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A
Welcome to Defenders, the teaching class of Dr. William Lane Craig. Today the Doctrine of God, Part 4. For more information and resources from Dr. Craig, go to reasonablefaith.org in our lesson
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we've been talking about God's attributes and in particular his attribute of aseity or self existence. And we saw that the most serious challenge posed to God's unique, incommunicable attribute of a satiety is Platonism, which is the view that there exist other uncreated, necessary eternal objects besides God. Things like mathematical objects, numbers and sets and functions, and so forth. And last week we began to review responses to the Challenge of Platonism. So if we could have the PowerPoint slide up again. We have discussed first of all the realist alternatives to Platonism, which would take mathematical objects either to be abstract ideas that are created by God, or else as concrete objects, namely thoughts in human minds, or else more plausibly, thoughts in the mind of God. Now these are all realist solutions to the problem posed by Platonism, because these solutions agree with the Platonists that in fact mathematical objects exist, there really are such things. But in addition to these realist solutions, you see on the right hand side of the diagram a range of anti realist solutions to the challenge of Platonism. And these are united in denying that there are any such things as mathematical objects. Mathematical objects simply do not exist. There are no such things. And these anti realist solutions immediately remove the challenge posed by the existence of abstract objects to God's being, the sole ultimate reality. Because on anti realism there just aren't any such objects and therefore God is the only uncreated self existent, necessary eternal being. So let's just review briefly some of these anti realist solutions. For example, free logic is a type of logic that has only been developed since about the 1970s, and it's a very recent development in the study of logic. And according to free logic, we can use terms to refer to things even though those things do not exist. For example, I can refer to the hole in your shoe. Your shoe exists, but it's not as though in addition to the shoe, there's something else, namely the hole in your shoe. The whole isn't a thing, it's not an object that exists. What you simply have is a shoe that is shaped in a certain way, but the whole isn't something different. Or if I say there's a lack of compassion in the world, I'm not committing myself to things called lacks. There aren't things out there in the world objects lacks. When I Say there's a lack of compassion in the world. Or if I say Wednesday is the day of the faculty meeting, I'm saying something true, but I'm not committing myself to the reality of Wednesdays. I'm not saying that Wednesdays are objects that actually exist. Or if I say the pilot's quick thinking averted the terrible accident on the Hudson river, the accident never happened, but I can still refer to it in a true sentence. So free logic is a logic that enables you to talk about and refer to things even though those things don't exist. And what the free logician can say is that sentences, mathematical sentences like two plus two equals four are true, even though the terms in those sentences don't actually refer to anything. There is no such thing as two plus two or four, any more than there is such a thing as the hole in your shirt or a lack or a Wednesday. So that's the alternative of free logic. Figuralism, the next on the list is a different form of anti realism. Figuralism points out that much of our language, a great deal of ordinary language, is figurative in nature. It's metaphorical in nature. If I say it's raining cats and dogs outside, I've said something that is true, but it doesn't mean there are animals falling from the sky. This is a figure of speech for saying that it's raining hard outside, and so it would be inept to take that statement literally. It is figuratively true that it's raining cats and dogs outside. Or if somebody's angry, I might say she's got a bee in her bonnet, and that's true, but not in a literal way. That's a figure of speech. And similarly, the figuralist will say that mathematical discourse is very plausibly interpreted as a sort of metaphorical or figurative discourse, and it isn't meant to be taken literally as referring to things like numbers. These are what one philosopher calls existential metaphors. They're figurative ways of speaking of things, but there really aren't such things in a literal sense. So that would be figuralism. Neutralism is yet a third form of anti realism. Neutralism agrees with free logic that we can use terms to refer to things that don't exist, that when we refer to things, our statements are just neutral with respect to whether those things exist. So if I say the weather in Atlanta today is balmy, I'm not committing myself to an object called the weather, as though the weather is something that exists. Or if I say the view of the Jezreel Valley from atop Mount Carmel was gorgeous. I'm not committing myself to an object. The view from the Jezreel Valley. It's not as though there is an object that is in the world called the view of the Jezreel Valley. Or if I say the price of the tickets was $10, I'm not committing myself to the reality of objects called prices. And in many, many different ways, we use terms in ordinary language to talk about things without committing ourselves to the reality of those things. Now, certainly sometimes we do mean to speak in a metaphysically committing way. If I say this table is made out of wood laminate there, I'm pretty clearly committing myself to the reality of the table. The table. And what will tip us off