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Questions on Numbers, Certainty, and the Trinity

September 28, 2020
Questions on Numbers, Certainty, and the Trinity


Dr. Craig answers questions on the nature of numbers, the need for certainty, and the relationship between the Argument From Contingency and the Trinity.

KEVIN HARRIS: Well, Bill, it is always fun for us to put you on the hot seat and get some of these questions answered. We get questions from all over the globe. In fact, this first question comes to us from Ecuador – Francisco in Ecuador. He says,

I’ve been following you for many years. Dr. Craig’s ministry has been a real blessing. I’m even making videos in Spanish based on many of the arguments I’ve seen that he uses and a YouTube channel. My question is concerning Dr. Craig’s position on anti-realism, numbers, and objective morality. Since morality does exist because it is grounded in God’s nature, could that also be the case for numbers and mathematics. I understand that, for example, it's strange that propositions and properties exist as in the conceptualist view, but mathematics do seem to have some of the characteristics of God such as perfection in the sense of consistency, in being exact, and infinity in a way, especially if they are in the mind of God. So if we separate mathematics or numbers from properties and propositions would you say that probably they exist in the mind or nature of God the same way moral values and duties exist? Secondly, if that's the case, could the conceptualist argument work only with mathematics or numbers? Thank you very much for your time. Francisco.

DR. CRAIG: Let's just address these in reverse order. Certainly if you do think that mathematical entities are somehow grounded in God's nature then you can run a conceptualist argument for God's existence based upon the reality of mathematical objects and the objectivity of mathematical truth. But I'm not convinced that a conceptualist view of mathematics is, in fact, the best. It's important to understand that I don't think that moral values are grounded or exist in the mind of God. Rather, I think that they are grounded in God himself as a concrete object. God is necessarily kind, loving, fair, generous, and so forth. So objective moral values are rooted in this concrete object which is God. Francisco seems to be willing to say that properties and propositions should not be grounded in God as the conceptualists think, but he wants to make room for mathematical entities to be grounded in God. That seems to me to be rather ad hoc. If you can get rid of abstract objects like propositions and properties then I don't see any reason to think that mathematical objects like numbers and sets are any more real than are properties and propositions and therefore should be put in the mind of God. He says that mathematics has the property of infinity. Well, so do propositions and properties. There would be an infinite number of propositions if propositions exist. And the infinity of mathematics is a quantitative concept that I think is inapplicable to God. God is not a collection of an actually infinite number of definite and discrete particulars. When theologians talk of God as infinite they mean it in a qualitative sense not a quantitative sense. God is morally perfect, eternal, omnipotent, omnipresent, and so forth. Moreover, and finally, I think there are certain difficulties the conceptualist faces in identifying mathematical objects with God's thoughts. For example, could sets be thoughts in the mind of God? Alvin Plantinga has suggested that maybe sets are God's collectings – his mental collectings of things into groups. Well, if you think about that, how is it then if sets are in the mind of God as thoughts that I could have access to sets? Suppose I collect mentally the objects on my desk into a unity. That would not be the set of all objects on my desk on this view. Why? Well, because that set exists in the mind of God as his collectings, and so I wouldn't have access to that set even though I talk about the set of all objects on my desk. But how could they not be the same? How could they be diverse? Because in set theory it's membership that determines sets. Sets which have the same members are ipso facto identical. So how could the set of objects on my desk that I mentally collect be different than the set of objects that God collects in his mind? So I think that it's just not very helpful to think of mathematical objects as thoughts in the mind of God.

KEVIN HARRIS: OK. I don't know if you've seen this article.[1] I got it from our friend Tim Stratton – a related topic. This professor, Laurie Rubel of Brooklyn College, says that basic math is culturally problematic. She says math is racist.

DR. CRAIG: Oh, gosh.

KEVIN HARRIS: Two plus two equals four is white supremacist patriarchy.

DR. CRAIG: Oh, Lord, help us.

KEVIN HARRIS: This is just getting insane. It's just a series of tweets. She says, “the idea that math (or data) is culturally neutral or in any way objective is a MYTH. i'm ready to move on with that understanding. who's coming with me?”

