Axiomatic Systems ?!?!

What does Axiomatic Systems have to do with a study of Christianity?  In fact, what are Axiomatic Systems?  Why would anyone care about Axiomatic Systems in the first place? Well, it’s because Christianity is an axiomatic system!

To give a little history, when I was growing I was one of the school math whizzes.  Math came easier to me than most, and I was fascinated with it. The incredible logic of it was (and still is to some small degree) awesomely beautiful.   So I was advanced in school, took calculus in high school, and started college as a math major.  I took more classes, Differential Equations, and so on.  One of the last classes I took was one called Axiomatic Systems.

So what are Axiomatic Systems?  Well, first we must look at what an axiom is.  An axiom is a truth or principle that is assumed because it is self-evident.  There is no way of proving or disproving an axiom, it is just so obvious it is universally accepted.  An axiom cannot have a single contradiction ever.  For example, in algebra one axiom is:

The whole of a quantity is greater than a part.

Pretty simple, right?  Does anybody disagree with this?  Is there any time a whole orange would be less than some of its segments.  Is there any time a bunch of 50 grapes would be less than say, 20 of those same grapes, taken from it?  No, of course not.  The whole bunch will always be greater than part of the grapes from the bunch.  And the whole orange will be greater than some of the segments.  This axiom is self-evident, and no one has found a contradiction.

There are quite a few other axioms that form the basis of algebra.  Examples include:

  • a + b = b + a
  • a times b = b times a

Now, whereas axioms are just self-evident truths, theorems are truths that are deduced from axioms or other theorems.  (I know all this may sound complicated, but bear with me, I will relate this to Christianity pretty soon.)  Most people have heard of the Pythagorean Theorem.  Of course, this theorem relates to triangles which are more related to trigonometry, but algebra is also involved in working with the theorem.

The Pythagorean Theorem says that the area of the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.  There are “proofs” that show how this is logically deduced.

Algebra is an axiomatic system because it is based on a number of axioms.  Trigonometry is another axiomatic system, and so forth.  An Axiomatic System is any set of axioms that can be used to logically derive theorems.

What made the Axiomatic Systems class both fascinating and maddening is that this class went through the exercises of taking existing axiomatic systems like abstract algebra and trigonometry and changing some of the axioms.  For example, there is an example in classic geometry that says that the shortest distance between two points is a straight line. Some of you may know that this particular axiom is changed in some higher systems. Einstein, for example, postulated that space-time is a curve and that the shortest distance between two points is a curve.

It is this example, and others like it, that brings me back to the study of original, primitive Christianity.

There are certain “truths” taught by different churches and denominations as basic tenets. These truths are presented in that they can neither be proven nor disproven.  That makes them axioms. Things deduced from these axioms, therefore, are theorems. That makes these theologies axiomatic systems.

As we have seen in different places of this website, however, there are many disputed doctrines, which means that we don’t have a clean and precise single axiomatic system that we can call Christianity.

One of the first things that we need to do when we have an axiomatic system that produces competing results is to examine the axioms and verify whether or not there are contradictions to the axioms.

Of course, we don’t have any churches or denominations that define their theology as axioms and theorems. However we do have creeds, and statements of belief. And when we look at these we find that at least some of these have axioms.  Some parts of the statements of belief are axioms, and others are deductions or theorems.  For example, some common statements in statements of belief define the status of the scriptures, the definition of the Trinity, and the role of the sacraments as well as more basic statements about the saving nature of believing in Christ.  For example, Christianity Today, a mainstream Christian magazine says the following on its website about the status of the scriptures:

“A. The sixty-six canonical books of the Bible as originally written were inspired of God, hence free from error. They constitute the only infallible guide in faith and practice.”[i]

This is presented as an axiom.  Since there are no copies of the originally written scriptures this statement cannot be either proven or disproven.  To the holders of this belief, this statement is represented as so obvious that it is unthinkable to think otherwise.

This axiom and a few others then form the basis for other statements.  The Chicago Statement on Biblical Inerrancy is a very long statement that expands on the meaning of the above simple statement. (Remember that this, as with most church doctrines, can have subtly different shades of meaning among proponents) It elaborated with phrases such as:

“We deny that the Scriptures receive their authority from the Church, tradition, or any other human source.,..

