Can An Infinite Multitude Exist?

Hello everyone. It’s good to be back and writing regularlyl again for Deeper Waters. We are studying the doctrine of God right now and the Summa Theologica of Thomas Aquinas. Those who do not have a copy can go to newadvent.org and read one there. Right now, we’re studying the infinity of God. We’re going to close up that topic tonight but first, prayer requests. First, I ask for prayers for my Christlikeness. Today has been a good day and I’ve got a good friend who’s working with me on a lot of issues especially in relation to my third prayer request. Second, for my financial situation. Third, for the area in my life related to both of these. For now, let’s get to the question.

Can an infinite multitude exist? Does there seem to be anything inherently impossible about the concept? After all, we can think of the adage that there is one angle at which a man may stand straight and an infinite number by which he may fall. When we say that, are we not making a truth statement? If we say the possibilities are endless, are we not pointing to an actual infinite?

This is done with math also. We can multiply numbers by infinity and we have all sorts of fun word games involving infinity. There is, for instance, the hotel with an infinite number of rooms and they clear out all the people who are in even numbered rooms and there’s still the same number of people in the hotel.

This is the point where we have to realize that because we can imagine something, that doesn’t mean it can be actualized. This is a situation I wish skeptics would realize concerning the Problem of Evil. So many think they can imagine all of these perfect scenarios where evil would not happen. Well you can imagine it, but that does not mean that those scenarios can be actualized.

Of course, as soon as we’re talking about created realities, Aquinas again says that these are limited by matter. They can be comprehended for they are made by their creator for a purpose. Since they are limited, they cannot be infinite. Now Aquinas has no problem with a potential infinite, but he does have a problem with an actual one.

What does all of this have to do with anything? I think for one thing, this will be important when we come to the question of God’s knowledge, which is a future topic. I’ll just try to whet your appetite a little bit here with the idea of “Does God know an infinite number of things?” This question will bear a relation to that one.

Furthermore, this helps us understand the nature of infinity. When we understand that better, we can understand God better for God’s nature is infinite. Yes everyone. Studying mathematics can help you come to a better understanding of God. All truth is God’s truth and the more we learn, the more we can come to know our God.

We shall start tomorrow on the existence of God in things.

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 newadvent.org. 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.

Is God Alone Infinite?

Hello everyone and welcome back to Deeper Waters. First off, I want everyone to know there might not be a new post for the next few days. I’m moving again and I’m not sure when I’ll have internet access. If you come here for awhile and there’s no new entry, don’t panic! I assure you I want to get connected back to the internet world as soon as I can. Now our topic tonight will be still the infinity of God. Our guide is the Summa Theologica of Thomas Aquinas that can be read at newadvent.org. First, I ask for prayers however in my Christlikeness. Moving does put me under some stress and probably really tries my character as well. Second, I ask for prayers for my finances. Third, I ask for prayers for the related area in my life.

Tonight’s question is if anything can be infinite besides God. One objection to look at is that God has infinite power and the power determines the effect. If the cause is infinite, then ought not the effect be capable of being infinite? If there cannot be another infinite thing, maybe it’s because God’s power isn’t infinite?

To begin with, let’s remember that infinite is simply a way of saying not finite. Now Aquinas does believe in a relative infinity. For instance, take a piece of wood. This piece of wood could be made into a limitless number of objects. However, by virtue of it being wood and of it being material, it can only have one form at a time. The wood will not be both a bed and a table. Now you could use a bed as a table or vice-versa or maybe find some mix, but I’m using a bed as a bed properly understood and the same for a table.

God is uniquely infinite because of, and we should all know by now, his simplicity. His being is not received into anything else and it is subsisting being alone. Because of that, it cannot be contained by any form. As was said earlier, form can limit matter and vice-versa. There is a possible difference with angels as they could be relatively infinite, however, they are not their own being and have been determined to have the form that they have.

This is the problem with the objection as well. A thing cannot be its own being. It is a combination of being + existence and thus is in some way limited. If it is limited, it cannot be infinite. One important point to note here is that Aquinas says that God cannot do something contradictory, which would be making here something that is finite and infinite both. In fact, this is the answer Aquinas would give to the question of “Can God create a rock so big he can’t lift it?” There is nothing new under the sun.

