## Saturday, December 8, 2012

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:

1. 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.
2. The Principal Principle: Epistemic probabilities should (except in exceptional cases) be set to equal objective chances when the latter are available.
Now imagine that there is a powerful physical theory, T0, according to which there is a special type of particle, U, that can only be produced through an exceedingly unlikely combination of events, so unlikely that it is unlikely that in the lifetime of the world the particle would ever be produced outside the lab. Scientists build the extremely expensive piece of apparatus to produce the particle. The apparatus is so expensive that it is unlikely it would ever be built again. But a rogue scientist gets hold of the apparatus at night and hooks up a bomb that will destroy the apparatus, and all results of any experiment, in five minutes. She also hooks an indeterministic fair coin flipper to the apparatus, so that if the coin comes up heads, U particle production is triggered, and if comes up tails, U particle production is not triggered. Consider now two theories:
• 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:

1. P(TT)=P(TH).

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.