Minding Your P's and Q's: The Covenantal Nature of Logic

It may seem strange if one spends little time thinking about it, but the fact that one can write down truths (in propositional or symbolic forms) about the real world, then deduce other truths from these -- only to find that they yield heretofore unknown and accurate information about the world is surprising (to put it mildly).

This could well have been the stuff of a dream I once had after consuming too much popcorn late at night. But this is just what happens when one performs logical operations correctly, and works with true premisses about the world -- or at least CAN happen. Mathematicians in fact have coined a phrase to highlight this oddity. They call it the "unreasonable effectiveness of mathematics."

That is to say, the pagan world of mathematicians has no way of accounting for the correspondence between what happens on blackboards and what happens in the real world. Why should there be any correlation between these? Why should the force of a stone one skips across a pond actually prove equal to its mass multiplied by it's acceleration -- because Newton's math said so? F=ma is one of Newton's famous three laws. Students have to know this to get the answer right on the test. But why should stones care?

Well, as the very smart readers of this blog already know: the Bible has the answer. The answer consists in two important aspects of what I shall have to call "biblical metaphysics."

Now "metaphysics" sounds like a very important word. And perhaps it is. It refers to that branch of logical inquiry which wants to ask "What kind of universe is this anyway?" Some put it this way, "What is the furniture of the cosmos" or colloquially, "What sort of stuff is REALLY out there?" So in metaphsyics people ask questions about the nature of time and matter, the existence of God and angels, and they talk of these things like they knew what they were saying.
The first part of what we wish to know -- namely why are math and logic so effective in the real world when they appear to be man-made constructs of a sort (after all logicians choose which axioms to include or not in this or that system of math or logic) -- comes by way of understanding the covenantal nature of logic itself.

God relates to his creatures by way of covenants. This is hard to miss after reading through the Bible, even the first time. You would have to struggle considerably to not notice how many people make covenants with God in the Bible, or that Jesus made a "new covenant" with his people. In fact, the Bible should read for the first part "Old Covenant" (or better Older Covenant) and "New Covenant" (or better "Newer Covenant").

The Bible, in short, is a covenant document -- not really a testament -- though this is in some respects a good analogy. But the analogy -- like that used in Hebrews -- is not the thing itself, but a picture of it. Clearly, the Bible is far more than a testament -- it is an entire legal code. Testaments do not run 66 books long. Jerome's "Latin Vulgate" was the first to introduce the translation "testament" for the Greek word "diatheke" (covenant) in Hebrews.

Easton's Bible Dictionary explains: "[Diatheke] occurs twelve times in the New Testament (Heb. 9:15, etc.) as the rendering of the Gr[eek] diatheke, which is twenty times rendered "covenant" in the Authorized Version, and always so in the Revised Version. The Vulgate translates incorrectly by testamentum, whence the names "Old" and "New Testament," by which we now designate the two sections into which the Bible is divided." Oops. All those printing presses over all those years. Old printing press habits die hard.

Moreover, testaments come from dead people (in a sense, you read them once one is deceased on behalf of the bequeathing decedent) -- and yet Jesus is more alive than you are, I can assure you; Hebrews 9:17 reads: "For a testament is of force after men are dead: otherwise it is of no strength at all while the testator liveth." It is not exactly a constitution (though that might also make a good analogy in some respects), and it is certainly not a declaration of independence; and it refers to itself most often as the Word or Law of the Lord.

So why the confusion here? Testaments are a kind of covenant document, but not all covenant documents are testaments (i.e. constitutions can be covenant documents, as are marriage certificates). Some obvious facts about the gospels themselves should show that this is only an inspired analogy. A testament is the LAST information given by a testator to those to whom he intends to leave his possessions. Jesus talked with the disciples after his death. This makes him no ordinary testator. And it shows that the Bible is an analogue for the idea of a testament, but it differs significantly from any other testament -- rendering the analogy false if one presses the analogy too far (beyond the intent of the author).