God alone is infinite and he is infinite in all that he is. Of course, we haven’t got to all that he is yet, but as we go further through this study, we will come to appreciate why Aquinas goes through in the order that he does.

We shall continue this next time.

Is God Infinite?

Hello everyone and welcome back to Deeper Waters. We are diving into the ocean of truth and learning what we can about the doctrine of God. Our guide for this is the Summa Theologica of Thomas Aquinas. Those of you who do not have a copy are free to go to newadvent.org and read a copy of the Summa online. First, I wish to offer my prayer requests. I ask first for my Christlikeness as I’m noticing a number of attitudes that I seem to have that I don’t wish to have and I’m asking the divine surgeon to remove those from me. Second, I ask for prayers for my financial situation. Finally, I ask for prayers for the third related area in my life. For now, let’s get to tonight’s question.

Is God infinite? Thus, we begin our study of the infinity of God with this one and since we’re studying the infinity of God, it must follow that God is infinite for Aquinas. However, like any other great medieval philosopher, he will be answering the question first. As I’ve stated earlier, the medievals did not simply take things on faith. They analyzed their arguments.

The objections largely come from Aristotle. Aristotle said that everything that was infinite had parts and matter. However, it was shown earlier that God has no parts and no matter. Therefore, it cannot be the case that he is infinite. Second, infinite is related to quantity, but in God there is no quantity. He does not possess X amount of something. Therefore, God cannot be infinite.

One aspect to keep in mind is that to say God is infinite is really to exclude him from the category of finite things. We cannot comprehend the infinite. For the medievals, this was the via negativa way of understanding God. It is that we realize how different God is from the creation and we largely know more about what God is not than about what he is.

Aquinas says that the ancients did think the first principle was infinite, but they thought matter was the first principle as well. They assumed that it must be a material infinite and that an infinite body must then be behind all things. Aquinas has already argued however that there is a first principle, vis a vis the five ways, and through the argument of simplicity has shown that he is free of matter.

However, Aquinas says that any form is limited by the matter that it takes. In turn, matter is made finite by the form it receives. Matter has the potential to be many things but once it receives a form, it is terminated by that form as it were. Once matter clings to my form, in a sense, it is limited to being me if it must be something.

God however has no matter to him and his form is being. His being is also not received in anything, which is what is important as well about the argument we looked at last night, and is therefore not limited in anything. The conclusion that Aquinas reaches then and rightly so is that since God is not limited, he is without limits, i.e. infinite.

We shall continue tomorrow.

Are All Things Good By The Divine Goodness?

Hello everyone. It’s good to see you back here at Deeper Waters where we dive into the ocean of truth and if this is your first visit, welcome aboard. I hope you’ll be a regular. We’re studying the goodness of God and we’re going to wrap that up tonight. Our guide has been the Summa Theologica of Thomas Aquinas. You can read it online at newadvent.org. Before that however, I ask for prayer requests. First off, I ask for prayer for my Christlikeness and realizing what I really need to spend my time thinking on. Second, I ask for prayers for my financial situation. Finally, I ask for prayers for a third related area of my life.

Are all things good by the divine goodness? This is an interesting one because I think for most of us, our first inclination is to say “Yes.” However, as I examine this question, I can see why Aquinas actually says no to this. Of course, he does clarify that no, but I believe in the way that he answers that he is wanting to avoid having a pantheistic belief.

For instance, let’s suppose that all had not their own being, but simply the divine being. In that case, they would in fact be included in the nature of God, which is something that Spinoza would have agreed with. The being that you and I possess in that case would of course be the divine being as we would not have any being outside of that being to have.

If that is the case, then why do the same with goodness? If all we have in us is divine goodness, then we do not have any goodness of our own. If we do not have any goodness of our own, then we do not have any being of our own. Our being is not ours, but is simply the divine being in us. We are not pagans however. We realize that we are not God.

Now I said that Aquinas does qualify the answer. He does say that we are good by the divine goodness as the exemplar cause. That is the cause after which something is. We could only have goodness if there was a divine goodness that our goodness was based on just as we could only have being if there was a divine being that our being was based on.

This is important because my being is my own. I am a human being. I am not an angel being. I am not a God being. I am not a dog being or cat being. I am human. I need to be that which I was meant to be. Humans are not meant to be angels and we’re not meant to be animals and we’re not meant to be God either.