to whether or not a person is thinking that there is a real object will usually be personal effects, rhetorical statements maybe emphasizing this it really does exist, or the context. But the neutralist will agree with the free logician that we often use terms to talk about things without thinking there are objects that correspond to those. And. And so he would agree with respect to mathematical objects that when we say statements like three times three is nine, that those terms are just neutral as to whether or not you're committed to the reality of objects, mathematical objects. The neutralist goes farther, however, than the free logician, because the free logician thinks that if you say there is something, then you are committing yourself to the reality of that thing. And the neutralist would say that even expressions like there is are ontologically neutral. I can say, for example, there are deep differences between Republicans and Democrats without thinking that I've committed myself to objects in the world called differences, and. And that some are deep. The word there is in English just, or the expression there is and there are are just very light in their ontological commitments. And it will be again, personal factors such as context, inflection of your voice, saying, well, there really is an abstract object that will tip you off as to whether or not you mean to make an ontological commitment. So the neutralist goes even further than the free logician. The neutralist will say that really there isn't anything in language that in virtue of its meaning, commits you to saying there really are those objects that either correspond to the terms you use or are the things you say there is or there are. And neutralism is a view, I'll just say personally, to which I am very attracted. It seems to me that this gives a very plausible account of ordinary language, and when applied to mathematical discourse, it allows you to affirm the truth of mathematics, but to simply say it's neutral in terms of its commitments to objects. Fictionalism now is a quite different form of anti realism. The fictionalist, like the Platonist, agrees that if you use terms to refer to something, or if you say there is or there are something, then you are committed to the reality of the things that you say there are or that you refer to. So the fictionalist accepts those criteria for ontological commitment that the neutralist and the free logician reject. But why is the fictionalist, then not a Platonist? Because the fictionalists think that those statements referring to or saying that there is or there are certain things are false. They're fictional, they're not true. So the fictionalist will take the radical line that it is not true that two plus two equals four. It is not true that three is is greater than one. It is not true that there is a prime number between two and four. And if you say, well, that's crazy, those seem to be obvious truths, even necessary truths. The fictionals will remind you that on his view, to say two plus two equals four is to make a radical metaphysical statement that there is an abstract object named 2/2 and there is an abstract object named 4, and that those two objects are the same object. And that is not at all obvious. So the fictionalist will say, if you accept these criteria for how we make ontological commitments, then it is far from obvious that the statements of elementary arithmetic are true. They actually turn out to be radical metaphysical assertions that we have no reason to think are true. Now the fictionalist will say these statements are true within the story of mathematics, within standard arithmetic, they're true. And in this sense they're like statements of fiction. It is not true that Sherlock Holmes lives at 22B Baker Street. There is no such place. There was no such person. But in the Arthur Conan Doyle stories it is true that Sherlock Holmes lived at 22B Baker Street. And so the fictionalists will say statements of mathematics are true in the story of mathematics, in the same way that some of these statements are true in the Conan Doyle stories of Sherlock Holmes, but other statements will be false. It is not true, for example, that Sherlock Holmes met Henri Poirot in those stories. So that would not be true in the story Sherlock Holmes. And neither is it true in the story of standard mathematics that two plus three equals four. So that's fictionalism. Pretense theory is another anti realism that takes inspiration from theories of fiction, and they work largely off of the brilliant pioneering work of a philosopher at the University of Michigan named Kenneth Walton. Walton's work on fiction holds that fiction is an extension of children's games of make believe. Walton notes that children invest enormous amounts of time and energy in games of make believe. And he says, it would be very surprising if when people reach adulthood, they just give this up all of a sudden and no longer make believe. And Walton says, in fact, we don't give it up. This is what fiction and drama and film and literature and art is all about. These are, in effect, adult games of make believe. And he says, what is crucial to fiction is not that the statements are false. A novel about the future, like George Orwell's 1984, could turn out to be true. It could all turn out to be true. But. But it's still fiction. Or the story of Hamlet might be true on some other planet, somewhere in another galaxy in the universe for all we know, but Hamlet is still fiction. So it's not the falsity of the story that makes something fictional. Rather, in Walton's analysis, what makes something fictional is that it is prescribed to be imagined as true. We are to imagine that there is a Danish prince named Hamlet and that he did such and such, or we are to imagine that there was a detective living