We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and a (...) four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane - which obeys the Euclidean axioms in [Tarski and Givant, 1999] - and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagora’s theorem. We conclude with a Representation Theorem relating models of our system that satisfy second order continuity to the mathematical structure called ‘Minkowski spacetime’ in physics textbooks. (shrink)

Dasgupta :35–67, 2009) has argued that material individuals, such as particles and laptops, are metaphysically objectionable and must be eliminated from our fundamental theories of the world. He proposes to eliminate them by redescribing all the fundamental facts of the world in a variant of predicate functor logic. We study the status, on this theory, of a putative fact particularly recalcitrant to a formulation within predicate functor logic: his own claim that there are no fundamental or primitive material individuals. We (...) consider three regimentations of the denial of primitive individuals and show that—under some plausible hypotheses about fundamental truths and the fundamentality operator—they cannot be consistently translated in predicate functor logic by Dasgupta’s usual strategy. We conclude by discussing two approaches to salvage Generalism, in the absence of such a translation. (shrink)

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in Maudlin and Malament. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of Tarski : a predicate of betwenness and a four place (...) predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane—which obeys the Euclidean axioms in Tarski and Givant, 175–214 1999)—and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagoras’ theorem. We conclude with a Representation Theorem relating models \ of our system \ that satisfy second order continuity to the mathematical structure \, called ‘Minkowski spacetime’ in physics textbooks. (shrink)

Bas Van Fraassen is a nifty philosopher of science. He received his PhD in Pittsburgh in 1966, under the guidance of Adolf Grünbaum, he taught at Yale University, the university of Toronto, the University of Southern California, he has been McCosh Professor of Philosophy in Princeton, and eventually joined the department of philosophy at San Francisco State University, where he has the title of Distinguished Professor of Philosophy. He first gained attention with his book An Introduction to the Philosophy of (...) Time and Space where he tried to develop a formal theory of space and time based on the notion of causality. The book had an enormous legacy, with experts of the likes of John Earman and David Malament joining the debate. However, he achieved V.I.P. status with his classic The Scientific Image, where he defends a combination of empiricism and antirealism towards unobservable entities based on a re-definition of what the scientific enterprise is. His last achievement is the tome Scientific Representation: Paradoxes of Perspectives, where he combines his scientific empiricism with the view that theories are best thought as models or structures, rather than sets of sentences. In this interview, we talk about his philosophical influences and the birth of The Scientific Image during a journey through North-Africa, Turkey and Eastern Europe, we talk about saving the phenomena and suspending judgement over the existence of unobservable entities, living in world full of mysteries and leaving unanswerable questions unanswered, rationality and irrationality, living in a simulation, the historical interplay between theorizing and experimenting, the meaning of particle detectors for an empiricist, the unity of science and physicalism, the condemnation of Galilei by the Church, and the distinction between Appearance and Reality…. (shrink)

Modal relationism is the view that our best physical theories can dispense with substantival space or spacetime in favor of possible configurations of particles. Kenneth Manders argued that the substantivalist conception is equivalent to this Leibnizian conception of space. To do so, Manders provides a translation f from the Newtonian theory T N into the Leibnizian modal relationist account T L. In this paper, we show that the translation does not establish equivalence, since there is no translation g : T (...) L → T N that preserves theoremhood. This seems to show that the modal relationist theory T L is less parsimonious than its substantivalist rival. (shrink)

This paper defends two claims about the criterion of commitment of W.V.O Quine. The first claim is that the criterion can be made extensional. The second is that a proper formulation becomes an analytic truth. We spend a few preliminary sections clarifying our intended notion of ontological commitment. We will not go very far in our investigation of the criterion if we do not distinguish the things a theory postulates, what its adherents, or anybody else, believe in, and which of (...) these entities we have compelling reasons to accept. A look at [Quine 1953] shows that the criterion concerned the postulation of entities by theories, but it is often misread as an attempt to say something about either or. The core of the paper is an exposition of two formulations of the criterion. I first state a schema improving on that of [Scheffler and Chomsky 1959]. The second formulation is a single principle and construes commitment as a relation between theories and predicates: ontological commitment to the entities that satisfy a given predicate. Both criteria are extensional and are formulated for constructional systems, in the sense of [Carnap 1928] and [Goodman 1951], rather than for theories construed as interpreted sets of sentences. This solves a problem raised by [Halvorson 2019]. Their analyticity is substantiated by showing that their most controversial consequences are instances of Tarski’s Convention. (shrink)