In his argument that time intervals can exist without change, Shoemaker gives us an interesting thought experiment. For those unfamiliar, here it is:

Assume that an entire universe is divided into three parts -- A, B, and C. Every 3 years, everything in A freezes for a year. Every 4, everything in B freezes for a year, and every 5 for C. After 3 years, we know that region A is frozen because B and C observe that nothing is changing in A (the same applies when B is frozen, when C is frozen, when A and B are frozen, etc). Each region is unfrozen after one year. This cycle continues indefinitely. After 60 years, however, A, B, and C freeze at the same time. Because the regions became unfrozen in the past, we can assume using induction that A, B, and C will unfreeze, and that time has passed without change.

The part of this argument I am concerned with is "After 3 years, we know that region A is frozen because B and C observe that nothing is changing in A (the same applies when B is frozen, when C is frozen, when A and B are frozen, etc)." How can B and C observe a frozen A if nothing is changing in A? In order to observe something, at the very least a single photon must travel from region B to region A and back to B in order for B to observe A. However, this can't happen because nothing is changing in A. Has this created serious problems for Shoemaker's argument, and has any philosopher taken note of this problem and developed it into an argument?


  • First, Shoemaker's argument is about time intervals that go by without changes, not about "time without change" (freezing and unfreezing explicitly presupposes change). And second, it is about mere logical possibility of such intervals. So the story about traveling photons is irrelevant, logic is not bound by the laws of physics in the particular universe we happen to inhabit. Another universe may have action at a distance and no photons. The argument does have flaws, see e.g. Altuna's analysis, but this is not one of them. – Conifold Oct 17 '19 at 23:13
  • @Conifold Ah, so I just "looked too deep" into the metaphor? I also added that the argument is about time intervals, not time itself. – N. Bar Oct 17 '19 at 23:18
  • The argument seems to adopt a naively realistic view of time and change and therefore to be deeply flawed. It is not possible to prove that time passes even when things are changing, and even change itself may be questioned as more than a mental construction. So i'd say the argument is philosophically naive and not answerable in the terms in which it is phrased. . . – user20253 Oct 18 '19 at 12:11
  • @PeterJ, please don't claim that "even change itself may be questioned as more than a mental construction" in a link-less comment claiming a philosopher with a different view is therefore naive. if one claims that change, or existence, or awareness, and the likes, are nothing more than mental illusions the onus is on him to make sense of such claims - and preferably with a link to a paper which is not too tedious to read nor utterly silly. – nir Oct 18 '19 at 13:54
  • @N.Bar, I actually believe the story of travelling photons is very relevant - a beautiful observation. It does not matter if one can supposedly imagine a universe without photons. one still needs to explain what they mean by "observe that nothing is changing" - maybe we can generally speak of information instead of photons - but the problem remains. It seems that if universe A is completely "frozen" then B cannot actually observe it - maybe instead they can observe something like a black hole from which no information is sent. – nir Oct 18 '19 at 14:01

Even if we assume that B and C can (somehow) observer A while it's frozen, the argument doesn't hold if the A,B and C freeze a the same time, cause the moment they do they can no longer be unfrozen because they don't have any reference by which they measure how much time they has been frozen, because the measure of time (i.e the duration that change take) is measured with respect to something changing (i.e reference) either internally or externally and that's because change is a relational phenomena, so the 1 year condition for Universes to be unfrozen make no sense anymore because they can't measure this duration without any change (internal or external) that can refer to this duration of time. For more explanation, the moment they freeze at the same time no other year will passe anymore.

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