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- [00:01]
A
Welcome to Defenders, the teaching class of Dr. William Lane Craig today the Doctrine of God Part 3. For more information and resources from Dr. Craig, go to reasonablefaith.org we're studying the attributes of God, and the first of God's infinite attributes that we've turned to examine is God's aseity or self existence. And we saw last time that a robust understanding of this attribute implies not simply that God exists independently of everything else, which would in itself be remarkable, but even more fundamentally that God exists by a necessity of his own nature. So that if it's even possible that God exists, then it follows that God necessarily exists and therefore God's aseity entails or implies two further divine attributes, namely God's eternality that God is permanent, he never came into being, will never go out of being and second, God's necessity that he is a being whose non existence is impossible, a necessary being. Now in contemporary philosophy this is usually expressed by saying that God exists in all possible worlds. But that seemed to be a problematic concept to some in the class last week, and it shouldn't be. This is meant to be simply a heuristic device, not a piece of serious ontology. Thinking of possible worlds is simply a way of saying that if something is possible, then that means there is a possible world in which that thing exists. And if something is necessary, then it exists in all possible worlds. But I've been reading a book lately by the philosopher Bob Hale entitled Necessary Beings. Hale is a secular philosopher, very brilliant, and this is a study of necessity and necessary beings. And the way Hale explicates necessity can perhaps be helpful to those who don't find the talk of possible worlds helpful. Hale says that something is absolutely necessary if it would be the case, no matter what else were the case, no matter what else might be the case, if something would still be the case, then that thing is absolutely necessary. So he says, you can fill in this shema, if blank were the case, then blank and you can fill in what you think to be a necessary truth. So for example, if blank were the case, then 2, 2, 4, and if 2 plus 2 would equal 4, no matter what you put in this blank, then 2, 2, 4 is absolutely necessary. So what I'm suggesting is that the proposition God exists fills this blank, and no matter what you put in the other blank, this statement would still be true. If the world did not exist, or if it were the case that the world did not exist, then God exists. If it were the case that there were no people, then it would be the case that God exists. So the proposition that God exists is absolutely necessary in the sense that no matter what else might be the case, it would be the case that God exists. So this is the notion of God as a necessary being. Now, this notion of God as a self existent being and the source of all reality outside of himself faces a very significant challenge from a philosophy called Platonism. Platonism holds that there are objects that are equally uncreated and eternal and necessary. So that God is not the sole ultimate reality. In fact, he's just one of an infinite number of uncreated, eternal, necessary beings. And the paradigm example of the objects that Platonists are talking about would be mathematical entities, mathematical objects like numbers and sets and functions and so forth, the sort of things that mathematicians talk about. Now, this raises the very interesting question, do numbers really exist? What do you think? Do you think that numbers really exist? Now, let's be sure we understand the question. We all recognize that numerals exist. For example, this is the numeral 2. But there are many different kinds of numerals. For example, here's the Roman numeral for two. And they both express or represent the same quantity. So we're not asking, are there numerals? Obviously there are numerals. We're asking, do numbers themselves exist? And I remember coming up from my office when I first began to study this and asking, jan, what do you think, honey? Do you think the number two exists? And we would discuss it over lunch as to whether that there was such a thing as the number two. Well, Platonists say, yes, that in addition to these numerals or these marks on the whiteboard, there's such a thing as the number two. So if I have two apples on the table, not only are there the two apples, but there's also the number two. So there's really three things. Well, there's actually an infinite number of things because there's one as well, right? And one plus one and two plus one and so forth. But you get the idea that there's not just concrete objects like chairs and apples and people and planets, and there are these abstract objects like numbers. And these objects are thought by the Platonists to exist just as robustly as concrete objects. Numbers on this view, are just like automobiles, only eternal, necessary and uncreated. But they exist just as robustly as automobiles do. And so the question is, do these sorts of objects really exist? If they do, they would typically be thought to be uncreated, eternal, necessary things, not things that are created by God. And So this would compromise God's role as the sole ultimate reality. It would not be true, as John 1:3 says, that through him all things came into being and that God is the source of all being. So let's take a look at a PowerPoint of alternatives discussing this subject. Now don't be overwhelmed by this PowerPoint. We'll pick it apart piece by piece so that you can appreciate what it says. Notice that we're taking mathematical objects as our point of departure. We could have picked other kinds of abstract objects like propositions, possible worlds, properties and so forth. But mathematical objects supply the clearest example of what we're talking about. Things like numbers. And notice there are three positions with respect to the existence of numbers. There is realism which says that these things exist, that there really are such things. On the other hand, there is anti realism which denies that these things actually exist. And then in the middle is a realism which says this is a meaningless question. There just is no fact of the matter about whether