in London who had a colleague named John Watson who did tremendous exploits, and then within this fictional world of imagination, the story can be unfolded. So what is essential to fiction, in Walton's view, is this act of making believe or imagining something to be true. The statements are prescribed to be imagined as true, and they may or may not actually be true. But in either case, what is essential to fiction is the prescription to be imagined as true. Now, apply this to mathematics. In mathematics, we are in a sense, prescribed to imagine the axioms to be true. You're prescribed to imagine the elementary arithmetic axioms to be true, and then you can derive all of your theorems, or you imagine the axioms of set theory to be true, and then the mathematician can derive all of his theorems. So the whole thing really is a sort of species of make believe. And far from being a crazy view of mathematics, this is a view of mathematics that many mathematicians themselves actually entertain. They would say that the mathematical axioms are postulates which you postulate, and then you derive your theorems or your deductions from them. But you're quite free as a mathematician to adopt a different set of postulates, a different set of axioms, and to explore that. And so there's a wide variety of set theories that are on offer today. There's not simply a single set theory in mathematics. There's a range of set theories, and these have different ontological commitments. Some commit you to sets, some commit you to a different sort of object called classes, which are different from sets. And so pretense theory will say that because you're merely pretending or imagining these things to be true, you're not committing yourself to the reality of these objects, and any more than you're committing yourself to the reality of Sherlock Holmes in imagining that this fictional world is the case. Neo Meinongianism is one of the wildest anti realisms. This stems from an Austrian philosopher, Alexios Meinong, who lived at the end of the 19th and into the early 20th century. And Meinong was concerned to develop a theory of objects. He called his philosophy object theory in German, Gegenstan's theory. And what Meinong maintained is that there are objects that do not exist. There are objects that do not exist, he says, although it may sound paradoxical, there are things of which it is true that there are no such things. Unicorns, centaurs, fairies, the accident that was prevented, holes. There are things which do not exist, Meinong would say. And he develops this whole theory about these objects. And so, on this view, the neo Meinongian, that is to say the modern follower of Meinong, of which there are several in the world today, would say that mathematical objects are objects that do not exist. And so that would be one alternative, one form of anti realism. Another one would be modal structuralism. This is a view that's been defended by Jeffrey Hellman, who is a philosopher of mathematics. And on this view, mathematics is about structures. Without going into great detail, the idea here is that numbers are positions in structures. So the third position in a structure would be three, the fourth position would be four and so forth. There aren't objects called numbers. They're just positions in a sort of abstract structure. Now, some structuralists in mathematics think that structures exist. This would be a kind of abstract object. A Platonist would say there are not numbers, but there are structures. But the modal structuralist will say there could have been such structures. So what he would say is that if there were numbers, then two plus two would equal four, or if there were numbers, the square root of nine would be three. And so you can see he reinterprets mathematics in such a way that it doesn't commit you to the reality of the objects that appear in those statements. These are simply paraphrased in such a way as to say that if there were such things it's possible that there are such things. If there were, then they would have these properties. So modal structuralism is what I referred to last week. It's a kind of paraphrastic strategy, that is to say you offer paraphrases of mathematical sentences that don't involve you in commitments to these abstract objects. Those are just some of the anti realisms that are on offer today. There is a real potpourri of alternatives and there are others that aren't even on this list. But I want to just share these with you to give you an idea of the field of options that is open. Now obviously in this class we haven't and are going to discuss any of these in detail. But I simply want to familiarize you with a range of options today. Lest someone think that the reality of mathematical objects poses an insuperable challenge to divine self existence and to say to the idea that God is the sole ultimate reality that is not in fact true. As you can see, there are great number of options available to the Christian theist today which would not commit you to the reality of uncreated abstract or uncreated objects of any sort. So Platonism is only one view, a tiny view in the whole range of views about the reality of these objects. And I think that these other views, many of them are very plausible. And in my book that I'm going to be publishing on this, I'll be defending a number of these views as plausible alternative to Platonism. But in order for Platonism to be a defeater, so to speak, of God's unique self existence, he would have to prove that Platonism is true and that all of these alternatives are false. And I don't think anybody believes there's a realistic prospect of doing that. Okay, is there any question or discussion about any of these options that appear on the slide or about the problem that we're dealing with? Okay, there's a question over here.
