Enantiomorphy and Time

Abstract

This article argues that time‐asymmetric processes in spacetime are enantiomorphs. Subsequently, the Kantian puzzle concerning enantiomorphs in space is reviewed to introduce a number of positions concerning enantiomorphy, and to arrive at a dilemma: one must either reject that orientations of enantiomorphs are determinate, or furnish space or objects with orientation. The discussion on space is then used to derive two problems in the debate on the direction of time. First, it is shown that certain kinds of reductionism about the direction of time are at variance with the claim that orientation of enantiomorphic objects is intrinsic. Second, it is argued that reductive explanations of time‐asymmetric processes presuppose that enantiomorphic processes do not have determinate orientation.

Acknowledgements

I want to thank David Atkinson, Craig Callender, Igor Douven, Erik Krabbe, Huw Price, Jos Uffink, and the anonymous referees for helpful comments. Needless to say, any mistakes and inaccuracies are my responsibility.

Notes

[1] If the folding exercise is confusing, it is also possible to imagine knee (b) going round a Möbius band by rigid motion.

[2] It seems possible to provide a definition of enantiomorphy that does not depend on rigid motions, along the lines of Möbius (1991): an object is enantiomorphic in n‐dimensional space if and only if it is not uniquely characterised by distances between its labelled parts. But for the present purpose, this definition is less suitable.

[3] The present result may be connected to the remark of Wittgenstein (1921) in Tractatus 6.36111: ‘Das Kantsche Problem von der rechten und linken Hand…besteht schon…im eindimensionalen Raum’. It is because in Minkowski spacetime, the time component is in a sense a separate one‐dimensional space that time‐asymmetric processes are enantiomorphic.

[4] It seems that in an n‐dimensional space, a relation that refers to orientation must involve at least n + 1 points. We may make ori‐r more specific by means of this.

[5] Smart (1964) advances an argument comparable with that of Remnant. The same responses apply to his position.

[6] As a nice parallel, this is just as counterintuitive as Mach’s view on the inertia of mass, which is also supposed to suddenly vanish when there are no other masses present in the universe.

[7] Matthews (1979) quotes Earman as saying ‘any other method’ and accuses Earman of suggesting that pp is a method, too, while pp is just a consistency requirement. But Earman’s text reads ‘any method’.

[8] The difference may give rise to an argument similar to Leibniz’s argument against Newtonian absolute space: there is no sufficient reason to create either the universe or its incongruent counterpart.