they exist or they don't exist. This is just meaningless. And there are some a realists today. Now taking a realism. First, an example of an a realist position would be so called conventionalism. This was a philosophy that was popular during the 1930s and 40s and it was based upon the verification principle of meaning. According to that principle, any statement that could not be verified through the five senses was a meaningless statement. It's a sort of scientism that attempts to dismiss vast tracts of human language as cognitively empty because these statements can't be empirically verified. And sentences like ethical statements or mathematical statements can't be empirically verified. These are about abstract objects, if they're about something at all. And therefore these sorts of metaphysical questions were regarded as meaningless. It's just a convention that we adopt in order to make science work and get along in society. But there isn't really any truth or falsity about whether or not the number two exists. It's just a convention which is arbitrarily adopted or rejected. So that philosophy was prevalent during the mid 20th century. I have to say, with the demise of the verification principle, this is not as widespread today because that principle of meaning is both too far reaching. It would dismiss vast reaches of human discourse and language as meaningless. And it also tends to be self defeating and self refuting. But there are some ah, realists who are around today. Now let's take on the other hand, the view of realism and. And realism with respect to mathematical objects can be of two types. First, realism could hold that these are abstract objects, as a Platonist believes, or there are realists who think that mathematical objects are in fact concrete objects. Now let's take the abstract alternative first, that these are abstract objects. They could be regarded as uncreated. And that's the Platonist view. This is the classical Platonist perspective, that there are numbers, they are abstract objects, and they are uncreated. That's Platonism. On the contemporary scene, some Christian philosophers have attempted to solve the problem posed to divine aseity by the existence of numbers by adopting a sort of modified Platonism according to which numbers exist alright as abstract objects, but these too are created by God. He has not only created all of the concrete objects in the world, but God has created all the numbers. Now this will force you to modify your view of creation somewhat, because in this case these numbers exist eternally and necessarily so. That means that God has been creating from eternity and that there is no possible world in which God alone exists. Creation becomes necessary on this view. And that, I think should give us theological pause. It does require you to modify in some significant ways your view of creation. But there are some Christian philosophers today who would defend absolute creationism. One of the most serious objections to absolute creationism is called the bootstrapping objection. That is to say that it involves a vicious circularity. And the easiest way to see this is by considering properties. The Platonist thinks that properties are also abstract objects like numbers, and that these exist necessarily and eternally. So consider God on absolute creationism having to create properties. Suppose he wants to create the property being powerful. He would already have to be powerful in order to create the property of being powerful, so that he would already have to have the property in order to create it, which is viciously circular. That is called the bootstrapping objection because it's sort of trying to pull yourself up by your own bootstraps. In order to create the property of being powerful, God would already have to have the property being powerful. And you could run a similar paradox with numbers. In order for God to create the number 1, 1 is the number of gods that there would need to be. There would need to be one God in order for God to create the number one. So again, you have a kind of vicious circularity or bootstrapping problem. And this has caused many contemporary Christian philosophers to have serious reservations about absolute creationism. This is not an alternative that has been widely defended today. And I think it's largely because of this bootstrapping objection that tends to afflict absolute creationism. Now let me ask if there's any discussion or question at this point about this alternative and the difficulties that it faces. Okay, Don Pendley, my question is very simple. How can the number two exist independent of a finite universe? Well, it would be meaningless. Well, now that's what a conventionalist says, right? That's adopting our realism. It's meaningless. But I don't think that that's difficult. Don, why would there need to be spatiotemporal objects in order for the number two to exist? Even if there were no universe, wouldn't it still be true that two plus one is three? Or even more basically, what about this, that one equals one or one is greater than zero? I mean, surely these sorts of elementary truths of arithmetic are true whether or not anything physical exists. It would seem to me that what you are doing is coming up with a language to define an infinite universe. Well, now, Don, that depends on what you mean by the universe. For the absolute creationist, he does think that these numbers and properties and things are part of creation. So he would say there's sort of two divisions in creation. There's the concrete objects, which include things like material objects, souls, angels. These are all part of the concrete world. But then he would say there's another division of creation that we don't usually talk about, and that would be this abstract realm of numbers and properties and possible worlds and propositions. And so if you use the word universe very broadly to include everything that is created. Yes. This view would say that there is necessarily eternally a created universe of abstract objects. Now, if you don't use it in that broad sense and you strict the universe to the realm of spatiotemporal objects, then no, the Platonist would say that these abstract entities exist independently of concrete things. They exist assay they are like God in that respect.
