In an earlier post, I defended the idea (which Trent Dougherty also came up with independently and earlier) that only theory-unexplained entities, or kinds of entities, count against the simplicity of a theory. Here is another argument for this. Start with these two principles:
- If theories T1 and T2 are otherwise equally evidenced and explanatorily powerful, but T1 is simpler, then T1 is more epistemically likely to be true than T2.
- The Principal Principle: Epistemic probabilities should (except in exceptional cases) be set to equal objective chances when the latter are available.
- TH: T0 is true, no U particles ever get produced except perhaps in a moment by this apparatus, heads will come up, and a U particle will be produced by the apparatus.
- TT: T0 is true, no U particles ever get produced except perhaps in a moment by this apparatus, tails will come up, and no a U particle will be produced by the apparatus.
By a very plausible application of the Principal Principle, since the chances of heads and tails are equal as the coin is fair:
But if the number of explained kinds of objects counts against simplicity, then TT is simpler than TH, since according to TT reality includes an extra kind of particle, the U particle. (If one doesn't think reality includes the future, run this thought experiment retrospectively after the explosion.) So by (2), then, P(TT)>P(TH). But this contradicts (3). Thus, by modus tollens, the number of explained kinds of objects does not count against simplicity.