Note also that this same chapter of Hebrews refers to the Bible earlier as a "covenant" (diatheke), using exactly the same Greek term as that translated only a few sentences later as "testament." Obviously, it can -- in some respects (but not all) -- be understood as a kind of testament. That was the author's point -- analogy, not identity. And the differences between them highlight this point. Another obvious difference is this: the Bible wasn't finished until A.D. 70 -- long after (40 years later) the death and resurrection of the testator. No other testator keeps on writing his last will and testament after he dies, and then carries on lengthy post-mortem conversations to help other people finish writing the will.

Interestingly, the Bible never calls itself "The Bible." This also shows our proclivity for adopting uniformly names for the Bible which are either not biblical or else "partially" correct --as with the Vulgates use of testamentum, and the modern wholesale adoption of this analogy as the title of the New Covenant documents. The Bible calls itself the Law of the Lord. The fact that the Bible represents itself as a legal code has far-reaching implications for doing theology. Logic is especially important in handling legal documents since they often determine what the sentence will be against or for the persons (or parties) involved in a legal dispute.

All the metaphors of the Law of the Lord confirm this understanding of what it is from cover to cover. God is a Judge (which is nearly the precise meaning of "Dani-el"), Jesus is an advocate with the Father (i.e. a Lawyer or defense attorney); and the Spirit is a "paraclaetos" -- translated only as "paraclete: since the precise sense depends almost entirely on the context in every case of its usage. No one has suggested it yet, but "Lobbyist" -- a modern political analogy -- is not far from the mark in several instances of its usage. Lobbyists intercede for consistituents, making appeal to those with power to change their conditions. Romans indicates that The Holy Spirit acts similarly on behalf of the saints. But it's only an analogy.

It is God's covenant faithfulness, which not only established the orderly and rational cosmos, but since he MUST act to fulfill all his promises and threats, it is this, his covenantal consistency, that forms the foundation of all logic. Logic flows from God, and God is a God of covenants; therefore logic is essentially a covenantal enterprise. To reason wrongly about his commands and Word is therefore not simply a mistake; it is culpable (criminal). But please note, and I will come to this point at greater length later (if the Lord wills), there is a very important difference between logic per se and any one particular logical system.

The ability to communicate in terms of symbols (or verbal tokens) is usually called "language." But language is much more than the accumulation of all the presently known or used languages (i.e. Spanish, English, French and the like). So also "logic" refers to far more than symbol the total sum of course one might take at a university under the rubric of modal or propositional forms of logic. If there were such a word in English, these would be called "logics," not LOGIC. Logical systems are man-made; Logic is not. Languages are man-made, but Language is not. In any case, whether this helps or no, I must move on for now to the next point.

When I write "logic is a puzzle," there is a sense in which this is true. But the claim entails no punishments. One can hardly be thrown in jail for failing to come up with a six-letter word for grasshopper (where 4 down occupies the spaces). But when I write, "Logic is covenantal" (since this is true), it means that "If you do logic poorly regarding important matters, you may be punished severely for your errors." Bad logic regarding the Bible, for instance, could easily lead to heresy (and often has), blasphemy or other serious sins and crimes.

Now God is orderly, and therefore, logical, by nature. He does not will to be logical -- but His own perfect orderliness gives rise to what we experience as logic and consistency (laws) in the physical world. This is the nature of both wisdom and truth. These are perfectly unified (truth is one) and internally consistent. The contrary, INconsistency, thus remains the target for lawyers when examining one's testimony -- to find lies. Lies are inconsistent with one another, while truth is by nature mutually affirmative. It has the mutual consent of all the parts.

It is then because God is just, wise, and true BY NATURE -- that logic flows from Him. This metaphysical view of God has something of a lengthy name -- divine logical essentialism. It sits over against logical voluntarism, which sees logic as the outgrowth of God's choices rather than HIS NATURE.

Though I will not here critique it at any length, suffice it to say that logical voluntarism results in the absurdity that two different kinds of logic -- one for God and a different one for men -- occupies the real world. In light of the biblical doctrine of the full deity and true humanity of Christ, this would render him intellectually schizophrenic (were it true), in that it would force him to apply two different kinds of logic simultaneously at all times.