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B
Bruce, both of your comments. The number two only has significance as it corresponds to temporal objects. I mean, the concept, the abstraction of the number 2 or 1 or 1 greater than 0 has no meaning apart from a correspondence to physical objects. So that's where I see the problem with this. They derive from a number of physical objects and the correspondence.
- [17:40]
A
So Bruce, on your view, in a world in which God didn't create any physical objects, wouldn't there still be three members of the Trinity?
- [17:49]
B
Well, certainly, but that's part of self defining who God is. I mean, we ascribe a value of three to the Trinity because we can observe a concept of threeness or twoness or whatever, but we don't. Because. But it doesn't have any Value if there's no entity?
- [18:16]
A
Well, I mean, in this case, there is an entity. There's God, there's one God, and there are three members of the Trinity. So you've already got arithmetic going right there, even in the absence of any physical objects, because you've got three and you've got one, and then you've got arithmetic operations like three plus one.
- [18:37]
B
These are abstractions in beings that are tying a value to this in time and space. If you have a being that's not tied to time and space, this is meaningless.
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A
Okay, well, I'll just say again one more time. If God is timeless, wouldn't there still be one God? Wouldn't there still be three persons in the Trinity? It seems to me that these arithmetic truths don't have anything to do with temporality or time.
- [19:05]
B
Well, it's true, but we ascribe the value of oneness and threeness. It's for us, that are tied to time and space. This is why we have mathematics to use in the real world. It corresponds to things that happen in the real world. It's an expression of something.
- [19:22]
A
You do sound sort of like a conventionalist, I have to say. I mean, you're sort of saying there's no objective, mind, independent truth about the number of persons in the Trinity, that this is just something we use. So I'm trying to think, where on this chart does Bruce fit? You know, where would he go? Nowhere. Okay, here's a question. I was sort of confused when you were talking about apples. Like, if you had three apples and then you have the number three apples. But then you said there was like a fourth thing, which is this value that you have. What? Exactly. And then, and then you said you have that value, but then you have more values, an infinite number of values. What did you mean by. Well, I was referring to the numbers that if you have three apples on the table, are there only three things there? Well, the Platonist would say no, because he would say there is also the number three, which is the number of the apples. So there are three apples. And there is another thing, the number three. And then, as I said to Bruce, once you get the number three, you get all the other numbers as well. So you get an infinitude of numbers just in virtue of there being some objects. So the difficulty here is maybe grasping what the Platonist believes. Remember, the Platonist thinks that these are real, that these numbers really exist. These are metaphysical realities that are just as real as people and planets and electrons and so forth. Yes, Ben, let's Let Ben have a word here. Very brief coming off what she said, because it does seem like numbers are a way of describing reality to me initially. So if you took away one apple, then you have one apple, two apples, and then the number two. What if you took away all the apples, does the number 0 still exist there in its place? Well, I think that the Platonist would say so. He would say 0 is the number of apples on the table. And that gets into a real interesting question. All right, let's take one more comment and then we'll move along. Drew? Okay.
- [21:38]
C
I'm wondering how you would handle, say, Quine's objection that mathematics is at least quasi empirical. Like, he believed that in a world where if you had two apples and put them, you know, an apple in one hand, apple in the other hand, put them together, a third apple appears in that world, one plus one equals three, that there is at least some empirical element of mathematics. And so it's not metaphysically necessary.
