Education and Christian Faith

Mathematics

Professor: Dr. R.J. Rushdoony

Subject: Education

Genre: Speech

Lesson: 1

Track: 01?

Dictation Name: RR306A1

Date:

Let us begin with prayer.

Our Lord and our God, we thank Thee that Thou hast called us to serve Thee and given us so great a privilege to educate Thy children for Thy service and for the command of the things that are of this world in Thy name. Give us grace to see all things in terms of Thy Word, to exercise dominion in every subject and in every area of life, to the end that all things may be brought into captivity to Jesus Christ. Open our minds and lighten our understanding and grant that we may behold wondrous things out of Thy Word. In Jesus’ name, amen.

Our subject this morning is “Mathematics,” and our approach will be from the perspective of the philosophy of mathematics.

One of the first things we must recognize as we approach mathematics and any and every subject is this: there are no neutral facts in the universe; no neutral facts. There are no facts that men can approach, believer and unbeliever and say, ‘Here, we both see the same thing.’ No. Every fact in the universe is a God-created fact. There is not an atom, not a thing in all of creation that is not the handiwork of the triune God. As a result, to look at anything including numbers, from any other perspective than a biblical one is to falsify what you view.

Not only are all facts God-created, but all facts witness to and testify to their maker. The heavens declare the glory of God and the firmament showeth His handiwork. Day unto day uttereth speech and night unto night showeth knowledge and there is no place, we are told by the psalmist, where their voice is not heard. Moreover, the psalmist tells us in Psalm 139 that though he fled from God to the uttermost parts of the sea, behold Thou art there. Thou I make my bed in Hell, behold, Thou art there. That psalm, incidentally, is the theme, out of personal experience, of perhaps the greatest single poem in the English language, Francis Thompson’s The Hound of Heaven, where he describes his attempt to escape from God but he cannot escape from him. Everything, wherever he goes, witnesses to the sovereign God.

So that first, we have no neutral facts in the universe. Mathematics, no less than biology is an area where there is no neutrality. Moreover, we have no neutral men. Men are either for God or they are against Him. They are either covenant keepers or they are covenant breakers, so that all men when they approach all things will attempt to divorce them from God to abstract them from the world of God’s meaning. They want to see the world in a vacuum. No more than trees and people exist in a vacuum, do numbers exist in a vacuum. They are part of a God-created world. To insist that they be viewed in isolation from the fact of God as creator is to falsify them. There is no understanding of mathematics, nor the fact that mathematics has developed to the point it has in human history apart from the context of the Christian civilization. When math has developed, or rather elementary arithmetic in various civilizations, it has gone so far and no further, and it has collapsed because there has been no ground for it; no foundation. We are told that the Arab scholars developed a great deal of math. And it’s true—except what we are not told is that those Arab mathematicians were either Christian captives or they were the children of Christian captives who’d been placed in their {?}, so that they brought a Christian understanding of mathematics and when that element dropped out of the Muslim world, their science and their math withered.

There is no idea of two without the idea of one. There is no idea of one without a theistic faith. Why do I say that?

The basic problem of philosophy throughout the centuries has been the problem of the one and the many. I have book on the subject entitled simply The One and the Many. It is in the area of philosophy and is not a simple book to read because this is the root problem. What is the idea of the one and the many? Well, mankind through the centuries has wrestled with the problem what is basic to reality? Is it the unity, the oneness of things or the individuality, the particularity of things? If you stress the unity of things then individuality, particularity (numbers) becomes a problem. In Vedantic Hinduism, 1 + 1 = 1 because {?} is one. And there’s no place for individuality. So that although early in Hindu civilization before this type of faith developed, they began to develop numbers; the minute they came to Vedantic Humanism and other forms of the same faith, all is one, then 1 + 1 = 1.

If you go instead to an Atomistic faith, you have no unity. You have only individual things that cannot be related to one another. So you have an endless number of ones but nothing that binds the ones one to another; no unity.

