Principles of Mathematics - RR148E09

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Lesson[edit]

Professor: Rushdoony, Dr. R. J.
Title: Principles of Mathematics
Course: Course - Philosophy of Christian Eduction in Christian Schools
Subject: Subject:Education
Lesson#: 9
Length: 1:21:25
TapeCode: RR148E9
Audio: Chalcedon Archive
Transcript: .docx Format
Philosophy of Christian Eduction in Christian Schools.jpg

This transcript is unedited. It was:
Archived by the Mt. Olive Tape Library
Digitized, transcribed, and published by Christ Rules
Posted by with permission.


I must begin first of all by making it very clear that I’m perhaps the least knowledgeable person here in mathematics, so I see a few heads shaking so that gives me some reassurance. I do not want any questions that are too specific about the actual facts of mathematics because I shall be dealing here, as well as in areas where I am somewhat knowledgeable, with the principles. Some of your questions, at times, have been with respect to methodology. Now, we must remember that if the principles are sound, and this is what marks the truly Christian schools, sound principles. There can be variations of methodology, but these variations are not important. What does mark the fundamental difference is the philosophy of education and of the subject being taught, and of course, this is what I want to concentrate on as we deal with practical subjects, the philosophy of the subject.

You may recall that last week I dealt with the Princeton symposium of just a few years ago, in which the scientists involved with the moon shot, discussed the fact of How in the world it had been possible? How could they, with their mathematical computations, pinpoint a spot on the moon where man was going to land, and land him there? To them, it was not logical. It was not explainable. Why? Because, for them, mathematics was pure logic, simply the product of the human mind without any relationship to physical reality. Hence, for them, the logic of the mind could have no correlation or relativity to the physical universe. The only way they recognize that this could be so would be to posit God. This they were not ready to do. So, it remained a mystery for them, as well it must. If we drop the idea of God, then we convert all things into a mystery without any possibility of a solution. They have turned the universe into something that is fundamentally irrational and meaningless, in which not fact has any relationship to any other fact, and in which the logic of the human minds has no relationship to physical reality. [00:03:58]

There is only meaning and relationship in the universe...[edit]

There is only meaning and relationship in the universe, if it is a universe, if it is God-created. Let me illustrate that further. When I was a student at the university, doing work in the philosophy department, we were told specifically that it was simply a naïve and unscientific mentality that spoke of scientific laws. It was illegitimate, we were told, to speak of the law of causality, or of gravity, or of any other kind of scientific law. There was, at best, a probability concept. We were given an illustration of what this meant by one of the outstanding, pragmatic philosophers in the country. He said we can say there is a probability after some generations of observation, that the sun will rise each day in the East and set in the West, but we cannot say that it will, of necessity, do so, unless we can observe every sunrise and sunset from the first to the very last, only then can we say it is of necessity so.

Now, of course, this means that no one ever can. There will never be an observer from the first to the last day this side of God and His angels. However, of late, a number of thinkers have attacked the probability concept. Why? They have attacked it because they say the probability concept is, in essence, too theological. It still points too much to the possibility of a God. However, much these men, as they plan a moon shot, or work in a laboratory, assume the reality of the things they deal with, and however much they assume the validity of their mathematics and physics, and so on, when they speak in terms of the philosophy of science, they refuse to allow anything to point to the possibility of a fundamental order, or pattern, or law in the universe, lest it point to God. I think this gives you an idea of the extent to which these men are trying to eliminate from the area of thought anything that will smack of theology.

Now, this should not surprise us. You will recall, the other night, I dealt with Comte, and his three stages of development. First, the religious or mythical, concerned with meaning. Second, the philosophical, metaphysical, concerned still with meaning, and the third, the scientific, in which it is recognized that meaning is irrelevant, and man has only a pragmatic, an instrumental, a methodological and technological concern. He refuses to ask the question, “What does it mean?” That’s a question for the ignorant and the superstitious, because there is no meaning. [00:08:37]

Now, all that I have been saying is simply documenting...[edit]