- [22:05]
A
Yeah, I don't think that is his view, myself. I mean, Quine, who was a naturalist philosopher, felt forced to adopt Platonism about sets, at least so that this naturalist believed that there are these abstract entities that because they're referred to in our scientific theories. In our scientific theories, we have reference to things like numbers and functions and so forth, and so they must actually exist. So I don't think he was a conventionalist about necessity. Maybe that's what you're thinking.
- [22:43]
C
Yeah, maybe. I know. I've read that he was. At least he believed mathematics, I think, in Hilary Putnam, maybe as well, believed mathematics to be at least somewhat empirical. There was at least some empirical elements that grounded.
- [22:55]
A
Yeah. The only thing I can think of, Drew, that would connect in that way would be he didn't think that necessity and possibility were objective, that these were just conventions, as I described a moment ago.
- [23:09]
C
Do you have a response, then, to the formalist who says mathematics isn't metaphysically necessary, it's grounded in physical reality?
- [23:15]
A
Yeah, that is later on here on the chart, as you'll see. So let's put that aside and let David Sherrill ask the last question here on this section.
- [23:24]
C
I might have missed something important last week, so apologies if I did. But backing up one step. Is it really critical that God is the only uncreated necessary being? You mentioned John 1:3. And it does seem like it's a problem there when it says all things came into being through him, but then it qualifies and says apart from him, nothing came into being that has come into being right.
- [23:51]
A
The second clause of John 1:3 is weaker than the first clause. The first clause is a universal statement. All things came into being through him. You're quite right. If you punctuate the text that the way you read it, then it would be followed by a weaker clause that isn't the same as the first clause there. It simply says, not one thing that has come into being came into being without Him. One of the interesting things, David, is that the punctuation of that verse is very uncertain. Many scholars think that the punctuation should be, all things came into being through him, and without him, not one thing came into being, period. And then the next verse starts, what has come into being through him is life, and the life, et cetera, et cetera. So the question of the punctuation of this verse actually even comes into play. And if you look in your Greek New Testament, they will have a footnote about the uncertainty of how to punctuate the verse, which is amazing because the punctuation isn't in the original Greek. And so why are they having a footnote about how English translators punctuate the sentence when it has absolutely nothing to do with the Greek text? I've asked some Greek scholars about that, and they've said, this is really extraordinary that they would have this sort of comment. But I think you can show to many other passages that we did review last week where it says, for from him and to him, and through him are all things, period. And so John 1:3 is just a piece, I think, of a broader textual testimony to God's being, the unique, uncreated being. But David is certainly correct in saying some Christian philosophers are just willing to bite the bullet and say, yeah, there are things that are uncreated by God and co eternal with him and necessary and independent of him, and they just don't see any problem with it. And I have difficulty understanding how such a view could be reconciled with the Jewish concept of God, which seems to me to be clearly that God is the source of everything outside of himself. And God is not to be praised and worshiped because he's created this little small part of reality, namely the concrete realm. But he's to be praised and worshiped because he's the creator of everything that exists other than himself. So that certainly is something that is part of the debate. Some philosophers would respond by just saying, biting the bullet and saying, yeah, there are things that are independent of God and co necessary and co. Eternal. But I'm not willing to go that route myself. Well, I said that was the last question. So let me move on to the next alternative. Now, you see, next to abstract objects, there is a kind of realism that says that these things exist as concrete objects. And these could be two types of concrete objects. They could either be physical objects or they could be mental objects, that is to say, thoughts in somebody's mind, physical objects. One view or alternative that takes this view would be formalism, which says that mathematics is basically scratch marks on paper. There is no significance beyond that. Mathematical entities just are these marks on paper which are manipulated by mathematicians in. In accordance with certain rules. And that's all there is to it. There's not very many people that find that point of view persuasive today, because it certainly seems that the number two isn't to be identified with the mark on your piece of paper or the mark on my piece of paper that when we say two plus two equals four, we're talking about a general truth, not some specific mark that has been made on a piece of paper. And it's difficult to see how this view would be consistent with the necessity of mathematical truth. So there's the alternative of taking them as mental objects, thoughts in somebody's mind. This might either be a human mind or God's mind. The view that mathematical objects are just thoughts in people's minds is called