Too often, we tend to move in such a way. We tend to act like animals in our morality often. Some of us in the Christian world try to act like angels in a bad way, in that we think the material world doesn’t matter. Now angels don’t really think that I believe, but we think its angelic to focus solely on spiritual matters.

We are humans. We are part material and part spiritual. We have a body and a soul. It is our being and it is a gift from God. We need to embrace it. Let’s pray the prayer of Soren Kierkegaard. “And now Lord, with your help, I will become myself.”

We shall start discussing the infinity of God tomorrow.

Is God Alone Essentially Good?

Hello everyone and welcome back to Deeper Waters where we continue diving into the Ocean of Truth. We’re going through the Summa Theologica where we are studying the doctrine of God. For those who do not have this fine work of Thomas Aquinas, you’re free to go to NewAdvent.org. We’re right now studying the goodness of God. Before we begin, I wish to present my prayer requests. First, I ask for prayers in Christlikeness and I have seen the change again as I am working on overcoming some inhibitions and embracing all of life as Christ would have us do. Second, I ask for prayers with finances. Finally, I ask for prayers in a third related area in my life.

Is God alone essentially good? Aquinas has some objections to this. First off, haven’t we said goodness is just another way of understanding being? If goodness and being are really the same, then it seems that all beings are essentially good simply by virtue of the fact that they are beings.

Also, if good is what is desired, then the being of each thing is its good. However, everything is a being essentially, therefore everything is essentially good.

Finally, if something is not essentially good, then its goodness must come from something else. However, we cannot have an infinite regress and in order to do that then, we must have everything be good essentially.

I hope astute readers who have been paying attention to our doctrine of being thus far are already making the connections and seeing the problems.

Aquinas of course says that to God alone belongs the property of being essentially good. After all, God is the ultimate perfection and there is nothing lacking in him and he is goodness by his very nature. Of course, some of you might be wondering what is the answer to the objections. Why aren’t all other beings the same way?

The objections are ignoring that God alone is not just essentially good but essentially being. God is what we call a necessary being. It is impossible for him by nature to not be. If God was not, nothing else would be. This is one reason good metaphysics is so important. When you understand more of the doctrine of being, you see why the existence of God is so important and how nothing else exists necessarily by its own nature.

This is also why Spinoza can be seen as a challenge to Aquinas as he equated God with the universe and had everything necessary. Of course, I believe the Thomistic thought can triumph over Spinoza, but it is still a challenge that we ought not neglect. Every philosopher should rise to defend the philosophy that he embraces.

Thus, we conclude that other beings aren’t beings essentially but beings by participation. In the same way, they are not good essentially then but good by participation. Insofar as they have being, they are good essentially, but that being that they have is not essential but contingent. The answer to the third objection should be obvious then. You end the infinite regress by a being who is good essentially and not by participation, namely God.

We shall continue this doctrine tomorrow.

Is God The Highest Good?

Hello everyone and welcome to Deeper Waters. Tonight, put on your scuba gear again for we are continuing our plummet into the ocean of truth. We’re going through the doctrine of God and we’re talking about the goodness of God. Our guide on the journey is Thomas Aquinas using his Summa Theologica. A copy of that can be found at newadvent.org. I wish to offer my prayer requests before we begin. First, I ask for prayers for my Christlikeness. I have found I tend to be self-conscious lately, when I need to be other-conscious, especially Christ-conscious. Second, I ask for prayers for my financial situation. Finally, I ask for prayers for a third related area in my life to both of these.

Our question tonight. Is God the highest good? One objection will be that goodness seems to add something to God, but God is simple as has been shown. However, if we say he is good, then have we not added this to his being?

What about goodness being included in a genus? Doesn’t that put God on the comparison level? Are we not then saying that God can be compared to other things? All we have going on is a comparison game.

Basically then, we’re coming back to simplicity and asking if this goes against the simplicity of God. Of course, Thomas is going to say no and the way he explains this is by telling how we do God-talk properly.

One way we can talk about anything is univocally. If I say that my Dad is a man and I say that I am a man, I mean man in the same way. Now we are different men, but the idea of man hasn’t changed meaning. Whenever you use a word and it has one meaning throughout, that is univocal language.