DR. CRAIG: Well, not very many people because that would have to be a number of people – right? – that are going along with her; more than one! Wait a minute, Laurie, I thought you didn't believe in mathematics; that two is greater than one?

KEVIN HARRIS:How many of you are coming with me,” in other words. Many? Wait a minute. [laughter] Well, I don't mean to put her down. There seems to be just kind of a poisoning of the mind.

DR. CRAIG: It’s insanity of political correctness and post-modernism.

KEVIN HARRIS: OK. Let's go to the next question then. Kyle from the United States opens his question by basically saying, “Look. I've read the books, and I believe that theism is true over naturalism. Christianity.” However,

The one big stumbling block I have not been able to overcome. My issue is why should we convert to Christianity if we can never be certain that it's true. Why give up your life for something that has a chance of being false. I mean, if we had direct experience of God that we can empirically verify then I could see why that would overcome any doubts. However, even if I read all of these scholarly literature works, why should I make a leap of faith? I mean, if God requires us to turn our life to him then shouldn't he give us strong epistemic justification? The same kind of justification that you would reach to conclude that, let's say, your wife or your parents existed? Something that cannot be disputed. The philosophical and historical arguments are not a certainty as something like a direct experience.

I think you see where he's going here.

DR. CRAIG: Yes. I couldn't have a more different perspective on this question. When I was a non-Christian and first heard the Gospel it occurred to me if there's even a one in a million chance that this is true it's worth believing in it, because if it's true that there is a God who loves me, created me, and wants to give me forgiveness and eternal life, this is so tremendous a good that it's worth taking a chance on. I think it's quite the opposite of what Kyle here is saying. Far from requiring certainty, the great goods to be had from belief in God and in Christ are such that we ought to believe in it unless we have very good reason to think it's false. This is the essence of Pascal's wager, isn't it? Pascal said that you have infinity to gain and nothing to lose by believing in the Christian Gospel, whereas on an atheistic view if you believe in atheism you have infinity to lose and little to gain by becoming an atheist. So when you're confronted with a choice between belief and unbelief, it seems to me that the choice is very clear that the prudent choice is to believe in God. I think God has given sufficient evidence for every person to make a rational decision with respect to his existence, and that he's under no obligation to give us certainty about this. We should not demand certainty in a question this important and this life-changing. To just give one more illustration. William James talks about the will to believe. He imagines a choice that is forced upon you. Say you're on an alpine hiking expedition by yourself and you see that a mountain storm is coming up which is life-threatening. You come to a fork in the path, and you don't know which fork leads down to safety and which goes ahead. Suppose some other hiker passes you and says, “It's the left fork that leads to safety.” Now, should you just stand there immobilized saying, “Well, I don't really have any certain evidence that that's true. I don't really know that that's right or that he knew what he was talking about. So I'm just going to stay here and die on the mountainside rather than take the risk and go with the evidence where it points.” Clearly the rational thing to do in such a circumstance is to go with the evidence that you have even if it is uncertain. It would be folly to allow the lack of certainty to paralyze you and lead to your doom. And that is of course what is going to happen to the atheist if Christianity is true and the atheist stands there refusing to make a decision.

KEVIN HARRIS: I think we could commend Kyle because he's invested in his faith. He’s read Swinburne, and he's even read Graham Oppy to maybe get the opposite. He follows you and Reasonable Faith. He says it all comes down to the resurrection, at the end of his question. We would commend him.

DR. CRAIG: Oh, of course we would. Absolutely. I don't mean in any way to disparage Kyle. All I am saying is don't be deluded by this will-o’-the-wisp of seeking certainty rather than simply sufficient evidence.

KEVIN HARRIS: Sure. Next question.

Hi, Dr. Craig. I am truly blessed by the work you do and honored to serve as a chapter director. I came upon a video interaction between Josh Rasmussen and Mohammed Hijab where Josh hinted that Trinity is not easily compatible with the argument from contingency and how alternatives like modalism have been presented to mitigate the challenge. Later I came upon a video series done by a Muslim group in India who said they'll be showing from the argument from contingency how the God that the Kalam cosmological argument points toward has to be the absolute one monad – Allah – and not the Trinitarian God. Is there really any incompatibility between the argument from contingency and Trinity? If so, how do we reconcile it? Also what should be our principle by which we weigh philosophical arguments and biblical doctrine when we come across such supposed incompatibility. Shouldn't Scripture hold superiority? Thank you for your response. With love, from India. Jacob.

