We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field. Our approach was inspired by the work of Whitehead, though our (...) philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)

I examine two claims that arise in Brown’s account of inertial motion. Brown claims there is something objectionable about the way in which the motions of free particles in Newtonian theory and special relativity are coordinated. Brown also claims that since a geodesic principle can be derived in Einsteinian gravitation, the objectionable feature is explained away. I argue that there is nothing objectionable about inertia and that while the theorems that motivate Brown’s second claim can be said to figure in (...) a deductive-nomological explanation, their main contribution lies in their explication rather than their explanation of inertial motion. (shrink)

The aim of this paper is to elaborate a notion of explanation which is applicable to stochastic processes such as quantum processes. The model-theoretic approach was adopted in order to delimit appropriate classes, by defining set-theoretical predicates, of different kinds of physical transformations that quantum systems suffer, either of transitions or of transmutations, by interaction or in a spontaneous manner. To explain a singular quantum process consists in showing that it is feasible to model it as an indeterministic process of (...) certain specified kind. (shrink)

The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In order to make the (...) theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. -/- The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. (shrink)

In Creative Understanding, Roberto Torretti lays out a classification of possible relationships between physical theories by distinguishing four big types of relationships between two given theories considered in diachronic perspective: specialization, extension, reformulation, and substitution. Within the structuralist metatheory, this author and others also have propounded in several writings a diachronic typology of intertheoretical relations. Leaving besides differences of detail, both typologies reveal remarkable coincidences, although the structuralist typology is formally more precise than Torretti’s. However, in the last portion of (...) this article, I discuss a further type of intertheoretical relation in diachronic perspective, which, until recently, had not been considered by any approach in philosophy of science: what I call “crystallization” and is exemplified by the development of thermodynamics in the 19th century. (shrink)

Nuestro objetivo es analizar críticamente el enfoque de la noción de modelo de Alfred Tarski que Patrick Suppes integra en su concepción semanticista de las teorías científicas. En efecto, mostraremos cómo esta noción se configura en Suppes (1969; 1970) desde una revisión formal de la noción de modelo en Tarski (1936), focalizando nuestro análisis en tres ejes principales: i) una crítica a la perspectiva estática del semanticismo; ii) un análisis de las condiciones restrictivas y el lenguaje para la axiomatización de (...) teorías; y iii) la revisión de las nociones de ‘sistema axiomático’, ‘sistema formal’ y ‘método axiomático’. (shrink)

Einstein’s 1935 derivation of mass—energy equivalence is philosophically important because it contains both a criticism of purported demonstrations that proceed by analogy and strong motivations for the definitions of the ‘new’ dynamical quantities. In this paper, I argue that Einstein’s criticism and insights are still relevant today by showing how his derivation goes beyond Friedman’s demonstration of this result in his Foundations of Spacetime ¹heories. Along the way, I isolate three distinct physical claims associated with Einstein’s famous equation that are (...) sometimes not clearly distinguished in philosophical discussions of spacetime theory. (shrink)

Two metascientific concepts that have been ― and still are ― object of philosophical analysis are the concepts of model and theory. But while the concept of scientific theory was one of the concepts to which philosophers of science devoted most attention during the 20th century, it is only in recent decades that the concept of scientific model has come to occupy a central position in philosophical reflection. However, it has done so in such a way that, at present, as (...) Jim Bogen states in the back cover of the book Scientific Models in the Philosophy of Science, by Daniela Bailer-Jones, “[t]he standard philosophical literature on the role of models in scientific reasoning is voluminous, disorganized, and confusing”. In spite of this, one of the axes that would allow us to organize at least part of this literature, and with which Bailer-Jones’ book closes, is that which is identified as one of the “contemporary philosophical issues: how theories and models relate to each other” (Bailer-Jones 2009, p. 208).That is why, in this introduction to the special issues of Metatheoria devoted to the topic of “Models and Theories in Biology”, we will present the main advances that have been made in the philosophical analysis of the concepts of model and theory in general and in biology in particular, and we will also do the same with the answers that have been given to the problem of "how theories and models relate to each other”. (shrink)

We critically examine the role and status probabilities, as they enter via the Quantum Equilibrium Hypothesis, play in the standard, deterministic interpretation of deBroglie’s and Bohm’s Pilot Wave Theory (dBBT), by considering interpretations of probabilities in terms of ignorance, typicality and Humean Best Systems, respectively. We argue that there is an inherent conflict between dBBT and probabilities, thus construed. The conflict originates in dBBT’s deterministic nature, rooted in the Guidance Equation. Inquiring into the latter’s role within dBBT, we find it (...) explanatorily redundant (in particular for dBBT’s solution of the Measurement Problem, which only requires that the corpuscles possess definite positions), and subject to a number of difficulties. Following a suggestion from Bell, we propose to abandon the Guidance Equation, whilst retaining dBBT’s point particle-based Primitive Ontology, with positions as local beables. The resultant theory, which we identify as a stochastic, minimally deBroglie-Bohmian theory, describes a random walk through configuration space. Its probabilities, we propose, are best understood as dispositions of possible corpuscle configurations to manifest themselves. We subsequently evaluate the merits of sdBBT vis-à-vis dBBT, such as the justification of the Symmetrisation Postulate and the violation of the Action-Reaction Principle. Not only is sdBBT an attractive Bohmian theory that, whilst retaining dBBT's virtues, overcomes many of its shortcomings; it also sparks off a number of exciting follow-up questions, such as a comparison between sdBBT and other stochastic hidden-variable theories, e.g. Nelson Stochastics, or between sdBBT and the Everett interpretation. (shrink)

The purpose of this paper is to discuss and clarify the explanations commonly cited for the aerodynamic lift generated by a wing, and to then analyse, as a case study of engineering discovery, the aerodynamic revolutions which have taken place within Formula 1 in the past 40 years. The paper begins with an introduction that provides a succinct summary of the mathematics of fluid mechanics.