What Does Geometry Have to Do with Theology or Law?

"The laws of nature are but the mathematical thoughts of God."  --Euclid

In reading Dr. Gordon H. Clark's theological and philosophical works, I came to see that logic was the most important source for understanding anything at all. Without logic nothing makes sense. Yet the liberals will say that learning is intuitive, experiential, emotional and a whole host of other things.

Awhile back I did a teacher preparation course at Polk State College, Lakeland, Florida. I learned about differentiated learning styles, multiple intelligences, diversified teaching strategies, and moral relativism. "What's right for you is right for you, and what's right for me is what is right for me." Being an avid reader of the books by the late Dr. Gordon H. Clark, I immediately piped up and said, "Well, two plus two is four for me. Maybe two plus two is five or seven or ten for you?" If there is no absolute truth then nothing is meaningful. Relativism in morality means that there is no morality. Morality does not exist.

The same is true when it comes to epistemology or the study of knowledge. If there is no such thing as truth, then we can know nothing. Furthermore, focusing on teaching strategies rather than the common core essentials shortchanges students and deprives them of any possibility of reaching their fullest potential.  It is the material to be learned, stupid!  That is not to say that teaching strategies are not important.  But to focus only on mindless exercises and the student to the neglect of the purpose of education in the first place is self defeating.  Without knowledge being propagated and higher order thinking skills, namely logical thinking skills, then education is itself meaningless irrationalism with no purpose.

Dr. Gordon H. Clark was fond of pointing out that geometry starts out with unproven axioms to prove theorems or propositions. In fact, without logic geometry would be nonsense. For the Christian the beginning axiom is, "The Bible alone is the Word of God." This axiom or "basic postulate," as the video above calls it, is the beginning point from which all knowledge flows. Deductive thinking makes knowledge possible. That's because induction cannot prove deductions. Every branch of knowledge--whether it be history, science, physics, astronomy, etc.--begins with unproven axioms. Logical positivism, for example, started with the axiom that everything we know must be verified or falsified by the five senses. Of course, Dr. Clark devastated that argument by showing that empiricism can know nothing precisely because the mind interprets what the fives senses present to it. Thus, empiricism can lead to no knowledge whatsoever.  Furthermore, logical positivism refuted its own argument by starting with an axiom that is itself empirically beyond proof.

In geometry the axioms are not proved beforehand.  Theorems or propositions are proved from the axioms.  Although my opinion of Abraham Lincoln has evolved over time, as a young man I was particularly impressed by the fact that Lincoln essentially educated himself and passed the bar by self-study.  From an early age my father taught me to read and study on my own.  He even bought a full set of the Encyclopedia Brittannica for our home because he wanted his children to have an education.  I am not saying that this was the way to do it; however, it must be said that the encyclopedia had articles on theology, philosophy, mathematics, geometry, etc.  I read these articles with enthusiasm.  In fact, I first read about Calvinism and the issue of supralapsarianism and infralapsarianism from the Encyclopedia Brittannica.  I might point out that the Arminians started out with infralapsarianism and degenerated into their illogical system of theology from there.  The same is true of the 19th century neo-Calvinists who tried to mediate between Calvinism and Arminianism with their innovative three points of common grace, God's unrequited desire to save the reprobate, and other such irrational theological propositions.

Moreover, the interesting thing about Lincoln, as the video above points out, is that Lincoln based his study of law on the logic he learned from geometry.  Rebutting arguments is essential in the legal system.  Legal proofs are based on deductions made from prior law and case law.  Court cases in court room are won by logical arguments, not by emotional appeal.  Of course, juries are often swayed by a bit of both in closing arguments.  The bottom line, however, is logic.  Johnny Cochran was brilliant when he argued that, "If the glove does not fit, you must acquit."  The problem is that the prosecution blundered in its response to this challenge because the prosecutors did not know much logic.  The challenge, of course, is a logical fallacy because it does not follow that if the glove did not fit you must acquit.  Why not?  Well, there are several other explanations of why the glove did not fit when O. J. Simpson tried the gloves on in the courtroom.  One obvious one is that when Simpson put on the rubber gloves the dynamic changed the fit of the glove.  Another possibility is that the friction between the rubber glove and the dried blood soaked leather did not allow his hand to fit.  Another possibility is that dried blood can cause leather to shrink slightly.

Logic is essential to everything we do, including our reading of the Bible.  If the Bible is not revealed through logical propositions, then the Bible is meaningless metaphors and fairy tales that have no point of contact with any kind of knowledge whatsoever.  According to Dr. Clark, John 1:9 is not speaking about salvation but about logic (John 1:1) being the very image of God in every man who is born into the world.  That being the case then it follows that God reveals the truth in logical and rational propositions in Scripture.  The starting point for all knowledge for the Christian worldview is the beginning axiom that Scripture is the Word of God (2 Timothy 3:16).

How did Euclid know that mathematics were the thoughts of God?  He did not know this from empirical observation or from empiricial proofs.  But Euclid did assume that axiom as his beginning point.  From there Euclid used logic to build his entire system of geometry.  His axioms made possible the theorems from which he deduced the science of geometry.

If other branches of knowledge begin with unproven axioms, why would the Christian be forbidden to start with his or her own axiom?  That axiom is Scripture.

The difference between naturalism and theism--between the latest scientific opinions on evolution and creation; between the Freudian animal and the image of God; between belief in God and atheism--is based on their two different epistemologies.  Naturalism professes to learn by observation and analysis of experience; the theistic view depends on Biblical revelation.  No amount of observation and analysis can prove the theistic position.  Of course, no amount of observation and analysis can prove evolution or any other theory.  The secular philosophies all result in total skepticism.  In contrast, theism bases its knowledge on divinely revealed propositions.  They may not give us all truth; they may even give us very little truth; but there is no truth at all otherwise.  So much for the secular alternative.

Therefore the Christian evaluation of subjects in the curriculum and of pupils or students in school is rational and intellectualistic, in opposition to the emotionalism and anti-intellectualism of the present age.  

Dr. Gordon H. Clark.   A Christian Philosophy of Education.   (Trinity Foundation:  Unicoi, 2000).  P. 95.

Dr. Clark convincingly argues in the book that the result of socialistic philosophy in the public school system is a dumbing down of the educational system in general.  Christian schools outperform the godless public system for good reason.  Truth matters.