DR. CRAIG: Thank you, Jacob, for your serving as a chapter director. I think that's fantastic that you're doing this in your home country of India. Let me take the questions in reverse order. I do agree that Scripture should hold superiority. If I have a philosophical objection that I can't answer to the clear teaching of Scripture, I should believe Scripture and simply ascribe my inability to answer the objection to my own philosophical ignorance and ineptitude and keep working on it – keep trying to answer it. But there's no reason to think that I and my ingenuity should be able to answer every philosophical objection that I might encounter to Scriptural teaching. So I do agree that biblical doctrine takes precedence and has authority in what we believe. Now, there's a lot packed into this brief paragraph here. Let me try to explain what I think is going on, not having heard the dialogue between Rasmussen and Hijab on the Trinity. In the classic doctrine of the Trinity enunciated at the Council of Nicaea it includes this clause that the Son is begotten of the Father before all worlds. “Light from light, true God from true God, begotten, not made.” I suspect that what Josh is saying is that the notion that the second person of the Trinity is begotten from the first makes the second person of the Trinity contingent or dependent upon God the Father. He would not be contingent in the sense of being non-necessary. The Son would exist in every possible world. He would proceed necessarily from the Father, but nevertheless there would be a sort of contingency or dependency in that the Son is dependent upon the Father as the fount of the Son. And this would be incompatible perhaps with the argument from contingency – that every contingent being needs to have a ground of its being. One possible way of answering that would be to insist that on the doctrine of the Trinity the three persons of the Trinity are not three beings. They are not three substances. There is one tri-personal substance which exists necessarily and is uncreated even if between the persons there is a relationship of dependency of one person on the other. Since the persons are not substances or beings, it's not incompatible with the argument from contingency. On the other hand, I have to say that this doctrine that the Son is begotten from the Father in his divine nature is not biblically grounded. It is not based on the New Testament, therefore I do not hold to it myself. I certainly don't think that it's incumbent upon every Christian. If you do not hold to that notion that the Son is begotten in his divine nature from the Father then there's simply no inconsistency between the doctrine of the Trinity and the argument from contingency because in that case you have three uncreated, eternal, necessarily existing persons who do not share any sort of relationship of dependency among themselves. So I think these Muslims are trying to exploit this to advocate for Unitarianism over Trinitarianism when it really doesn't strike at the plurality of the persons in the Godhead.

KEVIN HARRIS: Just to expand on that a little bit, is the Trinity an example of revealed theology from the Scripture – the doctrine of the Trinity – as opposed to something that we arrived at philosophically?

DR. CRAIG: That's the classic position. People like Thomas Aquinas would say that the doctrine of the Trinity is something that cannot be attained by natural reason but is believed on the basis of the teaching and authority of Scripture. And that's the view I incline toward, but there are certain contemporary Christian philosophers like Richard Swinburne who gives arguments that God is necessarily tri-personal – that there could not have been any less than three persons in the Godhead and there could not have been any more than three.

KEVIN HARRIS: At any rate, we can do what you just did and that is even if it's revealed doctrine and we look at the doctrine we can’t examine it philosophically. I think that's been extremely helpful. It doesn't mean that it's impervious to philosophy; it just means that we didn't arrive at it necessarily strictly philosophically. It is an example of revealed doctrine.


KEVIN HARRIS: But then we can apply philosophy to it, just like you've done with the atonement.

DR. CRAIG: As I said in answer to the last questioner, if there were a conflict between the doctrine of the Trinity and the argument from contingency then you ought to give up the argument from contingency, not the doctrine of the Trinity. I have far more confidence that the doctrine of the Trinity is true than I do that the argument from contingency is sound. Fortunately, as I’ve just explained, I don’t see any conflict between the two and therefore I don’t think that this will serve as an effective apologetic for Islam or Unitarianism.[2]


[2]           Total Running Time: 20:46 (Copyright © 2020 William Lane Craig)