Existence exist. It is something specific, i.e. finite. Causality links actions to the entities. Things which come into being or pass out of being are described by processes. "Matter", whatever it turns out to ultimately be, is eternal. Time is a relational concept which used the rotaion of the earth relative to the sun to delimit a day, and its orbit of the sun (presumably in conjunction with referencing the location of stars) to delimit a year.
Due to numerous problematic identifications made by other excellent forum participants, let me try to restate my question more articulately.
Whatever the ultimate constituent(s) that comprise existence is finite. The number of permutations of these existents are finite. Given this, either a permutation or even sequences of permutations should repeat, with the only difference being that of when they occured. If time is the measurement of motion, and you are measuring the motion of the same entity taking the same path relative to all the other same entities, would the time be the same? Additionally, would there be a finite limit to the repetition of permutations?
The question itself is contradictory. If "two different states of affairs" are, indeed indistinguishable, then you have no evidence that they are indeed two different states.
The assertion of "two" presumes the ability to successfully distinguish.
Contrast this with a claim that two steel balls are indistinguishable. Such a claim presumes that the ball bearings could be observed at the same time, and be counted as being two. And the sameness of the steel balls exists within an assumed context regarding one's tools of examination. Given a microscope, and enough time, one could probably find an identifiable difference on the surfaces of the two balls. But given the naked eye, and a fairly inaccurate scale, the balls would seem identical. Of course, they aren't fully identical, or they would not be two balls, but one ball.
Any similar discussion about "identical states of affairs" requires you be very clear about what you are talking about. For instance, the arrangement of pieces on a chess board could be described as a state of affairs regarding the game of chess. But note that the context of the game of chess deliberately ignores certain irrelevant details, such as in what direction are white's knights (horse-shaped pieces) facing.
Now, if your context is, rather than looking at a chessboard, but instead looking at the whole universe, then that is invalid. The universe as such cannot be observed in toto. Every observer is in the universe.
But, even regardless of that, there's a deeper issue here: the meaning of "same".
Implicitly, the meaning of "same" is what Ayn Rand's Introduction to Objectivist Epistemology is all about. Sameness, as such is only observed by ignoring contextually irrelevant differences. That two things are the same implies that they have some differences which are to be ignored for the purpose at hand. Seeing two different things as the same is what allows us to place them under a single concept, and that's what ITOE is all about.
There is no such thing as intrinsic sameness. It is only in the eyes of an observer that two different things can be considered to be the same. Every observer of the universe is in the universe, and therefore is only aware of part of it.
Questions such as "Is this snapshot of the universe the same as that snapshot of the universe?" are, then, rendered senseless and irrelevant because they rely on the impossible being possible: the ability to step outside the universe, to observe and remember the state of the whole thing, and to successfully compare it with a future state. And, of course, if it's a future state, it's a future state and not the same time.
Things don't really "come into being" or "pass out of being." Macro-level objects can be transformed into other objects, but they don't pass in and out of existence.
The concept of time doesn't "use the rotation of the Earth" for anything. Humans use the duration of the rotation of the Earth as a basis on which to measure time. All measurement is based on comparison to some standard; time is no different.
That's an awfully big leap. I see no reason or basis in reality to say that any given permutation of sequences should repeat.
answered Jan 19 '12 at 01:34