This paper focuses on Kant's account of physical geography and his theory of the Earth. In spelling out the epistemological foundations of Kant's physical geography, the paper examines 1) their connection to the mode of holding-to-be-true, mathematical construction and empirical certainty and 2) their implications for Kant's view of cosmopolitan right. Moreover, by showing the role played by the mathematical model of the Earth for the foundations of Kant's Doctrine of Right, the exact relationship between the latter and physical geography (...) is highlighted. Finally, this paper shows how, in Kant's view, the progress of physical geography can be assured if and only if the free circulation of human beings is established and regulated by law. Therefore, examining the mutual relationship between the theory of Earth and the foundations of right opens new perspectives on the relationship between epistemology and practical philosophy within Kant's system. (shrink)

In The Explanatory Dispensability of Idealizations, Sam Baron suggests a possible strategy enabling the indispensability argument to break the symmetry between mathematical claims and idealization assumptions in scientific models. Baron’s distinction between mathematical and non-mathematical idealization, I claim, is in need of a more compelling criterion, because in scientific models idealization assumptions are expressed through mathematical claims. In this paper I argue that this mutual dependence of idealization and mathematics cannot be read in terms of symmetry and that Baron’s non-causal (...) notion of mathematical difference-making is not effective in justifying any symmetry-breaking between mathematics and idealization. The function of making a difference that Baron attributes to mathematics cannot be referred to physical facts, but to the features of quantities, such as step lengths or time intervals taken into account in the models. It appears, indeed, that it does not follow from Baron’s argument that idealizations do not help to carry the explanatory load at least for two reasons: mathematics is not independent of idealizations in modelling and idealizations help mathematics to carry the explanatory load of a model in different degrees. (shrink)

In the section of the Antinomy of pure Reason Kant presents three notions of infinity. By investigating these concepts of infinity, this paper highlights important ‘building blocks’ of the structure of the mathematical antinomies, such as the ability of reason of producing ascending and descending series, as well as the notions of given and givable series. These structural features are discussed in order to clarify Ernst Zermelo’s reading of Kant’s antinomy, according to which the latter is deeply rooted in the (...) tendency of the mind of producing “creative progress” and “inclusive closure”. The aim of this paper is to explain in which sense and why Kant’s treatment of the antinomies attracts the attention of Zermelo in the early 1900s and which aspects of his second axiomatic system have been inspired by Kant’s philosophy. Thus, by reading Kant’s antinomy ‘through Zermelo’s eyes’—with emphasis on the concept of regressive series in indefinitum and on that of regressive series ad infinitum – this paper identifies the echoes of Kant’s work in the making of the ZFC set theory. (shrink)

This contribution sheds light on the role of infinite idealization in structural analysis, by exploring how infinite elements and finite element methods are combined in civil engineering models. This combination, I claim, should be read in terms of a ‘complementarity function’ through which the representational ideal of completeness is reached in engineering model-building. Taking a cue from Weisberg’s definition of multiple-model idealization, I highlight how infinite idealizations are primarily meant to contribute to the prediction of structural behavior in Multiphysics approaches.

The question of the dimensionality of space has informed the development of physics since the beginning of the twentieth century in the quest for a unified picture of quantum processes and gravitation. Scientists have worked within various approaches to explain why the universe appears to have a certain number of spatial dimensions. The question of why space has three dimensions has a genuinely philosophical nature that can be shaped as a problem of justifying a contingent necessity of the world. In (...) contrast to explanations of three-dimensionality based on anthropic arguments, we support the search for a theory that provides a justification for the dimensionality of space based on a combination of deductive and inductive reasoning applied to science. In doing so, we argue that Kant correctly approached the question in “Thoughts on the true estimation of living forces” by connecting space dimensionality and the inverse square law. In expounding the strategy of Kant’s argument, we describe the main features of a general Kantian explanation of the dimensionality of space and discuss them with respect to current accounts of explanation in the philosophy of science, such as inference to the best explanation and the deductive-nomological model. (shrink)

a relação entre razão e natureza envolve um dos principais aspectos da crítica da teleologia de Kant. Visando destacar esta relação, investigarei o conceito de técnica da natureza, tal como introduzida na Crítica da faculdade de julgar. De acordo com Kant, a técnica da natureza permite as leis da razão a representarem o acordo dos princípios transcendentais da razão com a natureza. Deste modo, o conceito da técnica da natureza assume um papel prolífico ao expor, através de uma analogia com (...) as faculdades humanas, a atividade produtiva da natureza, como se sua atividade fosse orientada a fins.The relationship between reason and nature embodies one of the main aspects of Kant‟s critique of teleology. In order to highlight this relation, I shall investigate the concept of the technique of nature, as it has been introduced in Critique of the Power of Judgment. According to Kant, the technique of nature allows the laws of reason to represent the agreement of the transcendental principles of reason with nature. Thus, the concept of the technique of nature assumes a fruitful role by exposing, through an analogy with human faculties, the productive activity of nature, as if its activity were oriented towards ends. (shrink)

SPECIAL SECTION: BUILDING UNIVERSES: THE PHILOSOPHICAL AND MATHEMATICAL UNDERPINNINGS OF COSMOLOGY (EIGHTEENTH–TWENTIETH CENTURIES) .

By exploring the nature of scientific representative practices, I shall define a methodology that relates the use of symmetry to specific practical functions. In order to expound this approach, I shall investigate the role played by the conception of symmetry in representative practices from a philosophical and epistemological perspective. The paper proceeds as follows. In the first part, I introduce the reasons why our conception of representative practices should consider the aims and the objectives towards which they direct their interest. (...) Secondly, by using symmetry as a case study, I try to show that philosophy can find fruitful pathways of interaction with sciences, as it is the case when it deals with the practical implications of the employment of symmetry in modeling. In the third section of the paper I shall refer to other examples that highlight the use of symmetry in scientific representative practices. I shall conclude with some remarks on the implications that this approach involves in epistemology, especially on our conception of objectivity and symmetry. (shrink)

This book focuses on two central topics that could help us answer how Plato conceives of the physical world and its relationship to Forms. The first one is the Platonic concept of time. What is it, how is it defined, what is it not, and how does it help us describe the changing realities surrounding us? The second one is Plato’s understanding of the perceptible world. How is it related to Forms, and how exactly does it work? These are central, (...) wide-ranging, and highly contested questions garnering attention in recent Platonic scholarship. We have ensembled an international team that aims to offer bold, innovative, and thought-provoking answers to these questions. The nine contributions in this book represent a diverse range of starting points, methodologies, and interpretative traditions whose collective aim is to challenge your assumptions about Plato’s philosophy and help you rethink and revisit the Platonic corpus with fresh eyes. (shrink)