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)

Relationism is the view that our best physical theories can dispense with spacetime. To show the feasibility of relationism, philosophers have suggested a whole range of approaches, from the postulation of a physical plenum to the use of modality. Shamik Dasgupta has recently suggested using his Generalism to develop a relationist account of spacetime. This paper argues that Dasgupta’s Generalism offers no hope to the defenders of relationism. We first present Generalism in what we take to be its most perspicuous (...) formulation. We then discuss a recent argument by Sider (2020) against Generalism and show how to defuse it. Finally, we present a novel argument against Generalism based on Barrett’s criterion of parsimony (Barrett 2022). (shrink)

The paper studies in detail a precise formal construction of spacetime from matter suggested by the logician John Burgess. We presuppose a continuous and perdurantistic matter ontology. The result is a systematic method to translate claims about the geometry of a flat relativistic, or classical, spacetime into claims about geometrical relations between matter points. The approach is extended to electric and magnetic fields by treating them as multifields defined on matter, rather than as fields in the vacuum. A few tentative (...) suggestions are made to adapt the method to general relativity and to quantum theories. (shrink)