Now let’s take it in a practical fashion. When you have no real concept of the one and the many, you will say as you approach the doctrine of the Church, the Church is everything, the member is nothing. And you have Romanism. Or you can say the individual is everything and the Church is nothing, and you have Anarchism. You can do the same in the area of the State. The State (Totalitarian State) is everything, and the individual is nothing. Or the citizen and his rights are everything and the State is nothing and you have Libertarianism and Anarchism. You can have the same with marriage. Marriage is everything but the members thereof do not count; their feelings do not matter. There can be no breaking of the bond, as Rome says, no divorce. Or you can have the modern point of view—marriage depends entirely upon the individual’s feelings and it is to be broken if the individual is weary of it. Do you get the point? The basic problem whether it’s in the scientific sphere, the numeric sphere, the personal sphere, throughout the history of philosophy has been the problem of the one and the many.

No philosophy has ever solved, and this is why although very early, China had a great civilization, India had a great civilization; you had the Minoan culture of Crete, which incidentally had magnificent buildings with sewer lines, hot and cold running water, flush toilets, very much like that which we’ve developed in modern times, disappeared. There was no solution to the problem of the one and the many, and therefore life ended up either in meaninglessness or anarchy and the cultures collapsed. Only one faith has ever solved this basic problem of philosophy—the biblical faith, because in the doctrine of the Trinity, you have the equal ultimacy of the one and the many. One God, three persons; the oneness of God is as ultimate as he threeness of God, so there is both unity and individuality in the Godhead and therefor in all of creation there is an equal importance to the oneness of things, and the particularity or the individuality of things, and therefore, there is the possibility of a mathematics.

Let me illustrate the problem a little further on why this Trinitarian foundation of mathematics is basic. In another one of my books which is also in the area of philosophy, The Word of Flux, I cite the Princeton seminar of a few years ago by the mathematicians who, and astrophysicists who pinpointed the moonshot, controlled it and placed a man on a particular predetermined point on the moon. What was the seminar about after they had done this remarkable thing? The whole point of the seminar was what we did was impossible. We cannot explain how it was done. Why? Because, they said, our mathematics which led to the computations that pinpointed a man on the moon are simply the logic of man’s mind and have no relationship to the physical universe, to brute factuality.

Now let me explain the term ‘brute factuality’. That’s the view that the nonChristian has of the world out there, the nonChristian thinker. Brute means meaningless, unintelligent and unintelligible. It means that every fact in the universe is a totally meaningless fact, a product of chance. There is no law, no purpose, no design holding them together. The universe is a surd, a meaningless entity. How then, they said, can you have a realm of brute meaningless factuality without any purpose, order or law to it? And yet the logic of the human mind can place a man on the moon.

Well, one of the scientists remarked that of course there was a simple answer to it: God. But that was a cop-out. Do you see the point? They recognized that the one ground on which they operated is really theistic. If there were no God, they could not have pinpointed a man on the moon, but they wouldn’t acknowledge Him, nor that all their thinking depended on the reality of God. You see, we don’t prove that God exists, no, we begin with God. If we didn’t begin with God who is the foundation of all proof, nothing could be proven. So He is our starting point. We don’t begin and say we’re going to work our way up to proof of God. No—we begin with faith in God and in terms of that, all things follow.

We believe, therefore, that the logic of the human mind, the mathematics of the human mind, the thought of man, when it is orderly and in terms of God-given processes will have a relationship to the physical world because the order of the mind and the order of the world are God-created. Therefore there is a correlation. You see now why mathematics requires—of necessity—of necessity, a biblical foundation, a Trinitarian foundation or it becomes pure fiction; a game that man plays. A mental game.

Now if you’re interested in pursuing this matter further and doing some really thoughtful reading on this subject, let me recommend to you three things:

One, which is the most brilliant essay on this from a nonChristian point of view which says there is no such thing as mathematic, only mathematics and each particular form of mathematics represents a particular religious faith. But numbers have no reality. It is by Oswald Spengler who wrote the famous work, Decline and Fall of the West. I believe in the first volume it is that he has an essay on the meaning of numbers in which you have perhaps the most brilliant presentation of this anti-Christian and skeptical perspective. In other words, he’s an Atheist not only with respect to God, but also very logically with respect to mathematics. You have to give him credit for that, because most people today want to say, oh yes, this is valid but I don’t believe in God. Spengler knows you cannot do that. He does not believe in God and he says mathematics is pure convention.

