#5 assumes that processes are always going on which would increase entropy. If we observe after these processes have gone on for an infinite length of time, then entropy must be at maximum (i.e., the universe is at equilibrium).
If we claim that there were no processes going on before some arbitrary time (what I called time X), then you could observe non-equilibrium states finite (and bounded) lengths of time after time X. If there is a time X, we could make a new time scale in which we labeled it 0, sort of an absolute zero for time. I think the only way to claim that there were no processes would be to say there was at least one closed system in the universe which opened at time X (or time zero if your prefer).
Since #1 assumes that the energy in the universe is finite, regardless of its extent, the rest of my statements are only concerning a universe with finite energy.
Only in a universe with finite energy, but yes. If entropy in steadily increasing for an unbounded amount of time, the result is that entropy is unbounded. #6 follows from the rest (if it were polished up a bit to provide more rigor).
#2 says that the universe itself is a closed system. That is just saying that we can’t expect an extra energy to flow in from some other place (not created but moved) into our universe. In your posts, you seem to indicate that you don’t believe any energy was coming in or going out of the universe either by creation, destruction, or movement from outside the universe.
Only if he was “modern” enough to redefine how math works!
Certainly you’ve helped me here. I had missed the case where the energy in the universe is infinite. If there is infinite energy, we’d never run out of higher ordered energy, and we no longer have to be worried about the heat death of the universe. It might get a little warm, but we could always construct better air conditioners and insulation.
Great, that’s smart. You never know what new discoveries are around the corner. That’s why the Church doesn’t teach a literal 6 day creation or even flooding of the “whole” world. That doesn’t stop people from trying to, however.
The key was to take a finite amount of energy (#1), and show that if its entropy increases (#2 & #3) (not just staying the same (#4)) over an unbounded period of time, entropy must be at its maximum. Infinity overwhelms any finite value. #5 is really an if-then. #6 says the if-part is true (from the premise) and the consequences of the then-part of #5.
Thanks, I appreciate your thoughts on the matter.