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C
Yeah. A lot of these theories, they kind of remind me a lot of the transcendental argument, which I've kind of struggled with. It's the transcendental argument, which essentially, as I understand it, is that it's an argument for the spiritual existence saying that you couldn't have objects such as love or justice, and explain that with the naturalistic view. It seems like a lot of these theories would sort of be defeaters to the transcendental argument, which I find is an attractive argument. Yet I can't, I don't know if I can hold it. And so I was wondering what Your thought was.
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B
Well, I've never heard what you just described called the transcendental argument, as I've heard that expression used. It usually means that in order to affirm rationality and logical thinking, there needs to be some ground of this in God rather than in the evolutionary process. Because the evolutionary process doesn't aim at truth. It. It merely aims at survival. And we could survive without having true beliefs. As long as those beliefs are conducive to survival, truth doesn't need to come into the equation. And so on naturalism, the argument is that we have a defeater for thinking that our cognitive faculties are reliable. That's the way I hear and understand the transcendental argument. Now what you seem to be saying is that in order for there to be objects referred to by these abstract terms, you need to have God maybe as the ground for those. And I think that the divine conceptualist might well run an argument like that because he thinks these are thoughts in the mind of God. So I could see someone saying two plus two equals four. That requires the existence of numbers in order to be true. But what are numbers? Well, they must be thoughts in the mind of God. And so this is an argument for God's existence. And I would agree with what you said that anti realism would undercut that argument. I don't use that argument. I don't think it's a good argument because I agree with the neutralist on this. I don't see any reason to think that the the truth of two plus two equals four commits you to the reality of two plus two or four. So. Right. I usually hear that called the conceptualist argument for God's existence. And I do think that the person who wants to run that argument is going to have to defeat that whole right hand side of the diagram. And I think that would be really tough to do. Yes, Robbie?
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D
Okay, so what you're saying by the diagram is that these, I guess the left side of the column is referring to mathematical objects being mentally true but not metaphysically actual. Is that what you're.
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The left hand side, Robby?
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No, no, like the right side is defeating the left side in that sense.
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The right side are the anti realist views. Okay, These realist views think that there are mathematical objects, there are numbers, and they're either abstract like the Platonist thinks, or they're concrete, either physical or mental. So the realist views think that there really are numbers.
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D
Oh yeah, that's not right.
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Well, I don't think so, but I mean, we're leaving that open Right. I mean, because there are forms of realism like absolute creationism or divine conceptualism, which are consistent with saying God is the only uncreated self existent being and these other things are dependent upon God.
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D
And so those. And that wouldn't be the same as saying there are such things as, like there are such things as moral perfections like good or justice or things like that. How do we then come up with an argument to say that no, these things are real, but they're way more real than numbers can be?
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B
Right. Now what Robby points out here is that whereas I've taken mathematical objects as my point of departure, you could put in other things like that, for example, moral values. And here I would be a realist. I think that there are moral values, but I would not be a Platonist. I don't think that there is such a thing as justice or rapacity or greed as some sort of strange abstract object. I would say they're anchored in God, who is a concrete object. So this would fit very well with the view of, of God as the concrete paradigm and foundation of objective moral value.
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D
Correct. Okay, thank you.
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B
Okay. Yes. Dennis.
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E
Dennis, would it be possible for the anti realist ideas to backfire? Someone, for instance, asks, you believe that God is an uncreated object? Well, on anti realism, how can you say there's a God? You know, if.