Now, all that I have been saying is simply documenting the fact of this war against meaning, because meaning points to the world of God. Let me jump ahead for a moment to indicate how far this war against meaning goes. A very significant artist died a few years ago. His name was Marcel Duchamp. How many are you aware of his name? Yes. A few of you are. Marcel Duchamp, before World War 1, became quite famous at the armory show which was attended by all the notables of the day. It was the first shock treatment of the new, or modernistic art in the United States. Theodore Roosevelt and other notables attended, and reporters were interviewing all these notables on their reaction to the art show. Duchamp’s famous painting there was “A Nude Descending a Staircase. It was just a {?} cubistic forms and everybody was trying to figure out, “Where is the nude in that picture?” In fact, “What is the picture?” Now, Duchamp was a leader in the school of anti-art, warring against meaning. Subsequently, he refused even to take up a brush. He turned to the dumps, city dumps, and there went and picked up various broken items, culminating in a broken piece of porcelain, representing a bathroom fixture which he took and exhibited. He was mocking the idea of art and of meaning in art, and then, as a final stage, he abandoned any effort to even do that. There was no meaning, and any formal work in art was trying to establish a meaning. Duchamp then dedicated himself to creating a new language because, he said, all the existing languages pointed to the world of superstition, the first stage and the second stage of Comte’s thinking. And therefore, any language in which words had meaning, represented propositional truth and thus was theological. A language without meaning had to be created as the language for the humanity that was freed from God. Now, the more he tried to create it, the more it became obvious that it was totally impossible. How can you create words in a language in which nothing means anything, and so finally, Duchamp gave up the entire attempt and withdrew and spent the rest of his life, since he had means, in doing nothing but playing chess with a few friends. [00:12:15]

However, it is significant that somewhere in that process...[edit]

However, it is significant that somewhere in that process, before he gave up on the idea of a new language, Marcel Duchamp had himself photographed with a woman, both of them in the nude, and he holding an apple, and had it entitled “Adam and Eve.” He was the new Adam telling humanity, “This is the way to go for freedom,” freedom from meaning.”

Now, to turn more specifically to mathematics, in a very important European journal, about twenty years ago, the writer Hunebelle, discussed the new math as it was being set forth and taught, first of all in Europe by a Belgian mathematician, Papy, and he summed up what he had to say in that article in these words, and I submit that you cannot understand the purpose of the new math apart from this statement, and I quote, “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 ‘F.’ 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.”

Now, do you see the implications of this? Now, granted, that much of the new math still has a toe-hold on reality and has been used for practical purposes, but what Papy was saying was that in the pure form, as he contemplated it, he was trying to teach the children that they could abandon a pre-established world, a God-created world, that the world could be a man-created world. [00:15:48]

Now, the significant fact in Europe and elsewhere about...[edit]

Now, the significant fact in Europe and elsewhere about Papy’s work was that before it reached this country, one-third of all the teachers who taught math, for example, in Belgium, were under its influence and even more, half of all the parochial school teachers were under its influence, and it was one of the reasons for the collapse of a great deal of parochial education. It was based on a premise that man could become his own god, that man did not have to reckon with a pre-established God-created world. Now, of course, the roots of this are in Emmanuel Kant. Most of you, in any introductory course in philosophy, had an extensive introduction to Emmanuel Kant. To understand Kant, very briefly, we must go back to Descartes, and Descartes made the starting point of all modern philosophy, of humanistic philosophy, “I think, therefore I am.”

Now, as Christians, we do not begin with the autonomous mind of man, because first of all, man is not autonomous. He is not self-created, he is God-created. We begin with the fact of God. Beginning with God, Descartes went on and sought to prove the reality of God and of the universe. But in any philosophy, ultimately, your only real world is the world of your given, what you presuppose in the beginning is ultimately what you have. This is why every non-Christian position ultimately ends up with practically nothing. Oriental thought, philosophy, says nothingness is ultimate. Western philosophy winds up with only the autonomous mind of man, and that’s existentialism. Well, little by little, the philosophers who succeeded Descartes said, “We can have no knowledge of the external world that is valid knowledge, because all we have are sense impressions. They come to the mind secondhand. My eyes, my hands, my ears convey to me these sense impressions, that my mind has no direct contact with them, it is secondary. How do I know they are valid? I have no way of verifying them firsthand,” and of course, you have the long discussion in science and in philosophy, “If a giant tree falls in a forest, is there a sound if there is no one to hear it?” Is there not only a wave set in motion which the ear converts to sound, so that what actually happens and what you hear are two different things. [00:19:56]

