The notions of conservation and relativity lie at the heart of classical mechanics, and were critical to its early development. However, in Newton’s theory of mechanics, these symmetry principles were eclipsed by domain-specific laws. In view of the importance of symmetry principles in elucidating the structure of physical theories, it is natural to ask to what extent conservation and relativity determine the structure of mechanics. In this paper, we address this question by deriving classical mechanics—both nonrelativistic and relativistic—using relativity and (...) conservation as the primary guiding principles. The derivation proceeds in three distinct steps. First, conservation and relativity are used to derive the asymptotically conserved quantities of motion. Second, in order that energy and momentum be continuously conserved, the mechanical system is embedded in a larger energetic framework containing a massless component that is capable of bearing energy. Imposition of conservation and relativity then results, in the nonrelativistic case, in the conservation of mass and in the frame-invariance of massless energy; and, in the relativistic case, in the rules for transforming massless energy and momentum between frames. Third, a force framework for handling continuously interacting particles is established, wherein Newton’s second law is derived on the basis of relativity and a staccato model of motion-change. Finally, in light of the derivation, we elucidate the structure of mechanics by classifying the principles and assumptions that have been employed according to their explanatory role, distinguishing between symmetry principles and other types of principles that are needed to build up the theoretical edifice. (shrink)

The main intent of this thesis is to defend that the laws of nature are better thought as transcendent universals, such as platonic governism suggests, and that they are metaphysically necessary in a strong way, such as the heterodox version of such platonism defends. With this intention, we sustain that physical symmetries are essential consequences of the laws of nature – what solves the challenge of symmetries – thus being metaphysically necessary, without being governist's necessitation laws. First, we will show (...) what laws of nature are and the reasons to reject other metaphysical theories and to accept platonic governism. Soon after, we will present the challenge of symmetries and the reasons to prefer the platonic governist answer over dispositionalist, regularist, aristotelic (governism), counterfatualist and primitivist ones. At last, we will define what is the metaphysical necessity, argue for the strong metaphysical necessity of laws and their consequences, and show why the reasons for the contingency or weak necessity of laws are bad theoretical paths. (shrink)

This book deals with an internal theme of metaphysics, which is the metaphysics of the laws of nature. The author presents traditional contemporary theories, as well as his own original theory, and evaluates each one at a time. He also addresses the problem of the modality of the laws of nature and makes some criticism of the standard view of necessity as truth in all possible worlds, and shows an application of his discussion to the metaphysics of physics. / Este (...) livro trata de um tema interno à metafísica, que é a metafísica das leis da natureza. O autor apresenta as teorias tradicionais contemporâneas, tal como também a sua própria teoria original, e avalia cada uma delas por vez. Ele também aborda o problema da modalidade das leis da natureza e apresenta uma certa crítica à visão padrão da necessidade como verdade em todos os mundos possíveis, e mostra uma aplicação da sua discussão à metafísica da Física. (shrink)

In this paper, I will defend the thesis that fundamental natural laws are distinguished from accidental empirical generalizations neither by metaphysical necessity, 147–155, 2005, 2007) nor by contingent necessitation. The only sort of modal force that distinguishes natural laws, I will argue, arises from the peculiar physical property of mutual independence of elementary interactions exemplifying the laws. Mutual independence of elementary interactions means that their existence and their nature do not depend in any way on which other interactions presently occur. (...) It is exactly this general physical property of elementary interactions in the actual world that provides natural laws with their specific modal force and grounds the experience of nature’s ‘recalcitrance’. Thus, the modal force of natural laws is explained by contingent non-modal properties of nature. In the second part of the paper, I deal with some alleged counterexamples to my approach: constraint laws, compositional laws, symmetry principles and conservation laws. These sorts of laws turn out to be compatible with my approach: constraint laws and compositional laws do not represent the dynamics of interaction-types by themselves, but only as constitutive parts of a complete set of equations, whereas symmetry principles and conservation laws do not represent any specific dynamics, but only impose general constraints on possible interactions. (shrink)