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B
Well now, Dennis, how do you think I would answer that question?
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E
Well, because God is uncreated or because God. I don't know? That's what I'm asking.
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B
I would run cosmological, teleological, moral, ontological arguments for God's existence, which you don't have arguments. We've got reasons to think that God is real. We're not just postulating God's existence on the basis of language, that there are sentences like God is good or something like that. Therefore the term God must refer to an object, therefore God must exist. I agree with that kind of argument. I don't think works to use this kind of linguistic argument, but I think you've got to have a cause of the origin of the universe, for example. That's not a linguistic argument.
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F
Okay, Steve, you know, you're saying the right hand side could defeat God. So what keeps the divine conceptualist from saying modal structuralism is just one point. God accepts this and then creates this reality.
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B
That is what the conceptualist would say. These views are to a certain extent incompatible with each other. The anti realist says there are no mathematical objects. The divine conceptualist says, yes, there are. And they're thoughts in the mind of God. So he would say, God has the thought of these structures, and these structures are ideas in God's mind. So that would be a realist view of structuralism. So you can be a structuralist and be a realist, or you can be an anti realist. Either option is available to you. And I've not tried to decide in our class here which of these options is correct. That would be far too essential, ambitious a project. But just to let you know, there are lots of different options on the table today, and it would be very difficult to rule them out in such a way that Platonism is the only alternative left. Okay, one more question, and then I want to say some things by way of practical application.
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G
Okay, I'm struggling for a moment. You have for the realists, there are concrete objects or abstract objects, and I understand how a physical object is concrete. How is a mental object different, a mental, concrete object different from an abstract object?
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B
All right, I have to apologize somewhat for skimming the surface here because it leaves these unanswered questions. The question that Amy asked is a profound one. And she's saying, how do you differentiate between an abstract object and a concrete object? The most widespread and I think plausible answer to that question is that concrete objects are objects that have causal powers to do things, whereas abstract objects are causally impotent. They are causally a feat. The number seven has no causal effect upon anything. But obviously a mind or thoughts in someone's mind would have causal effects both on God's part and on our part. And so thoughts would be concrete events in some person's mind, whereas mathematical objects, as usually construed, that is to say, would be causally impotent and therefore abstract, not concrete. So concrete here doesn't mean material. It means causally efficacious or capable of having causal influence. Now, what practical application does all of this have to our lives? Well, let me mention just two. First of all, because God is the sole ultimate reality, God ought to be our ultimate concern in life. The theologian Paul Tillich actually defined God as the object of ultimate concern. Whatever is your object of ultimate concern is God for you. And since God is the sole ultimate reality, he is and ought to be our proper ultimate concern. To substitute anything else for God would be idolatry. Now, if I were to ask for a show of hands in the class today, how many idolaters do we have in the class today? I was going to say there'd probably be very few, but some have realized, I think already the implications of what I'm saying. If there's anything else in life that is more of concern to you than God then you're guilty of idolatry. If your ultimate concern is is not knowing and serving God better then you're worshiping a lesser God. You're falling into idolatry. So God's aseity and ultimate reality is a powerful reminder to us of where our ultimate concern ought to be. Second, God's self existence includes our selfishness. God's self existence ought to exclude our selfishness. Another word for self existence is independence. God is independent of everything else that exists. And this is what man and Satan want isn't it is independence. They want to go their own way to challenge God's self existence by opposing it, opposing to it their own independence. We want to oppose our selfhood to God's. I am. And selfishness I think can seem very natural until we reflect upon the being of God. But when we understand who God is and his self existence then I think we can see how foolish it is how insane it is to oppose our selfhood to God's self existent being and to not treat him as our ultimate concern and to submit ourselves to him. And so living for God, denying self in favor of God's self existence I I think makes good sense once we understand God's self existent nature. Let me just conclude by reading a benediction for us this morning. And this is from the book of Ephesians. If we might bow our heads to close. Peace be to the brethren and love with faith from God the Father and the Lord Jesus Christ. Grace be with all who love our Lord Jesus Christ with love undying.
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The copyright for the content of this recording is held by Dr. William Lane Craig. For more go to reasonablefaith.org.