Can The Past Be Infinite?

I had an interesting conversation about the nature of time today with a friend. I also just saw a post on a blog about the possibility of the infinite nature of time. This got me thinking about things a bit, and so I would like to do a bit of philosophical exercise which may stride on into a theological exercise.

Definition of Terms

Infinite - When I use the term infinite, I use it in the Aristotelian sense. Now, Aristotle uses two possible ways in which the infinite can exist, as a potential and as an actual. Aristotle argues that an actual infinite cannot exist, but this shall not be dealt with here. My concern is with the potential infinite. A potential infinite is said to be something that is measurable, but is unable to get to the end or beginning, or both, of a set.

For example. Let us take a number set between 1 and 10. Everything within that finite set of numbers (1 and 10) is infinitely divisible. It is not possible to reach a limit in divisibility. No matter how hard you try, it will never get to an end. Once you are "within the set", it can be potentially impossible to get to the end, for there is a potentially infinite series of numbers that one would have to "cross" in order to get to one. A potential infinite is also measurable, no matter how small it is.

Time - That which is the current state of reality in the present.

Discussion

St Augustine famously said "if you ask me what time is, I don't know what it is, but if you don't ask me, then I know". He is also famous for his discourse on time. He states that the past and the future are not real, for they no longer are in existence, but have ceased to be, or have not come to be. The only time that exists is the current moment. This leads to a very interesting view of reality itself, but I shall not get into it.

My question, though, is whether or not the past can be infinite in a potential manner. If Augustine is right and it no longer exists, then the question is pointless to ask for it makes no sense to talk about a reality that is no longer in existence.

However, and this is where philosophy and theology tango, Christ brings an interesting perspective into the idea of time. The infinite (in an actual and real sense, not in a potential sense) comes into contact with the finite, all in the Incarnation. As Ratzinger says, time and eternity are united. If this is the case, that eternity and time come into one contact, then it brings a sense of the eternal into the temporal world and a sense of the temporal world into eternity. This is a logical implication of the Incarnation.

Now, that means that each moment of existence, because of the Incarnation, is touched by the eternal and so, in a certain sense, is grafted to eternity to become an ever present reality. Thus, and I hate to say this, I think Augustine is wrong in his understanding of time because of the understanding of the Incarnation. I would like to point out that I am not giving a complete description of how time and eternity (that is, all instances of time) become eternal because that involves a much deeper understanding of the Incarnation that I wish not to get into at the moment.

My point is, though, that the past takes an a certain eternal character, which means it exists forever, as an everlasting moment, just as every moment in time, because of the fact that eternity and itself have been grafted to each other. Now, this gets me into the nature of the past as at least potentially infinite.

Taking my example from the definition earlier of a finite set that has infinite divisibility, I can apply this to time. Let us say that the set of the past is the total moments from the first instance in time to the present moment. If we look within that set, there is an infinitude of moments in which we can examine, breaking them down more and more into more minute moments. Thus, since the past is nothing more then a finite set of moments, and a potential infinite can be examined within that set, it makes sense to say that the past is, in a certain sense, infinite in the order of potentiality.

-Harrison