To infinity and beyond

I think it's time we had a philosophical look at the idea of infinity. The concept of infinity isn't an easy one in philosophy. There's more to it than meets the eye. There are even different types of infinities.

For instance you can have relative infinities. The number of odd integers is infinite but it is only half as infinite as the total number integers (both even and odd).

My reason for bringing this subject up is related to the earlier discussion on Richard Dawkins. It arises when discussing the arguments for God's existence wherein the atheist will postulate an infinite series of movers or causes or contingent beings to evade the conclusion that God exists. Some atheists object that we exclude the idea of there being an infinite series as impossible but are perfectly happy to assert that God is infinite.

Let's start at the beginning. St Thomas' argument against an infinite series is a simple syllogism.

If there were no first mover, cause etc (which would be the case if the series extended back infinitely) then there would be no second movers. But there are second movers. Therefore there is a First Mover.

Let me tackle this further. In every case we have a problem. Either it is need of a cause, mover or being that has existence in its own right. This is a need that will not go away until you arrive at (for example) a being that does not itself undergo motion thus not requiring another to put it into motion.

It is not necessarily a matter of going infinitely far back into time either. Causes can be acting simultaneously such as a stack of books each holding the one above up. It is an ontological need that must be satisfied or the self evident principle of sufficient reason is violated.

Let's look at a simple example to demonstrate what we mean. There is a book someone has borrowed. The person they borrowed it from in turn borrowed it from someone else who borrowed it from someone else. Now in order for the current person to have obtained the book there needs to be someone who originally had the book. There needs to be an owner. We can see this intuitively. Expanding the set of book borrowers - even infinitely - does not remove the requirement that such an owner exist to explain how the book made it into borrowed hands. Just as the motion of the hand of a watch cannot be explained by adding an infinite number of cogs. You need to look beyond the infinite set.

The book in my example represents existence. We are all "borrowers" of existence (although obviously not in the sense that we sought it out for we did not exist to do so). None of us has existence in our own right. We are not self existent beings. None of us contains within ourselves the reason for our existence (or anything else in the universe for that matter). Making the set of dependent beings infinitely large does not change the fact the set is dependent and demands just much explanation as any one thing contained within it.

This brings me to the next point I wanted to consider. The nature of the infinity of God. The most important thing to do, as St Thomas himself does in the Summa, is to distinguish God's infinity from two false infinites viz infinite magnitude and infinite multitude (neither of which can exist). Saying God is infinite does not mean he is larger than anyone can measure or older than anyone can count. Rather it means he is free from (is not limited by) such things as size and time. God is existence in it's fullness. He is existence. His existence is unlimited. It is not finite, hemmed in by size for example. It is infinite.