We deny that church creeds, councils, or declarations have authority greater than or equal to the authority of the Bible…

We affirm that the written Word in its entirety is revelation given by God.

We deny that the Bible is merely a witness to revelation, or only becomes revelation in encounter, or depends on the responses of men for its validity…

We affirm that God’s revelation in the Holy Scriptures was progressive.

We deny that later revelation, which may fulfill earlier revelation, ever corrects or contradicts it. We further deny that any normative revelation has been given since the completion of the New Testament writings…

We affirm that inspiration was the work in which God by His Spirit, through human writers, gave us His Word. The origin of Scripture is divine. The mode of divine inspiration remains largely a mystery to us.

We deny that inspiration can be reduced to human insight, or to heightened states of consciousness of any kind….

We affirm that inspiration, strictly speaking, applies only to the autographic text of Scripture, which in the providence of God can be ascertained from available manuscripts with great accuracy. We further affirm that copies and translations of Scripture are the Word of God to the extent that they faithfully represent the original.

We deny that any essential element of the Christian faith is affected by the absence of the autographs. We further deny that this absence renders the assertion of Biblical inerrancy invalid or irrelevant…

We deny that Biblical infallibility and inerrancy are limited to spiritual, religious, or redemptive themes, exclusive of assertions in the fields of history and science…

We affirm that the doctrine of inerrancy has been integral to the Church’s faith throughout its history.

We deny that inerrancy is a doctrine invented by scholastic Protestantism, or is a reactionary position postulated in response to negative higher criticism…”[ii]

The writers of this statement take the position that these statements cannot be disproven, that makes axioms.

The Southern Baptist Convention holds a very similar statement on the inerrancy and infallibility of scripture to Christianity Today.  A later statement after SBC’s statement on scripture is this:

“VI. The Church

A New Testament church of the Lord Jesus Christ is an autonomous local congregation of baptized believers, associated by covenant in the faith and fellowship of the gospel; observing the two ordinances of Christ, governed by His laws, exercising the gifts, rights, and privileges invested in them by His Word, and seeking to extend the gospel to the ends of the earth. Each congregation operates under the Lordship of Christ through democratic processes. In such a congregation each member is responsible and accountable to Christ as Lord. Its scriptural officers are pastors and deacons. While both men and women are gifted for service in the church, the office of pastor is limited to men as qualified by Scripture.”[iii]

If you look for “proof” on how the SBC gets this, the obvious answer is they will refer to numerous passages of Scripture to document that each of the ideas in this particular statement is deduced from the principal axiom, that being that the Scriptures, with the Holy Spirit being the teacher for us to understand the Scriptures, “proves” that this is how the church is to operate.   A clue that is relevant to our discussion is “associated by covenant”.  This denomination promotes Covenant Theology over Dispensationalism.

One key to working with axioms is to verify that they really are self-evident, i.e., that they do not have any contradictions.  And if you do find a contradiction, then the challenge is to see what the ramifications are.  Just as when one element is wrong in a story, it doesn’t mean the whole story is a lie, just the element that was wrong, and any related facts that were based on it, so the same goes for evaluating an axiomatic system.

Amazingly, after I took Axiomatic Systems I started losing interest in Math.  I found the classes too abstract (I can hear the laughs!), and for years I wondered why I was so interested at one point and so uninterested after that.  (So if you found this article hard to follow I totally understand.  It’s just that it is important to resolving a lot of the disputes between the differing doctrines.)  After I started studying all these competing Christian theologies, I was thankful I had taken the class as I realized that the concepts of working with axiomatic systems applied to this study.

We will go further in future articles examining this tool of axiomatic systems and how it can help us find out what is true or not about so many of these Christian theologies.  Hopefully, it can help us sift the wheat from the chaff concerning what is true Christianity.

[i] From the Christianity Today Website, this page located at

[ii] From The Chicago Statement on Biblical Inerrancy located at

[iii] official website of the Southern Baptist Convention. This page located at

© copyright 2011-2019 Mark W Smith, all rights reserved.

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