Well, of course, in Hume this culminated finally in...[edit]

Well, of course, in Hume this culminated finally in a total cynicism with regard to the possibility of knowledge. With Kant and his successors, the objective world became an aspect of the human mind, so that we could speak of the reality of the world and of whatever gods may be, as merely aspects of the human mind, so that instead of God being the creator of the world to the man, the mind of the man became the creator of God and the world. They became then, little more than limiting concepts used by the human mind. This is why Schopenhauer, after Kant, titled one of his books, The World as Will and Idea. Now, if the world is only will and idea, only an aspect of the mind of man, then it is natural that ultimately, this is applied to the realm of mathematics, and mathematics is simply an expression of the mind, a creation of the mind, not the creation of the mind of God, not an aspect of the reality He has created.

Now, of course, it is always impossible for man to escape reality, much as he tries, so even in his flights of fancy in the new math, man cannot separate himself from the real world totally. So, he always has a foot in the real world, as it were, that his purpose is to abolish a world of pre-established harmony, to use their term. That is, a God-created, a God-given world, and to created instead, a man-created world and to teach the child that the child is the creator.

One of our problems you see, in understanding these things is the fact that we, as Christians, are not crazy. It helps very much in understanding the new math and the new English, and everything else if you’re not in your right mind. So we have a problem in that respect. The key issue thus, is {?} mathematics is simply this: Is there a pre-established world, a God-created world, or does the mind of man create the world out of chaos? [00:23:20]

Now, at this point, of course, we can recognize that...[edit]

Now, at this point, of course, we can recognize that there are various forms of math possible. Oswald Spengler, in his book on the Decline of the West, has a great and very important chapter on mathematics. If mathematics is your field, I urge you to get Spengler’s Decline of the West, and read that long and rather technical but extremely important chapter. I believe it’s in the first volume. It’s titled, “The Meaning of Numbers.” Up to a point, we can agree with Spengler, although we cannot agree with his ultimate skepticism of any truth. What Spengler does say though, that is very important is this: The faith that you begin with will create a particular form of mathematics. So that, he says, the idea that mathematics was born with the Greeks and progressed to the modern world is totally false, and he analyzes the Greek idea of numbers and finds it radically different. The key difference is that the Greeks were radically hostile to the idea of infinity. The mathematics that developed out of the Christian perspective was not hostile to the idea of infinity because God, the creator, is infinite. He is so great that even the universe He has created is beyond our imagination and staggers it, so that, in a Christian culture, man was not afraid of the idea of infinity as Greek humanism was. Modern humanism, having been borne out of a Christian context, still has the idea of infinity.

Now, Spengler concludes after he surveys mathematics in different civilizations, that there is no such thing as mathematic, only mathematics, that each culture and each religious perspective creates its own idea of numbers and sees reality in terms of it. Spengler says, and I quote, “Every philosophy has hitherto grown up in conjunction with a mathematic belonging to it. Number is the symbol of causal necessity. Like the conception of God, it contains the ultimate meaning of the world as nature. The existence of numbers may therefore be called mystery, and the religious thought of every culture has felt their impress.” [00:27:08]

Now, he is right that various religions do create their...[edit]

Now, he is right that various religions do create their cultures and their mathematics, just as various cultures have their own languages. Languages reflect the faith and the thought processes of the culture. This is why it is so important in the modern world to destroy the language of scripture, to destroy the old translations because they create thought patterns which are anathema to modern humanism. But to say that there are many religions and many mathematics does not solve the question: Is there a true religion? And is there a true mathematic? And of course, we, as Christians believe there is. There is no common ground knowledge that is open to everybody of all religions and of all faiths, because everyone views the world with a totally different perspective. This was an amazing thing to me, let me add, when I was on the Indian reservation. I could be with Indians and we could see, what I thought was the same thing, and come up with a totally different perspective on what it was, what it meant, because we see things with the eyes of our faith, and the eyes of a man who has never had any contact with Christian faith, see the world around us very differently. They see different meanings and different things, so that it is not the same world that they live in.