In this paper I present two cases, taken from the history of science, in which mathematics and physics successfully interplay. These cases provide, respectively, an example of the successful application of mathematics in astronomy and an example of the successful application of mechanics in mathematics. I claim that an illustration of these cases has a twofold value in the context of the applicability debate. First, it enriches the debate with an historical perspective which is largely omitted in the contemporary discussion. (...) Second, it reveals a component of the applicability problem that has received little attention. This component concerns the successful application of physical principles in mathematical practice. With the help of the two examples, in the final part of the paper I address the following question: are successful applications of mathematics to physics and successful applications of physics to mathematics two sides of the same problem? (shrink)

The philosophical problem that stems from the successful application of mathematics in the empirical sciences has recently attracted growing interest within philosophers of mathematics and philosophers of science. Nevertheless, little attention has been devoted to the converse applicability issue of how physical considerations find successful application in mathematics. In this article, focusing on some case studies, I address the latter issue and argue that some successful applications of physics to mathematics essentially depend on the use of conservation principles. I conclude (...) with a short discussion of how the successful interplay between conservation principles and mathematics can be accounted for. (shrink)

How does metaphysical necessity relate to the modal force often associated with natural laws? Fine argues that natural necessity can neither be obtained from metaphysical necessity via forms of restriction nor of relativization — and therefore pleads for modal pluralism concerning natural and metaphysical necessity. Wolff, 898–906, 2013) aims at providing illustrative examples in support of applying Fine’s view to the laws of nature with specific recourse to the laws of physics: On the one hand, Wolff takes it that equations (...) of motion can count as examples of physical laws that are only naturally but not metaphysically necessary. On the other hand, Wolff argues that a certain conservation law obtainable via Noether’s second theorem is an instance of a metaphysically necessary physical law. I show how Wolff’s example for a putatively metaphysically necessary conservation law fails but argue that so-called topological currents can nevertheless count as metaphysically necessary conservation laws carrying physical content. I conclude with a remark on employing physics to answer questions in metaphysics. (shrink)

Philosophy and Phenomenological Research, Volume 99, Issue 3, Page 720-725, November 2019.

The notions of conservation and relativity lie at the heart of classical mechanics, and were critical to its early development. However, in Newton’s theory of mechanics, these symmetry principles were eclipsed by domain-specific laws. In view of the importance of symmetry principles in elucidating the structure of physical theories, it is natural to ask to what extent conservation and relativity determine the structure of mechanics. In this paper, we address this question by deriving classical mechanics—both nonrelativistic and relativistic—using relativity and (...) conservation as the primary guiding principles. The derivation proceeds in three distinct steps. First, conservation and relativity are used to derive the asymptotically conserved quantities of motion. Second, in order that energy and momentum be continuously conserved, the mechanical system is embedded in a larger energetic framework containing a massless component that is capable of bearing energy. Imposition of conservation and relativity then results, in the nonrelativistic case, in the conservation of mass and in the frame-invariance of massless energy; and, in the relativistic case, in the rules for transforming massless energy and momentum between frames. Third, a force framework for handling continuously interacting particles is established, wherein Newton’s second law is derived on the basis of relativity and a staccato model of motion-change. Finally, in light of the derivation, we elucidate the structure of mechanics by classifying the principles and assumptions that have been employed according to their explanatory role, distinguishing between symmetry principles and other types of principles that are needed to build up the theoretical edifice. (shrink)