The second way is equivocal language. Equivocal language would be like saying “I am going to deposit my money in the bank” and “I am going to go by the bank of the river.” Bank in that sense means two different things. Thus, equivocal is when you use the same word and it has two different meanings.

The last way is analogical language. Imagine writing out on a sheet of paper “2 + 2 = 4.” Now you can say “I see that” and when you say that, you mean you see the proposition written on the sheet of paper is visible to your eyes. However, you could also say “I see that” and you mean that you see with your mind that 2 + 2 = 4. See has different meanings, but there’s also a similarity to them, which is what analogical language is.

That’s how Aquinas answers the objection. God is a greater good not by degree than we are but by kind. You cannot add more and more goodness to us and get the goodness of God. This is something we need to realize. God is not a superman. You do not take our qualities and add them up and lo and behold, there’s God! He is altogether unique. Thus, he is the highest good not by comparison but by degree.

Also, goodness does not add to being. Goodness is a relation. We say God is good not in the sense that goodness is added but that he is what goodness itself depends upon. In the same way, God is knowable because the existence of knowledge is only possible because there is a God who exists.

Thus, we start to see more as we go along why simplicity is so important and why Aquinas started there. We shall see more of why he’s taken the route he has in the Summa as we continue tomorrow.

Is God Good?

Hello everyone and welcome back to Deeper Waters where we are once again taking a plunge into the ocean of truth. We’ve been studying the doctrine of God and the Summa Theologica has been our guide. Those who do not have ready access to a copy of the Summa can find one at newadvent.org that can be read online, although I have no objections to readers going to Amazon and buying a copy. Tonight, our question starts the chapter on the goodness of God. Before we get to our question, I wish to present my prayer requests. First off, I ask for prayer for my growing Christlikeness. Special people in my life are showing me great ways to improve. Second, I ask for prayers for my finances. Third, I ask for prayers for a third related area in my life. Now, let’s get to the question.

Is God good? As I prepare to write about this question, I wonder how many readers might be surprised to find out that the medievals actually asked this question. Some of us could say “Well it’s in the Bible that he is.” The medievals knew that, but they wanted to be able to demonstrate what they could apart from the Bible as well, particularly when dealing with those who did not accept any divine revelation.

But the question still remains. Aquinas of course answers in the affirmative and says that indeed God is good. This is because each creature that is out there seeks its own perfection. Everything is good according to its desirableness and everything desires its own perfection. Any effect that is perfect bears a likeness to its cause and so its cause in its perfection must be great. God as the first cause is the cause of goodness in all other things and he being the perfect one is good above all.

There is an objector however and he wants to know that if God is good because he is what all desire, then what of those who do not know God? What about those who even deny his existence? Are we going to say that they’re desiring God?

Aquinas’s answer?

Yes.

They desire God in that they desire their own perfection and that perfection can only be found in God. We would speak of seeking the transcendentals. I have said before that if someone is truly seeking the good, the true, and the beautiful, they will eventually find their way to God. It is not enough that they seek a thing that is good, true, or beautiful. They must seek that which is the cause of goodness, truth, and beauty.

When the atheist searches like this, they will find their way to God. Of course, in our world, it’s becoming more and more common to deny the existence of all three of these. Beauty has been one to go as we say that “beauty is in the eye of the beholder.” Moral relativism is removing goodness from us. Today with the postmodern movement, there are many who are questioning the existence of objective truth and if we can even know it if it exists.

What will happen when our society loses all sense of these? I don’t like to think about it. I don’t think it can happen entirely however. I don’t think anyone can live in constant denial of the good, the true, and the beautiful. As soon as you choose to do anything, you admit a goodness exists. Even if you choose suicide. You choose that because you think it better than other options.

Nevertheless, our society needs to return to embracing these three.

We shall continue studying the goodness of God tomorrow.

Is Goodness Rightly Divided?

Hello everyone and welcome back to Deeper Waters where we are diving into the ocean of truth, particularly in our study of the doctrine of God. Our guide for this study has been the Summa Theologica of Thomas Aquinas. An online version of it can be found at newadvent.org. In our study, we are discussing goodness itself. Before we get to tonight’s question, I’d like to share my prayer requests. First off, I ask for prayers for my personal Christlikeness. I am becoming more aware of how fallen I am regularly. Second, I ask for prayers for my finances. Finally, I ask for prayers for a third related area in my life. For now, let’s get to the final topic in goodness itself.

