We also noted that Zeno's paradoxes are epistemic paradoxes of conflict between reason and sense-experience.
1. Aristotle's Time Paradox. Regarding Time, he writes in his Physics,
"the following considerations would make one suspect that it either does not exist at all or barely, and in an obscure way. One part of it has been and is not, while the other is going to be and is not yet. Yet time-both infinite time and any time you like to take-is made up of these. One would naturally suppose that what is made up of things which do not exist could have no share in reality."
In other words, Aristotle is stating that something cannot be made up of nothing. But, when one thinks of time, the past is not there and the future is also not there (is still to come); the present itself is gone before we can talk of it; so, if none of its parts can be said to exist at the time they are said to exist, time is made up of non-existent parts; however, non-existent parts make a non-existent thing, something that doesn't exist.
2. John McTaggart's Unreality of Time Argument. In his 1908 essay, "The Unreality of Time", McTaggart argued that time must be unreal. According to him, positions in time, as they appear to us can be identified as either "Past, Present, and Future" (A-Series) or "Earlier and Later" (B-Series). For something to be earlier, it must always exist as earlier. For something to be later, it must always exist as later. Earlier can never become Later since Earlier is always Earlier. But, if this is true, then one event cannot change into another, because M (Earlier) has to be M always and N (Later) has to be N always in their positions in time. However, if one adds the Past-Present-Future order to this, then an event in the future becomes an event in the present and an event in the present becomes an event in the past; thus, one event changes into another. But, the problem is that in order to be able to talk of an event as an event that is present, that will be in the past, and that was in the future, one must already pre-suppose the reality of Past-Present-Future (i.e. the A-Series); otherwise, "will be" and "past" are incompatible, "was" and "future" are incompatible; one can only speak of was (past-tense) and past, is (present-tense) and present, will be (future-tense) and future. In order to say that an event is "present in the present, future in the past, past in the future" one must already presuppose the A-series to account for such speaking; but, this is question begging. However, if the A-Series cannot be established, we have already seen that the B-Series is contrary to our perception of time. To reject the A-Series is to reject the reality of time.
B-theorists reject the A-series of Past-Present-Future and, as in eternalism, consider events to just be there without any flow of time or change. Events are fixed as Earlier and Later. The B-theory tries to bridge the rational-empirical chasm by trying to retain immutability at the expense of unity for the sake of pluralistic realism; but, this is half-way logic. This may allow a tense-less universe to exist. Our experience of past-present-future is an illusion; in reality, they say, events just are; they don't happen. While there are some who think that this view has the support of the theory of relativity's rejection of absolute simultaneity (at least, as far as perception is concerned), the theory of relativity doesn't reject the notion of happening; an event is an happening; at least, happenings (motion, shrinking) are presupposed for the theory of relativity to be. But, if an event is a happening, and "happening" implies "change", then B-theory cannot actually talk about events, it must only talk of the universe just there. But, if B-theory cannot talk of events, what is it talking about? One may respond by saying that an event itself is composed of event-parts; however, aren't those event-parts (events in themselves) infinitely divisible into a Former and a Later. In such case, they must still first resolve the mereological paradox: Each part is divided into a former and a later part. Each former and the later part have a former and a later part of their own respectively, and so on ad infinitum. Thus, the size of the part would be zero and unlimited, which is paradoxical. Ted Sider's Stage Theory to explain temporary intrinsics or change tries to resolve the contradiction of stages other than S existing, but S itself possessing the temporal property of "I myself will be bent" (of futurely being bent by virtue of having a temporal counterpart tomorrow that is bent). I don't see how such a property makes S continuous with its supposed other stages. It does not explain how is it that the counterpart is bent "tomorrow". "Will be" of McTaggart's A-series brings us back to his original problem, I think. The B-theory has taken recourse to tenses, which cannot be avoided when one talks of time.
To say, for instance, that one can conceptualize t (e.g. July 12, 2015) is a set of x events, so that if trans-temporal vision was possible one could see x events happening at t is not enough; because, this doesn't repeal the fact of "happening". The only resolve would be to divide t into more parts, and so ad infinitum, in which case, by means of infinite rationalization of reality, one is logically compelled to deny the authenticity of phenomenal experience. Ultimately, such rationalization will only support some rational cosmology.
The eternalist view may appeal to those who may find in it some sort of explanation of how God knows the future before it has come to pass. But, again that would mean attempting to interpret God in temporally conceptual terms that are disputable. One can say what this may mean from the rational point of view and what it may mean from the empirical point of view, and perhaps use a via negativa method of speech to recognize what foreknowledge is not. However, attempts to logically explain divine foreknowledge would be like attempting to empty an ocean into a small hole. Mathematics may help us arrive at necessary, universal, mathematical principles; but, these mathematical principles are not divine attributes. And, when it comes to empirical concepts like knowledge, perception is limited by finitude.
Perhaps, among the many purposes of philosophy is also to help us recognize our epistemic limits. In the ultimate sense, temporal beings still don't have the objective vision of what it means to be trans-temporal. Then, how can they make a judgement about the nature of time? The antinomy of temporality is unavoidable. But, this doesn't mean that from their perspective they are not able to tell what at least time is not.
Check: W. L. Craig on A and B theories
See Also:Space as Non-Reality, Zeno's Arguments
Modified Feb 20, 2016.