Then, two essays from a Christian perspective by Dr. Vern S. Poythress, a Harvard PhD. in math. The first is titled, “Creation and Mathematics, or What Does God Have to do With Numbers?” It is in The Journal of Christian Reconstruction, vol. 1, no. 1 (and I’ll tell you in a moment how you can get that). And then again by Dr. Poythress, “A Biblical View of Mathematics” in a symposium edited by Gary North, “The Foundations of Christian Scholarship.” “The Foundations of Christian Scholarship.” Now these two essays, the first in the journal is an introduction and the one in the symposium goes into higher math from this Trinitarian foundation, are exceptionally outstanding reading. The book costs $7.50 and the journal, $4.00. We put out both, our foundation, so it comes to $11… $12…. $7.50 and…. No, $11.50. Now, if you’re interested in having those two write to us and state that you want the two things by Dr. Poythress and we’ll give them to you for $6.00, but do state that you were here in Dayton. And my address will be, just write to:

Chalcedon

P.O. Box 158

Vallecito, CA 95251

I think you’ll find those extremely helpful in understanding how there can be no mathematics apart from our faith.

Now let us go a step further. What is the new math trying to do? Let us turn now to a statement by a very interesting writer, Danielle Hunebelle, “Turning the Tables on Arithmetic” in a French periodical, Réalités, for December, 1963. And Hunebelle in this study, deals with Papy, one of the European founders of the new math and a session he was holding with the schoolteachers of Belgian, to instruct them in the new math. Hunebelle writes, “What is Papy doing? He is trying to create elementary mathematics in harmony with modern mathematics based on sets. For example, he tells beginners, ‘You are going to create a set.’ Then the child will suggest some kind of odd set; a teacher, a pickle, and a pinch of salt. ‘Now look at how important my decision is,’ Papy told me. I call this set ‘S.’ It now exists because I have created it. In old mathematics, you contemplated a pre-established world. Today it is I, it is the child who creates this world, who makes decisions, and is aware of the fact that he is deciding.” Do you get the implications of that? Papy says in the new math, we say there is no longer a pre-established world. That is his way of saying there is no longer a God.

It’s an amusing fact; I lecture very often on college and university campuses and I find for them pornography is not in the four-letter words you associate with pornography, but it is in mentioning God and Christ. They almost curl up in shock and die when you introduce the name of God and Christ into a university atmosphere.

So, when he speaks of pre-established harmony, he’s talking about God and the fact that He has created all things by His sovereign will. So the new math says there is no God, there is no world, there is no pre-established order. We create this world. We create this world. It’s a realm of brute factuality. It has no order. It has no purpose. It has no meaning. But it needs a divine word to brood as it were, upon this chaos and to bring order and meaning out of it, and this is man, the scientist, man the mathematician, who will create his own order and make himself god over it.

 

Now this is the heart of the new science, of the new math. We find this not only in mathematics but in other areas. You want to pursue it, Thomas Kuhn does this with science in general. He was the editor of The Encyclopedia of Chemistry and he wrote an introduction to it which was regarded as so important and has become extremely influential that it has been published separately as a paperback by the University of Chicago Press entitled, The Structure of Scientific Revolutions; The Structure of Scientific Revolutions.

Now, what does Kuhn declare in that book? Well in a sense, he’s doing the same thing that Papy is doing; only he is broadening his base to include all of the sciences. He said in that book that we have long had theories and hypotheses in science from the old theory of the Greeks about the four humors explaining man’s physiology and psychology, the Phlogiston Theory, on through Darwin and we’ve believed with all these theories that somehow we were getting to the truth of the world out there. But that assumes there’s a truth out there. And now we know better. So what are our hypotheses and our theories now? They are paradigms. They’re handles, with which we deal with brute factuality. We know that our paradigm has no truth to it; the truth does not exist, but it’s a handy tool to deal with something for a while. And he goes on to describe how the paradigm of bloodletting in medicine worked so well for generations. When people believed that if you had some bloodletting that was going to cure you of sickness, it cured you. But when they began to lose faith with it, they had another paradigm, and that paradigm works, and now people believe (although he doesn’t dare put it that baldly), that penicillin will cure you, so they’re cured by it. So he announces a virtual relativism. He draws back from a total one as the new scientific stance. The Structure of Scientific Revolutions is his title. You no longer deal with truth. Truth does not exist.

