Doctrine of God (Part 4): Anti-Realist Theories

Anti-Realist Theories

In our lesson we have been talking about God’s attribute of aseity or self-existence. We saw that the most serious challenge posed to God’s unique attribute of aseity is Platonism, which is the view that there exists other uncreated, necessary, eternal objects besides God – things like mathematical objects, numbers, sets, functions, and so forth. Last week we began to review responses to the challenge of Platonism. We have discussed, first of all, the arealist position that the question of the existence of math’l objects is a meaningless question and therefore has no answer.  Then we looked at realist alternatives to Platonism, which would take mathematical objects either to be abstract objects that are created by God or else concrete objects, namely, thoughts in either human minds or, more plausibly, thoughts in the mind of God. These are all realist solutions to the problem posed by Platonism because these solutions agree with the Platonist that, in fact, mathematical objects exist – there really are such things.

But in addition to these realist solutions, you’ll see on the right hand side of the diagram a range of anti-realist solutions to the challenge of Platonism. 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. 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.

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. It is a very recent development in the study of logic. 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 is not as though in addition to the shoe there is something else, namely, the hole in your shoe. The hole isn’t a thing. It is not an object that exists. What you simply have is a shoe that is shaped in a certain way, but the hole isn’t some additional thing. Or if I say, “There is a lack of compassion in the world,” I am not committing myself to the existence of things called “lacks.” There aren’t things out there in the world – objects – as “lacks.” Or if I say “Wednesday is the day of the deacons meeting,” I am saying something true, but I am not committing myself to the reality of Wednesdays. I am not saying that Wednesdays are objects that actually exist. So Free Logic is a logic that enables you to talk about and refer to things even though those things don’t exist. What the Free Logician can say is that mathematical sentences, like 2+2=4, are true even though the terms in those sentences don’t actually refer to anything. There is no such thing as 2+2 or as 4 any more than there is such a thing as the hole in your shirt or a lack or a Wednesday. That is 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 is raining cats and dogs outside,” I’ve said something that is true, but I don’t mean there are animals falling from the sky. This is a figure of speech for saying that it is raining hard outside. So it would be inept to take that statement literally. It is figuratively true that it is raining cats and dogs outside. Or if somebody is angry, I might say, “She has a bee in her bonnet.” That’s true, but not in a literal way. That is a figure of speech. Similarly, the Figuralist will say that mathematical discourse is very plausibly interpreted as a sort of metaphorical or figurative discourse. It isn’t meant to be taken literally as referring to things like numbers. Such math’l terms are what one philosopher calls existential metaphors. They are figurative ways of speaking of things, but there really aren’t such things in a literal sense. 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. 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 chilly” I am 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 am not committing myself to an object “the view of the Jezreel Valley.” It is 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 ten dollars” I am not committing myself to the reality of objects called “prices.” 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 am pretty clearly committing myself to the reality of the table. What will tip us off to whether or not a person is thinking that there is a real object will usually be rhetorical devices—for example, emphasizing by one’s tone of voice like “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 terms. So he would agree with respect to mathematical objects when we say statements like 3 x 3 = 9, those terms are just neutral as to whether or not you’re committed to the reality of 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. 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 that some are “deep.” The expressions “there is” and “there are” in English are very light in their ontological commitments. It will be, again, personal factors such as context, inflection of your voice, saying “there really is an abstract object” that will tip you off as to whether or not someone means to make an ontological commitment. So the Neutralist goes even further than the Free Logician. The Neutralist will say that there isn’t anything in language that in virtue of its meaning commits you to saying that there really are objects corresponding to the terms you use or that you say “there is” or “there are.”

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. When applied to mathematical discourse, it allows you to affirm the truth of mathematics but to simply say it is neutral in terms of its commitments to objects.