In one of the publications that our little foundation, Chalcedon, The Foundations of Christian Scholarship, edited by Gary North, we have a chapter on mathematics by Dr. Vern Poythress and Poythress, I think, states the case with particular clarity. He says, “It may surprise the reader to learn that not everyone agrees that two plus two equals four is true, but on second thought, it must be apparent that no radical monist can remained satisfied with two plus two equals four. If, with Parmenides, one of the early and key philosophers of Greece, one thinks that all is one. If, with Vedontic Hinduism, he thinks that all plurality is illusion. Two plus two equals for is an illusory statement. Then, on the ultimate level of being, one plus one equals one. 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 if Trinitarian, polytheistic, or chance-produced plurality. At the same time, the simplest arithmetical truths also presuppose ultimate metaphysical unity for the world, at least sufficient unity to guard the continued existence of sames. Two apples remain apples while I am counting them. The symbol “2” is, in the same sense, the same symbol at different times, standing for the same number. [00:31:43]

So, at the very beginning of arithmetic, we are already...[edit]

So, at the very beginning of arithmetic, we are already 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, two plus two equals four falls into limbo. The agreement over mathematical truth is achieved partly by the process described so elegantly by Thomas Kuhn and Michael Filane{?} of excluding from the scientific community people of different convictions.

Now, what is Poythress saying there? It’s not a simple statement. What he is saying, and I have devoted a book to this subject, The One and the Many, it’s not easy reading because it is perhaps the basic question in philosophy. The subject of the book is the one and the many. Now, the basic problem in philosophy which has bedeviled the history of philosophical thought in China, India, Ancient Greece, and Iran, in Egypt, and throughout the history of Christendom has been: What is ultimate? Is the oneness of things ultimate or is the many-ness of things ultimate? Now, your answer to that question is very important, because if you say it is the unity or the oneness that is important, then you have no particularly. Then, individuals cease to exist. Then, the many-ness of things ceases to exist and one plus one equals one, because everything is one, and mathematics perishes ultimately because all plurality is an illusion, but if you emphasize instead the plurality of things and say, “No, there is particularity, there is a many-ness,” then all you have is plurality, particularity, and no unity. It can never come together as any sum. And then, you have what you have for example, in modern existentialism, “Do your own thing,” because there is nothing that is binding upon everyone. [00:35:05]

To illustrate, the cynic school of thought in Greek...[edit]

To illustrate, the cynic school of thought in Greek culture is perhaps best known by the person of Diogenes, and Diogenes is pictured in {?} as going around with a lantern in broad daylight, living in a barrel at night, looking for an honest man, and saying there was no such thing, because honestly is a category above and beyond particularity. Therefore, honesty does not exist, virtue does not exist, truth does not exist, only particulars individuals exist, and so the cynic said there is no such thing as God, nor truth, nor mathematics, nor morality. The cynics insisted that man should regard himself as another animal like the dogs, and in fact, the word “cynic” comes from “kynos,” canine in English, dogs. They insisted that man should have the freedom, sexually, to behave like animals because everything else was illusion. Significantly, in the Berkeley demonstrations, the students were demanding, over the public address system, the right to copulate openly on the campus like the dogs, and were denying the idea of any overriding truth in philosophy, religion, society, mathematics, or anywhere else. For them, two plus two could never equal four. You only had endless “ones.” One plus one couldn’t equal one. You only had endless particulars. This is why they saw no further point in studies.

Now again, as I said, it is hard for us to grasp this mentality because we, as Christians, are not crazy. We think theologically, whether we do it self-consciously or not. We assume that there is God’s fundamental order in the universe. Now, through the history of thought, except for systematically, rigorously, Christian thought, civilization has been ambivalent. It has fallen either into the idea of the one or of the many, and in either case, it has destroyed the possibility of science, or of mathematics, or of anything. This is why, when you’ve had a burst in some cultures, as in India, and in Arabic culture, of various sciences and mathematics especially, it has a short life. It perishes, because the faith of those cultures lacks an answer to this problem of numbers, of the one and the many. Lacking that answer, it ultimately destroys the possibility of science, and it collapses. This is why, only in Christian civilization have you been able to develop mathematics, science, and society. [00:39:21]

Moreover, if you have no sound idea of the one and...[edit]