Of course, some other scientists have dealt with this problem not so optimistically. Dr. Gunther Stent, a molecular biologist at the University of California at Berkeley has dealt with this in his book on the dream of reason or the end of the golden age, I believe is the title [ The Coming of the Golden Age; a view of the end of progress]. At any rate, Dr. Stent deals with the fact that for generations, men believed that once we’ve dropped the God concept, again, like Papy, he doesn’t use the word God, they somehow fight shy of that. And he says that we have dropped that. We thought we would be free, that the Golden Age of mankind would emerge when we abandoned God. But what happened? Everything has lost its meaning. We now have random notes played as though they were music and artists who will take paint and put it on their motorcycle wheels and drive back and forth across the canvass and there’s no meaning anywhere and we’re losing men in the sciences because no one is interested in a discovery of truth—they don’t believe in truth. So they go into physics or biology or math just the way the collect cigar bands or rock records. It just happens to be their thing. And he said before long no one will be interested in studying because the pleasure principle is taking over mankind. We’ll all become Polynesians living for pleasure and in a couple of centuries mankind will disappear.

Well the reaction of the Natural History Magazine review when it was reviews, I believe in April or May of 1971, was this: he praised the book thoroughly but when he came to Stent’s prediction that mankind would disappear in two centuries, he said I cannot buy Dr. Stent’s optimism.

[Laughter]

Now this is the end result, you see, of the new math and of the new science as they themselves see it. It means meaninglessness. But we believe God is the creator. There is a given order in all of creation and one form of that order is mathematically expressed. The key issue is, as Papy saw it. Is there a pre-established world, a God-created world? Or does the mind of man bring order out of a world of chaos?

Spengler, whom I cited earlier, says, “Every philosophy,” (and he also says every religion) “has hitherto grown up in conjunction” [tape glitch] “… {?} impress.” The most you see that Spengler can say for mathematics is that it is a mystery. Why the quest for order? Why the feeling of man that there is a necessary logic and numerical concept that relates to reality? He cannot answer that. He only denies that there is such a thing. No mathematics is true for Spengler.

But of course, we must say that he is right in condemning many of the mathematics that have existed, just as we condemn all religions that have existed but one. The fact that there is error does not eliminate truth. Poythress says, on the other hand, in his Biblical View of Mathematics and the Foundations of Christian Scholarship, “It may surprise the reader to learn that not everyone agrees that 2 + 2 = 4 or that it is true. But on second thought, it must be apparent that no radical monist can remain satisfied with 2 + 2 =4. If with Parmenides (the Greek philosopher of antiquity), one thinks that all is one. If with Vedantic Hinduism he thinks that all plurality is illusion, 2 + 2 = 4 is an illusory statement on the ultimate level of being 1 + 1 = 1. What does this imply? Even the simplest arithmetical truths can be sustained only in a worldview which acknowledges an ultimate metaphysical plurality in the world, whether Trinitarian, polytheistic, or chance-produced plurality. At the same time, the simplest arithmetical truths only also presuppose ultimate metaphysical unity for the world, at least sufficient unity to guard the continued existence of sayings. Two apples remain apples when I am counting them. The symbol ‘2’ is in some sense the same symbol at different times standing for the same number. So at the very beginning of arithmetic, we are plunged into the metaphysical problem of unity and plurality, of the one and the many. As Van Til and Rushdoony have pointed out, this problem finds its solution only in the doctrine of the ontological trinity. For the moment, we shall not dwell on the thorny metaphysical arguments, but note only that without some real unity and plurality, 2 + 2 = 4 falls into limbo. The agreement over mathematical truth is achieved partly by the process described so elegantly by Thomas Kuhn and Michael Polanyi of excluding from the scientific community people of differing convictions.”

Thus for us, we have the key to mathematics as we do to every area of life and thought in our faith, in the doctrine of God as creator, in the God who in His infallible Word declares He is the Lord, that He is one God, three persons. “I am the Lord and beside me there is none other.” So there is no other key to truth, no other key to meaning. Thus, we do not deny the pre-established world of God in order to play God. We think God’s thoughts after Him and our knowledge is gained in that matter. The issue of mathematics thus is a religious one.