A third "logic of translation" for the other two would also need be present in his mind at all times. If this sounds unnaturally complex, you are understanding the point well. This position would also necessarily eliminate statements from the Bible like "Come let us reason TOGETHER says the Lord, though your sins are as scarlet they shall be like wool; though they are as crimson they shall be as snow."

God is interested in reasoning with men; this is what makes the appeal of the gospel of Christ eminently rational (logical). God reasons from the heart, and He does it in a way which makes it -- in the Law of the Lord -- clear and reasonable. This puts men "without excuse," since the Bible shows the kind of internal consistency sufficient to prove its case to rational creatures by a due use of the ordinary means we all possess.

Finally, on this note, it is interesting to point out that the Greek word "logos" (word) forms the root of the term we use "logic." The word that God spoke, which not only brought all things into existence, but it also ORDERED them in a highly rational fashion. John uses the phrase "En arche" matching the Septuagint's opening line for the beginning of the cosmos, to describe God the Son -- "en ho logos" (was the Word). This is as close to calling the Son of the Living God the Prime Mover of Logic ("Reason" with a capital "R") as you can get. With respect to His deity, Christ IS reason or logic -- in the same sense in which we call Him "The Truth."

Now because God's eternal power and divine nature (one aspect of which is Reason) have been made plain from what has been made (Romans 1:20-21), we see that the created ORDER -- there's that word again -- shows forth the logical character of the Creators' own nature, albeit imperfectly. Mankind, being the highest form of creation, shows God's image more accurately than the lower creation. This is why the command to learn from the lower creation forms a stinging rebuke to fallen men (i.e. Go to the ant, O sluggard, learn her ways and be wise).

The relevant point here is that men use logic with surprising insight (now and again), clearly showing their superiority of mind over the lower creation. Ants work very hard but haven't yet discovered propositional logic. In this way, the image the Creator. This conjoining of features which men share with the Creator uniquely -- language, logic, and the other intellectual, communicative and manipulative skills (the arts and sciences. etc) -- highlights this image of God in men. Not many mammals can write HTML source code.

Now it is this -- please pardon my syllable overload -- "triangulation" of rational agents which renders math and logic so "effective" in the real world. Here's how it goes. God, being inherently (not voluntarily) rational, created mankind in his own image, and the rest of the created order reflects this orderliness as well. This gives the minds of men a certain "correspondence" to the natural world since both are media of natural revelation -- a revelation of the rational Creator.

Thus, the rationality of a logician's mind -- expressed, let us say, on a blackboard in the form of something symbolic or propositional -- tends to (or might) have a correspondence to a world which was ordered by the same Creator who fashioned the logician's mind. In other words, because both man and the lower creation share a common RATIONAL Creator, they tend to "match."

One theologian put it this way: Logic is rational expression in the real world of the way God thinks and expects us to think, in order to think God's thoughts after Him. It is a reflection of God's own thinking. Now the lower creation -- ants and company -- shows forth wisdom too. But is not their own. It comes from the Lord. "For the Lord gives wisdom, and from his mouth come knowledge and understanding."

This actually EXPLAINS then why math and logic can and do yield great insights from time to time into the way things are, and how to get along more efficiently in God's world. Here, the Christian worldview EXPECTS math and logic to be highly effective in the fulfilling of the dominion mandate. Their effectiveness is anything but unreasonable. It is divine, bequeathed to men, expected, and even commanded from men.

This interesting surprise to the pagan world of scholars (both logicians and mathematicians) stems from the fact that they do their reasoning within the framework of a worldview which cannot provide the foundations of logic and science, cannot explain why the most basic features of the world appear as they do, cannot -- though they are ever learning -- bring them to a knowledge of the Truth.

But the Bible has the answer, and it is not only rational, it explains why reason is possible at all. So here is your valid and sound syllogism for the day.

1. Something must be true (The denial of this proposition eliminates itself).

2. Either the Christian worldview is true, or something else is.

3. It is not the case that something else is true.

4. Therefore, we must conclude that the Christian worldview specifies that outlook which is true.
Bottom line: The contrary to the Christian worldview is (logically) impossible. For God always keeps covenant. Faithful is the Lord. Amen.