Moreover, if you have no sound idea of the one and the many, your culture breaks up into either totalitarianism, the tyranny of the one, or into particularity, the tyranny of anarchy. Only in one context, the Christian context, has there ever been an answer to the problem of the one and the many, and it rests in the doctrine of God. The doctrine of the trinity. This is basic to mathematics. I won’t go into it, but just to indicate the general principle. For a detailed exposition, let me refer you to Dr. Poythress’s article, in Gary North, “Foundations of Christian Scholarship. But, in our doctrine of God, three persons; Father, Son and Holy Ghost, one God. You have the equal ultimacy of the one and the many. What is ultimate in God is both His particularity, His many-ness, His unity, His oneness. Neither the one nor the other predominates. As a result, you see, only in Christianity is it possible to develop any idea of numbers that does justice to the oneness of things and the many-ness of things. In every other culture, the idea of numbers breaks down. This is why, because he founded his thinking on the doctrine of the trinity, Dr. Poythress was able to develop a valid foundation for mathematics, and to deny the idea that it is a man-created thing, that it has a part in the pre-established harmony of things as ordained by God.

Thus, you see, the issue in mathematics is ultimately and essentially a theological one. In every area of life, this is the foundation. God, having created all things, ultimately in every area of life and thought, all things are understandable only in terms of Him. [00:42:37]

It has been rather amusing to me, and I’ve been on...[edit]

It has been rather amusing to me, and I’ve been on some campuses in the past year or two, that one of the things that creates the most intense hostility comes from math departments that are aware of our publication of Poythress’s thesis, first in one of our “Journals of Christian Reconstruction,” and then his more thorough development of it in “The Foundations of Christian Scholarship.” It has been a red flag to them, because it has been so important to them to establish an alien foundation for mathematics, one that rests on the autonomy of the human mind, on the ultimacy of the human mind as the creator. Are there any questions now? Yes?

[Audience] {?}

[Rushdoony] I can’t hear you, can you . . .?

[Audience] {?}

[Rushdoony] Oh, yes. Alright, now. If your basic theological premise, you see, the oneness or many-ness. Now, if you believe that the oneness of things is ultimate, then you will emphasize in every sphere of life the oneness of things. You will say that the state is everything because particulars, individuals, specific numbers, are nothing. You will say the church is everything and the member is nothing. You will say that the idea of marriage is everything, and the man and the woman and the children in marriage are nothing. Do you get the drift of that? Now similarly, if you emphasize the numerical particularity as ultimate, then you become an anarchist. You say the idea of marriage is nothing, it’s what the man or the woman wants. You will say that the church is nothing, the individual member is everything. You will say that the state is nothing, the individual is everything and you will become an anarchist, and of course, this is precisely why you have this tremendous ambivalence throughout history between totalitarianism and anarchism in one culture after another, because of their inability to come to grips with this problem. This has marked, for example, Greek culture and Roman culture. When Aristotle was reintroduced, and Plato, into Christian thought in the early Middle Ages, it came to dominate and created the same impasse, and finally destroyed the Medieval period. When it was reintroduced to the Enlightenment into the modern era, it undercut the Reformation, and has created the world that we know today, with the extremes of totalitarianism, you see, and anarchism, and no idea of anything in between, because you cannot have a balance between the two and see the reality of both the one and the many, apart from the doctrine of the trinity, because only the doctrine of the trinity sets forth the equal ultimacy of the one and the many. This is, as I said earlier, the basic problem in all of human thought; the one and the many. Modern philosophy has given up trying to solve it, so they simply refuse to deal with it. Yes? [00:47:20]

[Audience] {?}

[Rushdoony] I couldn’t quite hear you.

[Audience] {?}

[Rushdoony] Yes, let me give you the reference on that. The author of the article was Danielle Hunebelle. The title of the article, “Turning the Tables on Arithmetic.” “Turning the Tables on Arithmetic in Realites,” spelled exactly like “realities” without an “I” in the last syllable. Realites #157, December 1962, page 42. You should find that in almost any university library, and it will give you, not only this quote, but several pages of technical analysis which set forth the reason why this new math is so basic to the modern perspective. Yes?