It has amused me lately that some of the hostility I’ve encountered on a couple of campuses in the last year in view of my, the one and the many and the influence it has had, has been from mathematicians who are Atheists. They see the point. It is time we did also.

We have about ten minutes before the final bell. Are there any questions now?

Yes…

[Audience] The, the new math was deliberate?

[Rushdoony] The new math is deliberate, like the new grammar. In the new grammar, there are no rules of grammar, nor of meaning, nor of anything. The new grammar rests on an Atheistic foundation that there is no absolute definition and that words are not propositional truths.

The new math, similarly, denies that there is a given order in reality. Yes, so emphatically, the new math is.

Now, a lot of the new math doesn’t entirely separate itself from traditional math so it keeps a foot, as it were, in both camps. And most of your textbooks will be written that way. But it’s only when you get into the heart of it that you have the obvious statement as with Papy. That here we play God. We are creators.

Yes…

[Audience] Uh, 1968, I {?} the mathematics at the University of Kansas. I was given the definition of mathematics as though it was something created by man, for no one {?} every time {?}

[Rushdoony] Yes, ah, that is something that is not limited to that school. In one university after another, students are told that mathematics is not related to reality nor does it have any practical utility. It’s an exercise; an intellectual game. Their point in so stating is simply their presupposition being anti-Christian. They want to deny meaning to reality. If you deny meaning to reality, where then is meaning going to come from? And where will there be planning and control in the world if not from the mind of man? Man will play God.

Any other questions or comments?

Yes…

[Audience] {?}The new math should be separated from {?} in Christian school {?}

[Rushdoony] Yes. The new math should be taken out of the Christian school because it puts the wrong ideas in the mind of a child. The child (even though the teacher never conveys such an idea) does pick up the idea which is essentially what the tempter said in Genesis 3:5, ye shall be as god, knowing (and the word knowing there has the force of determining for yourself) what constitutes good and evil, and therefore what constitutes true or false, the real and the unreal. You are god. And this is picked up by children.

Yes…

[Audience] I {?} on the section on devout logic, and I’ve never been {?} teacher on {?}. Would you eliminate that?

[Rushdoony] Yes, the symbolic logic is a part of the whole of this new perspective and it’s best to avoid it totally.

Yes….

[Audience] What are some practical ways philosophy was man-made, to students who see no relevancy to, to accepting the scripture?

[Rushdoony] Well, this is not an easy thing to teach, but you have to begin with the doctrine of God, the triune God, the one and the many, and that’s why what Poythress writes, if you study and re-study that, he gets into elementary math and then into higher math. That will give you a key as to the basic philosophy of math.

Those two essays, even before we came out with them, word of them got around to graduate students in math across country and they were waiting for the publication of the journal and then especially the book so they could use them in their classes. And they’ve had a tremendous impact across country. Mathematicians are beginning to be aware of their threat to their Relativism.

[Audience] Are there any textbooks available and {?} the university as opposed to the {?}

[Rushdoony] I really couldn’t say. I’m not familiar with the textbook situation, but it is of course universe (the Christian perspective) vs. multiverse (in which anything can be real).

Yes…

[Audience] Yes, I want to make a couple of comments.

First of all, I appreciate this so much and I’m sorry I couldn’t be here the whole time. I’ve read in books where Christian educators have said that for many people, mathematics is the most difficult subject in which to see the Christian relationship to {?} in other words, they say it’s teaching facts, but all facts do not, no facts {?} …relates directly to our statement 1 + 1 = license by the State because in every subject, even the most difficult {?} Christian faith, even mathematics is based on a Christian faith and therefore it’s part of our religion and the State does not have the right to control our religion. So, I just wanted to say that, perhaps you already understand how important this is to our stand on that.

And the second thing, we have a number of controversies in books, ah, the books as, {?} be with us at this time, and so we’ve got a number of these books in time for our {?} this afternoon and if you would be interested in securing some that we don’t have, we’d be happy to send you a list of those books for when we make them available and then I’d also like to put a plug in at this point for Mr. Rushdoony’s newest book called Revolt Against Maturity and {?} book I’ve been reading myself, and we’ve got a whole bunch of them down here, and so I’m sure that many of you will want to read it. It’s very good.

[Rushdoony] Thank you.

Well, if there are no further questions, I’ll give you a head start on the lunch line. [Laughter]