Fictionalism 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” something, then you are committed to the reality of the things that you refer to or that you say “there are.”  So why is the Fictionalist then not a Platonist? Because Fictionalists think that those statements referring to or saying that “there is” or “there are” certain things are false. They are fictional. They are not true. So the Fictionalist will take the radical line that it is not true that 2+2=4. It is not true that 3 is greater than 1. It is not true that there is a prime number between 2 and 4. If you say that is crazy – those seem to be obvious truths, even necessary truths – the Fictionalist will remind you that on his view to say 2+2=4 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 statements of elementary arithmetic are true. They actually turn out to be radical metaphysical assertions that we have no reason to think are true. That’s Fictionalism.

Pretense Theory is another anti-realism that takes inspiration from theories of fiction. They work largely off of the brilliant pioneering work of a philosopher at the University of Michigan named Kendall 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. 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. Walton says, in fact, we don’t give it up. This is what fiction and drama and film and literature and art are all about. These are, in effect, adult games of make-believe. 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, but it is 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. It is 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 named Sherlock Holmes who had a colleague named John Watson who was a great crime solver. 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. 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.

Apply this to mathematics. In mathematics, we are, in a sense, prescribed to imagine the mathematical axioms to be true. You are prescribed to imagine the elementary arithmetic axioms to be true. Then you can derive all of your theorems. Or you imagine the axioms of set theory to be true. Then the mathematician can derive all of his theorems. So the whole thing is a species of make-believe. 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 adopt and then you derive your deductions from them. But you are quite free as a mathematician to adopt a different set of postulates, a different set of axioms, and to explore that. So there is a wide variety of set theories that are on offer today. There is not simply a single set theory in mathematics. There is a range of set theories. These have different ontological commitments. Some commit you to sets. Some commit you to a different sort of objects called classes that are different from sets. So Pretense Theory will say that because you are merely pretending or imagining these things to be true, you are not committing yourself to the reality of these objects anymore than you are committing yourself to the reality of Sherlock Holmes in imagining that his fictional world is the case.

Neo-Meinongianism is one of the wildest anti-realisms. This stems from an Austrian philosopher Alexius Meinong who lived at the end of the 19^th and into the early 20^th century. Meinong was concerned to develop a theory of objects. He called his philosophy “Object Theory” – in German, Gegenstandstheorie. What Meinong maintained is that 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. He develops a whole theory about these objects. 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. That would be another form of anti-realism.

Those are just some of the anti-realisms that are on offer today. There is a real potpourri of alternatives. There are others that aren’t even on this list. I want to just share these with you to give you an idea of the field of options that is open. Obviously, in this class, we aren’t going to discuss any of these in detail, but I simply want to familiarize you with the range of options today lest someone think that the reality of mathematical objects poses an insuperable challenge to divine aseity – to the idea that God is the sole ultimate reality. That is not, in fact, true. As you can see, there are a great number of options available to the Christian theist today which would not commit you to the reality of uncreated objects of any sort. Platonism is only one view – a small view – in the whole range of views about the reality of these objects. I think that these other views, many of them, are very plausible. In order for Platonism to be a defeater of God’s unique self-existence, the Platonist would have to prove that Platonism is true and that all of these alternatives are false. I don’t think anybody believes there is a realistic prospect of doing that.

b. Application

What practical application does all of this have to our lives? Let me mention just two.

1. 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. 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. If I were to ask for a show of hands in the class today, how many idolaters do we have in the class today there would probably be very few. If there is anything else in life that is more of concern to you than God, you are guilty of idolatry. If your ultimate concern is not knowing and serving God better, then you are worshiping a lesser god. You are falling into idolatry. God’s aseity and ultimate reality is a powerful reminder to us of where our ultimate concern ought to be.

2. Second, God’s self-existence ought to exclude our selfishness. Another word for self-existence is independence. God is independent of everything else that exists. This is what man and Satan want, isn’t it? Independence. They want to go their own way; to challenge God’s self-existence by opposing to it their own independence. We want to oppose our selfhood to God’s “I am.” 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. Living for God, denying self in favor of God’s self-existence, I think makes good sense once we understand God’s self-existent nature.