[Audience] {?}

[Rushdoony] What do I think about Christian schools with teachers educated in state schools? Well, I’m not going to condemn people educated in state schools. I’m one of them. I’ve fought it, and I’ve outgrown it, and I trust others have as well. However, I believe today, as the issues have become very clear, we should look for teachers who have seen the issue early enough, but of course, some people do wake up to issues rather tardily. Now, unless the state requires certification of teachers in Christian schools, I do not think we should go to the state institution for certification, and I do believe that we should work toward all such laws. I think we should work toward having Christian schools certify their own teachers, training and certifying them, because ours is a different philosophy of education, and as a result, in root and branch, we are different. Hence, there is a radical inability on the part of anyone who is not a Christian and has not had the exposure to the significance of Christian education to grasp the fact that the entire philosophy of education is different. You’re not dealing with the same thing. [00:51:41]

So, I do believe that we’re going to see, increasingly...[edit]

So, I do believe that we’re going to see, increasingly, in the next ten years especially, a battle. First of all, the state institutions are progressively going to try to deny Christian institutions the right to exist, Christian colleges and Christian associations the right to certify, or to train Christian school teachers. There’s a reason for it. They want to choke off the supply. Now, let me indicate something of the nature of the problem. One area in which we’ve had an influence on some very fine professors in various secular institutions has been economics, and one of the most important professors of economics in this country has told me there is no institution in the world today where a man who is thoroughly Christian, and thoroughly conservative in his economics, can get a degree, a doctor’s degree, in economics. Now, what’s the purpose of that? Why, it’s very simple. They choked off the supply. All over the country today there are colleges, and occasionally universities where some businessman on the board fights hard and finally he’s told, “Alright, you can bring in a conservative on economics,” and so he’s happy, and he looks around for one and he can’t get one. They’re not being graduated, that is, or given doctorate. They’re flunked out. To be very specific now, in one case a young man, working at a major university, the top student, was told by someone in the department, he was working for a doctorate, to “Get out before they flunk you, because they will never tolerate anyone with your faith and your economic points of view to get a degree,” and if you’re flunked out, then you’re ineligible for admission to any other graduate school anywhere in the country, and he found out very quickly that there wasn’t a graduate school in the country where this would not happen to him. He did find a professor who, while not a Christian, was a kindly person and he invited him to work for his doctorate at their university, a major one, in the department of history, and worked on economic history and that way, he’d get a degree. Well, subsequently, one of those two friendly professors left, so he only had the one to protect him. The one was important enough so that he felt he would get through. Now, when it came time for his doctoral examination, he had been the best student in the department, no question about it. It was a written examination of three hours in length. I asked him when it was over how he did. He said, “If I had written the questions I couldn’t have picked better questions for me to answer. I couldn’t have done better,” and I told him, “They’ll flunk you.” I was right, they did. They also destroyed the paper, that was routine, and he was not given the names of the three faculty members who had graded him. No appeals, you see. Well, he had one chance more at it, and I said, “They’ll let you pass. They’re just roughing you up to hurt you because they resent the fact that you’re getting {?}.” He didn’t feel he did as well on the second, but he was fast. When it came time to write his dissertation they {?} him one way or the other, so he had to spend an extra year. They knew they were going to have to give him the degree, but they were punishing him in the process. [00:56:45]

Now, that’s the kind of thing that’s happening increasingly...[edit]

Now, that’s the kind of thing that’s happening increasingly in one field after another. There are still field where a Christian can get through, but in some fields, they’ve already strangled every possible school, and choked off the possibility of a Christian getting through and getting a degree. So you see? We’re going to, whether it is in preparing teachers or giving masters and then doctoral degrees to Christians who are going to teach in Christian colleges or wherever, we’re going to have to do it ourselves. They’re not going to tolerate us. Now, you can still get by. I’ve given you one of two fields, and in particular economics which is the worst right now, the very worst, but it is going to be the direction of things progressively. So, we had better work in that direction. We had better support those institutions which are making strides to correct that situation by creating programs for degrees in a Christian context. Does that help answer your question? I gave you a lot more than you asked for, but I got wound up. Yes?

[Audience] {?}

[Rushdoony] Could you repeat? I lost you there.

