Tuesday, December 11, 2007

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.


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.


Sunday, December 02, 2007

Philosophical Geek Out!

I am currently in the process of reading Aquinas' commentary on Aristotle's metaphysics. It is really an amazing piece of work and the fruit of much thinking!

I am currently on Book V, Lesson 2, in which the discussion on causation happens.

For those that don't know, there are 4 causal modes in Aristotle's Metaphysics within 2 types of causation.

The 2 types are:

1) Intrinsic Causation - That which is generated from within (will give examples of this in a bit).
2) Extrinsic Causation - That which is generated from without (will, again, give examples of this in a bit).

Within Intrinsic Causation there are 2 modes of this type that can be called causes:

1.a) Material Cause - That which gives the matter for a thing to be. For example, a bronze statue has as its material cause bronze. The bronze does not come from without the bronze, but is part of the statue itself. Therefore it is intrinsic.

1.b) Formal Cause (Sidenote, this cause is both an intrinsic and extrinsic cause). That which gives a thing the form necessary for it to be what it is. For example, the form of a statue is from within. The form is that which gives "definition" to the matter, to make the matter knowable to the intellect.

Within Extrinsic Causation there are 3 mods of this type that can be called causes:

2.a) Formal Cause - When a thing is made in the likeness of another thing and thus receives its form from that thing though it cannot be that thing. This type of formal cause is of the imitative sort. To bring us back to our statue example, though within it it has the form of statue, and, let us say, it is made to resemble John Paul II, it receives the form of "John Paul II" from John Paul II, who is exterior to the statue and thus a cause for it to be a resemblance of him.

2.b) Efficient Cause - That which brings a thing to movement or rest. For example to throw a ball is to be the efficient cause of the ball, for its accidental properties (such as placement and movement) are changing. The catcher of the ball is also an efficient cause because he is again changing the accidental properties of the ball and bringing it to rest. In another sense, Efficient Cause is that which brings a thing into being, which involves motion.

There are 4 types of the type "Efficient Cause" which Aquinas gets from Avicenna; Perfective, Dispositive, Auxiliary, and Advisory. I will not go into that for now, but the distinctions truly blow the mind away!

3.b) Final Cause - That which is the sake for why a thing is done. To bring us back to the example of the ball, the ball is thrown in order for the other person to catch it. Thus, the final cause of the ball in that action is to be caught.

Now, within Final Causation, there are 2 distinctions; ultimate end and intermediary end. This is the reason for why I posted this post. The ultimate cause is the ultimate "raison d'etre" for a thing to act. Aquinas would say that the ultimate final cause of man is to spend eternity in loving communion with God. But intermediary final causes are things that are necessary in order for the final end, the ultimate final cause, to happen.

Now, to bring it back to the ball example, it would seem to me that Aristotle and Aquinas (if I recall correctly) would argue that intermediary final causes are infinite in nature.

Let me give you an example from Math. Let us say we have the numeric distance between 1 and 2. Between that finite set is an infinite possibility of division. One could never move past 1 to 2, for they could continually go further and further down the decimal scale.

The same in our ball example. When someone throws a ball, the ultimate end is for the other to catch it. But in order for that to happen, there must be an infinite set of motions within the finite set of the throw and the catch.

This would seem to make sense since Aristotle argued that the universe is what he calls a potential infinite. It is measurable, yet without any seeming point to measure. If we went within the set of numbers between 1 and 2, we could say the same, as if there were no beginning or end, though there is, but from within the set, it would be impossible.

It is interesting how this seems to logically follow from Aristotle's theory of the 4 causes and how this shows up within his discussions later on in regards to the infinite.