Can A Magnitude Be Infinite?

Hello everyone and welcome back to Deeper Waters! I see that we’ve had readers come to the blog while I’ve been away which is good. I will give warning however that I am thinking my grandmother in another state is likely to pass away soon. If that happens, I will be going out of town and not posting then so if you don’t see any posts consistently again soon, you’ll know what has happened. For now, let’s continue our study of the doctrine of God using the Summa Theologica of Thomas Aquinas. That can be read at Before getting into that however, I wish to list my prayer requests. First off, I ask that you all pray for my Christlikeness. I am in the crucible as it were I believe and it is a painful place, but I expect to shine when I come out. Second, for my finances. Third, for a related area in my life to both of these. For now, let’s get to tonight’s question.

Can a magnitude be infinite? Thomas says no. This is a topic tonight that is largely mathematical and this brings out an important distinction. Mathematics does not depend on matter for its existence. However, matter is needed to understand its existence. You can imagine a triangle easily enough, but for real triangles to exist, there must be matter.

In math, something can be potentially infinite. Picture the number line. You can always add one more to whatever number you’re thinking. However, there will never come a point where you will add one number and say “Ah! I have reached infinity.” We can think about infinite numbers in idea, but I do not believe they can exist in actuality.

Aquinas also says that this is because of matter as well. Matter is a limiting principle to a thing and if a thing possesses matter, then it is by nature limited. If something is limited by something external to itself, then it can in no way be infinite. Magnitude is a measure of quantity and matter and so in that case, something cannot be an infinite magnitude.

What about geometric figures? It’s when we look at this that we can begin to appreciate also the deep education of the medieval period as Aquinas can talk about many areas of knowledge in his studies. He says an infinite body will not work in a straight line because nothing moves naturally unless it is out of its place, but if something was infinite, it would be in every place.

Why not a circle? It could not be since a circle requires that would require that the body move to a place that had already been occupied by another part. However, a circle has lines drawn from the center and thus two spots would be an infinite distance apart and thus one could never reach the other place.

Yes. It’s complicated.

Why is this important? Aquinas is showing that God alone is infinite and that he does not have a body. Mathematics is not the enemy of Christianity nor is any other branch of learning and the sooner Christians learn that, the better off they’ll be. We can enter any area of study without fear.

We shall continue tomorrow.

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