A System of Axioms for Minkowski Spacetime

Journal of Philosophical Logic (1):1-37 (2020)
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Abstract

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formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished].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.

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References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Philosophy of Physics: Space and Time.Tim Maudlin - 2012 - Princeton University Press.
The Logic in Philosophy of Science.Hans Halvorson - 2019 - Cambridge and New York: Cambridge University Press.
Glymour and Quine on Theoretical Equivalence.Thomas William Barrett & Hans Halvorson - 2016 - Journal of Philosophical Logic 45 (5):467-483.

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