Does the following argument involve a fallacy?

Question

Does the following argument involve a fallacy? Or does it not? If you think it does, which might reasonably be construed as the fallacy in this argument?

There are several theories of cyclical time in the literature. Consider this one: ‘The cyclical theory of time claims that each particular state of the universe will, after an enormously long, though finite period of time, occur in exactly the same way in which it has already occurred an infinite number of times in the past. […] In other words, cosmic history may be regarded as an infinite series of identical cycles: what is happening now has happened already an infinite number of times in the past and will happen again an infinite number of times in the future.’
Is there any reason to believe that this theory is false? Probably not. To begin with, its truth is logically possible. Secondly, no evidence can be adduced against this theory: because the cycles are enormously long we have no hope to survive till the next cycle so that we might check whether it is identical to ours or not. These considerations lead one to believe that the theory is true.

(a) denying the antecedent (b) the black and white fallacy (c) ad ignorantiam (appeal to ignorance) (d) no fallacy

Answer 1

In order to argue, we need a basis to start from. If we start from present science, then the theory is untenable. Already a bunch of some hundred radioactive atoms will never act in a determinsitic way because for instance the time of decay of a single atom is not determined by so-called hidden variables but is subject to probabilistic behaviour.

The existence of unknown deterministic causes (so-called local hidden variables) determining the fate of an atom has been excluded theoretically and experimentally by quantum theory. The key-word is Bell-test experiments conducted in the 1980 years. A pair of particles (electrons or photons) is prepared in a so-called entangled state. Then the spin or polarization of each particle is separately measured. The results show a correlations that cannot result from a preceding state where each particle has a fixed spin or polarization, decoupled from the other particle.

So we have to accept probabilistic behaviour which never can reproduce identical states of a bunch of atoms, let alone of the whole universe.

And an answer for religiously motivated people: Wouldn't it become very boring for God if the same old way repeated over and over again?

Answer 2

The theory itself can be reasonable, but it needs further premises to justify it. The argument itself is certainly fallacious, however that does not mean that the theory is. The biggest issue I see with this discussion is the following phrase: "no evidence can be adduced against this theory: because the cycles are enormously long we have no hope to survive till the next cycle so that we might check whether it is identical to ours or not".

The above phrase is an appeal to ignorance, as has been mentioned in the comments: just because we can't (or don't) know that it is not true, doesn't mean that we can be in any way sure that it is true. Additionally, the theory itself has not been presented in its entirety. The position might be a direct consequence of the theory, but it has not been shown to be so you have a jump in logical reasoning as well.