whole. I will argue in this paper that Kant puts forward a single account, in which the combination of these two features demonstrate the peculiarity of the human understanding manifested in the encounter with organisms. This account explains the necessity of the regulative maxims of mechanism and teleology, and thus completes Kant’s analysis of the antinomy of the teleological power of judgment

Locke and Leibniz on Freedom and Necessity

Locke and Leibniz are often classified as proponents of compatibilist theories of human freedom, since both maintain that freedom is consistent with determinism and that the difference between being and not being free turns on how one is determined. However, we will argue in this paper that their versions of compatibilism are essentially different and that they have significantly distinct commitments to compatibilism. To this end, we will first analyze the definitions and examples for freedom and necessity that Locke and Leibniz present in sections 8-13 of chapter 21 of the Essay on Human Understanding and the Nouveaux essais respectively, and then conjecture how Locke and Leibniz would have continued the discussion, if they had had the opportunity to engage in an exchange of opinions. In this way, we believe, one will be in a position to understand why Leibniz thinks that Locke’s discussion of freedom “est un des plus prolixes et des plus subtils de son ouvrage.

The Depth and Breadth of John Bell's Physics

John Bell's investigations in foundations of quantum mechanics, particle physics, and quantum field theory are recalled.Comment: 46 pages, 1 figure, LaTeX; editorial corrections; email correspondence to R. Jackiw <[email protected]

Rational Value of Information Estimation for Measurement Selection

Computing value of information (VOI) is a crucial task in various aspects of decision-making under uncertainty, such as in meta-reasoning for search; in selecting measurements to make, prior to choosing a course of action; and in managing the exploration vs. exploitation tradeoff. Since such applications typically require numerous VOI computations during a single run, it is essential that VOI be computed efficiently. We examine the issue of anytime estimation of VOI, as frequently it suffices to get a crude estimate of the VOI, thus saving considerable computational resources. As a case study, we examine VOI estimation in the measurement selection problem. Empirical evaluation of the proposed scheme in this domain shows that computational resources can indeed be significantly reduced, at little cost in expected rewards achieved in the overall decision problem.Comment: 7 pages, 2 figures, presented at URPDM2010; plots fixe