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Wei_Dai comments on Implications of an infinite versus a finite universe - Less Wrong
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Which kind of model does an instrumentalist use to guide their actions in this situation? The ones with infinities, the ones without, or a probabilistic mixture of the two kinds? It seems like you're saying just use the ones without infinities (since in either of the other two cases we do have to deal with Boltzmann brains). But how do you justify that?
In what situation? Calculus of infinitesimals is a convenient tool invented by Newton and Leibnitz to calculate planetary orbits and other things. The same can be done with differences and not differentials (and is, for numerical calculations), but requires more work. The situation is similar in most other areas. Kronecker delta is a convenient tool in physics and electrical engineering, without necessarily meaning that there is an infinitely strong and infinitely short spike of current somewhere in your circuit.
In the situation that infinite and finite cosmological models can both explain all current observations. Isn't that the topic of this thread?
The original concern was that the evidence points to the infinite universe, therefore everything imaginable happens somewhere. While this can be a fun speculation, I am merely pointing out that the evidence so far points to a very large universe, but not necessarily infinite or even close to large enough for Boltzmann brains.