In this paper, I will defend the thesis that fundamental natural laws are distinguished from accidental empirical generalizations neither by metaphysical necessity (e.g. Ellis 1999, 2001; Bird in Analysis, 65(2), 147–155, 2005, 2007) nor by contingent necessitation (Armstrong 1983). The only sort of modal force that distinguishes natural laws, I will argue, arises from the peculiar physical property of mutual independence of elementary interactions exemplifying the laws. Mutual independence of elementary interactions means that their existence and their nature do not (...) depend in any way on which other interactions presently occur. It is exactly this general physical property of elementary interactions in the actual world that provides natural laws with their specific modal force and grounds the experience of nature’s ‘recalcitrance’. Thus, the modal force of natural laws is explained by contingent non-modal properties of nature. In the second part of the paper, I deal with some alleged counterexamples to my approach: constraint laws, compositional laws, symmetry principles and conservation laws. These sorts of laws turn out to be compatible with my approach: constraint laws and compositional laws do not represent the dynamics of interaction-types by themselves, but only as constitutive parts of a complete set of equations, whereas symmetry principles and conservation laws do not represent any specific dynamics, but only impose general constraints on possible interactions. (shrink)

O desenvolvimento da filosofia acadêmica no Brasil é direcionada, entre vários fatores, pelas investigações dos diversos Grupos de Trabalho (GTs) da Associação Nacional de Pós-Graduação em Filosofia (ANPOF). Esses GTs se dividem de acordo com a temática investigada. O GT de Metafísica Analítica é relativamente novo e ainda tem poucos membros, mas os temas nele trabalhados são variados e todos centrais no debate metafísico contemporâneo internacional. A sua investigação se caracteriza pelo rigor lógico e conceitual com o qual aborda esses (...) tradicionais tópicos da metafísica. Embora os assuntos tratados tenham sido, em sua grande maioria, tópicos abordados e discutidos em reuniões remotas do GT, nem todos os membros do nosso grupo estão aqui representados. Esperamos apresentar seus trabalhos em futuros livros. Por enquanto, queremos apenas divulgar ao público acadêmico algumas de nossas produções, trabalhadas e produzidas exclusivamente para este livro. Segundo a caracterização tradicional, com a qual plenamente concordamos, a metafísica se ocupa com a natureza mais íntima e geral da realidade. Essa metafísica é, por um lado, ambiciosa: não pretende apenas expor a realidade segundo o modo como ela se apresenta para nós, mas como ela é ‘em si mesma’. Por outro lado, ela é modesta: ela sabe da sua dívida para com as outras disciplinas, especialmente lógica, linguagem e epistemologia. Além disso, ela se entende como sempre tentativa, provisória, aberta a críticas e revisões. Neste livro, tratamos temas como as categorias ontológicas fundamentais e as suas relações de dependência e de fundamentalidade, a natureza da composição mereológica, da persistência temporal e do próprio tempo, a natureza dos objetos abstratos e dos mundos possíveis, as naturezas do mundo quântico, da causalidade nômica do mundo físico, e, finalmente, de um dos objetos mais característicos da presença humana no nosso mundo físico, que é o objeto de arte. É claro que essa coletânea está longe de apresentar exaustivamente todos os tópicos da metafísica. Tentamos selecionar e organizar os textos da forma mais fluida possível, de modo que eles possam levar tanto a uma reflexão específica quanto a uma reflexão geral sobre a natureza da realidade. Ainda que tenha uma inerente incompletude, o livro serve à finalidade de levar o/a estudante de graduação e pós-graduação a refletir sobre temas contemporâneos da Metafísica Analítica. Justamente por ter esse objetivo de formentar a pesquisa em metafísica analítica nacional, optamos por traduzir muitos termos do inglês que ainda não tem uma tradução canônica, a fim de evitar anglicismos e contribuir para uma leitura mais natural. Muito mais do que leitores complacentes, esse livro pede por leitores críticos, debatedores corajosos, que estejam dispostos a contribuir e a propor novas teorias e argumentos. Agradecemos a todos os membros do GT de Metafísica Analítica da ANPOF e a todos os autores deste livro, que decidiram apresentar publicamente suas pesquisas à academia; aos membros do Grupo de Pesquisa Investigação Filosófica, que decidiram pela publicação deste livro; à Pró-Reitoria de PósGraduação e Pesquisa da Universidade Federal do Amapá, que o financiou; e ao NEPFIL Online e à Editora da UFPel, que o editaram e publicaram. [Guido Imaguire e Rodrigo Reis Lastra Cid, Organizadores] . (shrink)