psychologism. And this would say that you have ideas of the number two or of two plus two equals four, and that's what these mathematical objects are. They're just ideas in people's minds. Now, that view again is not very widely adopted today because again of the inter subjectivity of mathematics. If Kevin has the idea of two plus two, and two plus two is an idea in Kevin's mind, then what's Stephanie thinking of when she thinks two plus two? It's not the idea or thought that's in Kevin's mind, isn't in her mind. Different people have different thoughts, so how could these mathematical objects just be your thoughts? Moreover, there are infinite numbers of mathematical objects and infinite mathematical truths, and there aren't enough people to have all those thoughts, so you can't ground them in human minds. Moreover, human beings aren't necessary. They only have existed for a period of time on this planet. So are we to think then that these mathematical objects haven't always existed, or that it hasn't always been true that 2 +2 equals 4? These are the sorts of problems that attempt psychologism that has made it unpopular today. And so more Christian philosophers have chosen to adopt divine conceptualism. And this is historically the mainstream Christian position. From Oregon and St. Augustine, through Thomas Aquinas, through William Occam, on into the late Middle Ages, the standard Christian view has been that what Plato thought were these abstract entities are really thoughts in the mind of God. And so the Church Fathers moved the realm of Platonic. They moved the realm of Platonic ideas into the mind of God and made them God's thoughts. And this is immune to the sort of objections that psychologism falls prey to, because in this case, for example, the number two is uniquely that object that God is thinking when he thinks two, that is the number two. And because God is eternal and necessary, he can be the ground of necessary mathematical truths. Because he is infinite and omniscient, he can ground an infinite number of mathematical truths and have an infinite number of mathematical objects as objects of his thought. So that divine conceptualism is an alternative that finds quite a few defenders on the contemporary scene. And in this way, one would avoid having entities outside God, as it were. Entities apart from God, which would be numbers and other mathematical objects. They don't really exist. What really exists will be God and his thoughts. Any question about any of these alternatives that would have realism thinking of numbers and mathematical objects as concrete objects? Yes, Taewon. Can we simply see that number as adjective? And so the adjective can come in two ways. Well, men see object and then describe. Man see noun, and then describe it with objective. But God actually has this conceptualism, the object adjective, in him, and then he create nouns. So it's different perspective. All right, you know, I'm simplifying. I'm skating over the surface here. And this question that she just asked is very penetrating. And so it requires me to say a little bit more. You're quite right, Taewon. The adjectival use of numbers isn't committing to objects. So if I say there are three members of the Trinity, that doesn't commit you to the number three. In order to commit you to numbers, you have to use the word as a noun. As you said, three is the number of the members of the Trinity. Or again, if I say three men entered the tavern, there's no commitment there to the number three. It's just an adjective. But if I say three is the number of men who entered the tavern, then I have committed myself to the reality of the number three because I've used it as a substantive, as a noun that refers to some object out there. So the difficulty is that those two sentences seem to be synonymous. Right? The number of men who entered the tavern is three. Three men entered the tavern. So does that sentence convey the metaphysical commitments that the Platonist thinks or that the anti realist thinks? And this gets into a huge debate over whether or not we can reduce all of our commitments by expressing them adjectivally. And I would say that there's a pretty general consensus that that cannot be done. This is. Well, do you see on Anti realism here on the chart one of the strategies for anti realism? Yeah, it's not on this one. One of the alternatives that is not listed would be what we could call paraphrastic strategies where you would paraphrase away your commitment to numbers by using adjectives instead of nouns. And I think, as I said, it's fairly widely acknowledged that a paraphrastic strategy is going to face huge obstacles. And so many Platonists would say this isn't going to avoid the problem. But there are others who have offered these kinds of strategies. I can think of a couple. For example, there's philosopher at Berkeley called Charles Chihara, and then there's another philosopher named Jeffrey Hellman. And both of them have offered what are essentially ways of paraphrasing arithmetic and numbers so that you get rid of them and you aren't committed to them. So, yes, your question is very good and would represent one of the anti realist alternatives. Okay, with that, we need to draw it to a close. And I will read our benediction to bring the class to an end. Let's bow our heads from Second Corinthians, chapter 13 and verse 14. The grace of the Lord Jesus Christ and the love of God and the fellowship of the Holy Spirit be with you all. Amen. The copyright for the content of this recording is held by Dr. William Lane Craig. For more go to reasonablefaith.org.