When Aquinas asks if goodness is rightly divided, he wants to know if it’s rightly divided into the beneficial, the useful, and the pleasant. If the appetite is moved towards something that is meant to serve as a benefit to something else, then Aquinas says that that is what is called the useful. The thing that is sought after for its own sake and not for anything beyond itself is called the befitting. That which is sought after that ends in rest of the thing desired is called the pleasant. Naturally, with the last two, there can be some overlap.

I find this question interesting because just yesterday, I had someone asking me if goodness and pleasure were the same. I think an excellent read on that for a questioner is the Philebus of Plato. However, I hope that person comes to this blog tonight because we will naturally be looking at that question.

Let’s consider the category of the useful. An excellent example of this is money. Some people might like a lot of money as a status symbol, but generally, money is good for what it can do for you. It’s the reason we have things like cars. It’s good for what it can do. I’m thankful my apartment has heating this time of year because of the good that I can get from that.

The beneficial is that which is desired for its own sake. For Aristotle, this was happiness mainly. Everyone desires happiness for its own sake and not for anything beyond itself. When we get to the medieval thinkers, we find that they sum this up in the beatific vision. This would be when you died and you got to see God as he is. Once you see God, all your questions are answered.

Tomorrow, we shall begin covering the goodness of God.

The pleasant is that which we long to rest in. Romantic love is an excellent example of this. When someone loves someone of the opposite sex, they long to rest in the embrace of that person. One wishes to embrace the goodness simply to embrace it and not for any other reason. People work so they can play. They don’t play so they can work.

All of these are proper ways in which the good is understood. We as Christians should learn to seek these out and treat them rightly. For instance, we should be careful in that we don’t treat something good in itself as just something merely useful. Don’t treat the guy who checks you out at the grocery store as an object for instance. He’s a person as well.

Is Goodness In Limit, Species, and Order?

Hello everyone and welcome back to Deeper Waters where we are diving into the ocean of truth. We’re studying the doctrine of God now and right now, we’re studying goodness itself. The Summa Theologica of Thomas Aquinas, which can be read at newadvent.org, is being our guide on this journey. Before we start looking at tonight’s topic, I wish to present my nightly prayer requests. The first is my prayer for Christlikeness to which I’ve come to realize today that there are some things that you don’t have to have absolute certainty on, and that’s fine. Second, I ask for prayers for my financial situation, which does seem to be improving. Finally, I ask for prayers for a third area in my life. For now, let’s get to the question.

These kinds of topics we’re talking about relate to the created order. God is without limit, he has no species, and he does not have order. To begin with an interesting study, let us consider the topic of angelology. When we think about angels, there are two mistakes we can make. We can give them no heed and treat them like they don’t exist, or we can make them be everything.

Aquinas did do much thinking about angels. He was and is called the Angelic Doctor. Angels by their nature are immaterial creatures. They consist of form + existence. We as human beings do have a soul that is a form, but we are also differentiated by the matter that we possess. The matter in my body is not the same as the matter in your body. Matter cannot be in two places at once.

However, angels cannot be differentiated in this way because there is no matter to them. Thus, the only way they differ is by form. Because of this, two angels cannot have the same form. There is not an angel nature that is shared by many angels, although the nature they share can be similar. You and I can share the same human nature because we are differentiated by matter.

Because of this, each angel is its own species. As Peter Kreeft says, “When he made Michael, he broke the mold.” There can be no other, and for this reason Christ does not die for angels, for he would have to assume angel nature somehow and then he would have to die in the place of the angel, which could not happen since angels cannot die anyway.

But for us, these are good things. There is limit to the creation. There are various species. There is order. God has set the boundaries whereby the universe is to be and we are meant to play our part in that.

What does this say for us today on an applicational level. God made us to be who we were meant to be. Now we are fallen, but he is shaping us into the likeness of his Son. Romans 8:28-29 makes it clear that we will be conformed. It is a guarantee. Who we are is good and God has made us to be like his Son.

We shall continue tomorrow.