[Audience] {?}

[Rushdoony] Yes. Washington State requires that teachers in Christian schools have certification, and the sad fact is the Christian schools there did nothing to fight it. I hope, in not too many years, they will wake up to the issues and recognize it was a serious mistake to accept that. This is not true in California and other western states. In California, you can certify your own teachers in a Christian school. They need not even have a college degree. I know one Christian school in the L.A. area where the best teacher, a very remarkable woman who never went to college. She’s one of the best-read woman I know, a brilliant woman, but this school felt she was well worth hiring, and she’s been outstanding. Yes?

[Audience] {?} [01:00:04]

[Rushdoony] Oh yes...[edit]

[Rushdoony] Oh yes. Well, that’s a purely association requirement and it’s wrong, of course. There are many who disagree with it and there are many schools that refuse to join the Western Association for that reason. They feel that it is a very seriously dangerous concession.

[Audience] {?}

[Rushdoony] In California, there is no state requirement on the part of the State Board of Education. Counties ask that you submit attendance reports, but even that has nothing mandatory about it and some schools never bother to. All that is necessary, in the state of California, for a Christian school to do, is to meet the local building code and zoning requirements, and that will vary from city to city and county to county. So, in some areas, it’s very simple, no problem at all. Yes?

[Audience] {?}

[Rushdoony] The question is did the new math ever have any practical necessity. Well, remember I said a great deal of the new math keeps a foot in the real world, so it has both had a practical utility and, at the same time, has tried to establish this autonomy of man and to create the impression that we can live in a man-created world. So, some of the new math has had a useful function and has not been truly new math. It hasn’t been pure theory, so it would take someone who knows more about math than I do to sort out the two. Yes?

[Audience] As a rule of thumb, can you recommend a Christian school stay totally away from the new math?

[Rushdoony] The question is, as a rule of thumb, would I recommend that a Christian school stay totally away from the new math. I would say that the closer they are to the old math, the better. Now, in some situations, it might be helpful to have a little bit about the new math if the colleges in the area require some kind of testing in it. You’re going to have to go to a degree on local situations. If there are tests required, as some states have had but it’s just about disappeared, of all twelfth grade graduates, or of all college entrance students, and it becomes necessary for them to have a limited knowledge of the new math, then perhaps you should go into it, to a limited degree.

[Audience] Historically, what culture has best represented the ultimacy of the one and the many and where is our culture in relationship to the one and the many?

[Rushdoony] The question is, historically, what culture is best represented the equal ultimacy of the one and the many and where is our culture today in relationship to the problem. Well, it has only been clearest in its expression in some periods of Reformation history and American history, where you have this balance between the one and the many, between anarchism and totalitarianism, to put it in political terms. Our country today is polarizing among the humanists between totalitarianism and anarchism. The new left was largely anarchistic, but there are strong totalitarian elements in the new left. Yes? [01:05:05]

[Audience] {?}

[Rushdoony] Yes. Well, first of all, we must remember that, until recently, many of your great scientists, men like Maxwell, for example, were through and through Christian in their perspective, so that you cannot really trace the history of science, especially in the English speaking world, apart from a history of Puritanism. The founding members of the Royal Society were Puritans to the core, and that very important aspect of some of your basic material sciences, as well as math, remained until fairly recent times, a strongly Christian aspect. It is now, of course, in drastic erosion, but it was emphatically there, and I will be touching on that when I deal with the sciences. The fact, for example, that a man like Isaac Newton gave only a part of his life to his mathematical principles and idea of gravity, and good deal of his life to mathematical computations dealing with the book of Revelation. He spent more time on that than he did on what he know him for. That’s an aspect of Newton that very few people are aware of, but some of the strangest interpretations of Revelation that we have come from a long succession of scientific men who took math and applied it to Revelation. Yes?

[Audience] {?} fall in the forest {?} what’s a Christian answer to that?

[Rushdoony] The question is, if a tree falls in the forest and there is no one there to hear it, is there a sound and what is the Christian answer to that question. Well, there was an attempt both to formulate that question and give a Christian answer on the part of Bishop Berkeley or Barkley as he knew it, and if you look in the discourses of Bishop Barkley, you will find an answer, and not one that we would agree with. What Bishop Barkley had to say was, that there is no physical, hard, material world out there, and in a sense, his ideas both suggest Mary Baker Eddy and also modern science, because his thesis was that we have simply energy in motion, that the whole idea of the material world as a hard thing is a myth, and that these atoms are actually energy in motion and can be no more than light, and that they come directly from the mind of God. Now, of course, the weakness in Barkley’s perspective was that although in many respects he jumped ahead of about two hundred years of science and saw the ideas of a hard, material universe disappear into energy, and problems in defining what is that energy, he identified that so closely with the mind of God, that he made it virtually a part of God, so that you had a defective doctrine of God. So, while Bishop Barkley’s answer is a remarkable one, we cannot entirely agree with it. [01:10:14]

Now, because we are Christians, first of all, we have...[edit]

Now, because we are Christians, first of all, we have a problem that the humanist does not have. I’m going to take a little while and I’m going to go around the barn a few times to answer your question because I feel it’s so basic and important a one that we need to deal with it. One of the things that marks humanistic science is its love of precise definitions. It feels that things can be defined and comprehended, and so, for example, as science defines (we’re talking now in very popular terms) man, man is reduced to his physical nature. He is described in terms of his bodily characteristics, and so on. But we see man as something more than the sum total of his physical aspects. Moreover, we believe that because all things were created by God, nothing can be defined purely in terms of this world and what you see. There’s more to me than you see. I am a new creation in Jesus Christ. There is more to the ungodly man than you see. He is a covenant breaker, one who is created in the image of God. With all his being, he is at war with God. So the fundamental facts about every person is something you do not see, that they are God’s creation, and definition can comprehend nothing in the universe. As a matter of fact, when you try to define something, you always fall short. When you try to explain something purely and simply in terms of the materials universe, the reality escapes you because everything in this world in terms of its basic meaning and purpose, as well as its creation, comes from the hand of God, from the mind of God. So, the scientific demand for a precise description, say of the mind, it’s an impossibility. We cannot define the mind of man. It always escapes them. I like to use, when somebody raises the question of definition, if you feel that you can define things a la modern humanism easily and precisely because everything is so readily comprehendible by the mind of man, try defining to somebody who has never seen or tasted a strawberry, the taste of a strawberry. It’s an impossibility. You can’t do it. Definition, you see, presupposes that it is the mind of man that will comprehend. [01:14:15]

So, scientifically, and I’m jumping ahead, we do not...[edit]

So, scientifically, and I’m jumping ahead, we do not attempt to define and to comprehend things. We classify. This was the task of Adam in the Garden of Eden. When God commanded Adam to name the animals, that was a scientific task, because to name in the Bible means to classify. This is why men changed their names, as they changed their nature. We don’t know what Abram’s first name was, but we know that when God called him, he named him Abram, Father of Many, and later again he changed his name to Abraham, Father of a Great Multitude, and in that process, Abraham had to bear that name by faith, and how people must have snickered when he went into Canaan and they asked him his name and he said, “Abraham.”

“Oh, how many children do you have? Ten, fifteen, twenty?”

“None.”

They must have snickered at the idea that a man would dare to carry a name like that. So, when Adam was asked to name the animals, he was asked to classify them. So, for us, science is classification and description. The meaning, because it comes from God, is to be understood in terms of God. But, a comprehensive definition escapes us. This is why we can deal with sound, as Christians, and recognized that sounds, in some sense, are real, but we never attempt to define sound, because when the physical universe is so great that it escapes our ability to comprehend, and God is so much greater that we can never know Him exhaustively and totally, although we can know Him truly. For us to think about definition in any precise form is to be guilty of the presumption that marks humanistic science. Does that help?

[laughter] [01:17:12]

You see, as humanists at heart, we want everything...[edit]

You see, as humanists at heart, we want everything clear cut, because when we have something that is clear cut, we are masters over it and we are lords over it, but we don’t have that power. Any other questions? Well, we . . . yes?

[Audience] {?}

[Rushdoony] Couldn’t modern math be introduced in terms of a Christian purpose and framework? I don’t understand what that would be, but if it’s possibly, perhaps it could be, but we must remember the basically radical intent it had, and if we do use it we should always make the child aware of the presupposition, because what the modern mathematician like Papy is saying to the child is, “Ye shall be as God, and you shall create your own god,” and with that, we cannot agree. Now, as I indicated there is a great deal of what passes for modern math that is not precisely what Papy is dealing with, and we must make a differentiation there. Well, that’s all for today. [01:19:22]

End of tape.