Background to the problem
In the Nov.-Dec. 1980 issue of The Trinity Review entitled God and Logic, which is available online, Dr. Gordon Clark, translates the first Verse of John 1:1 thus:
“In the beginning was Logic, and Logic was with God, and Logic was God.”
Until recently, I did not have the tools with which to evaluate such a bold statement. But now that I have understood the natures of Truth and logic, I can see that Dr. Clark made a grave error in identifying Logic with God.
Dr. Clark bases his definition for Logos by referring loosely to the most authoritative Lexicons, and also noting the similarity of the words Logos and Logic! But his conclusion that Logos means Logic does not hold up under scrutiny. Even though Logos and Logic have three letters in common, they have different meanings. A search of the lexicons by Liddell & Scott, and Bauer Arndt Gingrich reveals dozens of meanings for the word Logos, but not a single one of the instances used means Logic.
Furthermore, if the Apostle meant Logic, he would have used the Greek word for Logic which existed then and is still in use today: λογικη. (See Rom. 12:1 and 1Pet. 2:2) In addition, according to the Fourth Revised Edition of the Greek New Testament by Kurt Aland et al. there is no manuscript evidence that the word λογικη ever appears in the copies of the manuscripts of the Fourth Gospel.
We must conclude that the word Logos (λογος) that is used in the Gospel of John does NOT mean Logic.
What Dr. Clark meant to state and did state elsewhere is that God is a Logical Being. And since He is a logical being, then any of His communication with men would also be logical, comprehensible, etc.
But then the inevitable question arises: Is God a being who needs to Submit to the “laws” of Logic? Would not that make the “laws” of logic superior to God Himself? Did Aristotle have access to God’s mind when he formulated the “laws” of logic? If Logic is God, was Aristotle then able to acquire knowledge of God without resorting to the Scriptures? Dr. Clark has not answered these questions satisfactorily. But since he did not want to dismiss Logic as unimportant, he goes further into the wrong direction and tries to IDENTIFY Logic with God. But is that a Biblical stance?
We need to analyze the phrase “Logic is God,” to see if such a proposition is Biblically sound.
We know from page 1 that the word IS can have FOUR possible meanings.
1- The IS of Existence
2- The IS of Predication
3- The IS of Class-Inclusion
4- The IS of Identity
1- Existence - Logic IS = Logic Exists
Since we are not arguing about the existence of Logic, the IS of existence is not our concern.
2- Predication - Logic IS God
This would mean that God is an attribute, quality or characteristic of Logic. This proposition makes no sense.
3- Class-Inclusion - Logic IS God
This would mean that Logic belongs to a Class of beings called God. Clearly this is not what Dr. Clark meant.
4- Identity - Logic IS God
Logic and God are Identities. Logic and God are Syntitles; (Not synonyms, since “God” is a Title and NOT a Name.) That is, Logic and God are two Titles referring to the same person.
If Logic and God are Identicates, then we should be able to reverse the proposition and still have a valid biblical concept: God is Logic.
Are Logic and God Identical? Does being logical means being Godly? Is knowing the laws of logic the same as knowing God? What is Logic? What about Logic is God? Are the laws and God Identical? Is being logical being God? What does “Logic is God” mean?
If we begin with the definition of logic as “the principles of valid inference and correct reasoning,” did Dr. Clark really mean to say that the “principles of valid inference and correct reasoning” are God?
Since knowing Truth is being Indwelt by God, does that mean that being logical means being indwelt by God? Does it mean that one who knows the “laws” of Logic is being indwelt by God?
In trying to maintain that God and his revelation are logical, Dr. Clark has betrayed his poor understanding of the nature of God and the nature of Logic.
By trying to deify Logic, Dr. Clark believed that he had protected the Logical integrity of God and the Scriptures. But that is unnecessary. Laws of Logic are needed by ignorant humans. Laws of logic have no bearing on God’s mind or thoughts. Dr. Clark’s serious error is due to the fact that he had not understood the nature of Omniscience and the purpose of logic.
It is thus surprising to note that the most insightful words on the question of the nature of logic and its relationship to God, has been written by a philosopher of mathematics. His article is here.
Laws of Logic are idealizations
which cannot be rigorously applied
to our present reality.
1. The law of Identity.
The law of identity states that an object is identical to itself: A ≡ A.
OBJECTIONS: We cannot point to any object or make a statement about any created being that remains identical to itself even for an instant. For this “law” to be valid, we must be able to state a proposition about something which is immutable, but such objects DO NOT exist. The “law” of Identity cannot be applied to any part of any experience by anyone living on this earth. To consider anything other than God as Immutable would be to deny plain Biblical teaching, leading to innumerable serious errors.
Bringing to mind the only being that has an Immutable nature: Truth/God, we see that the “law” of Identity is an attempt to mimic the immutable nature of Truth by trying to ascribe immutability to fallen men’s erroneous thoughts and to a fallen, mutable creation.
The first “law” of logic upon which the rest of the “laws” are founded, is shown to be an impossible to describe, much less an attainable, ideal. It is an attempt to replace Truth/God with figments of men’s self-deceiving imaginations.
To confuse “laws” of logic with Truth or as a tool to attain Truth has been a hindrance to understanding the correct definition of the nature of Truth and the nature of God.
2. The law of Non-Contradiction.
The law of non-contradiction states that a Proposition cannot be Both True and False at the same time and in the same respect.
OBJECTION: This “law” is based upon the erroneous belief that humanly invented propositions are restricted to the two truth-values of True or False. Again, it is a vain attempt to try and mimic the nature of Truth, knowledge of which can come only from a self-revealing God and solely about Himself.
In its simplest aspect, it is a trivial “law.” Once we understand the definitions of the words True and False, we see that this “law” does not apply to any statement that we invent in our daily conversations.
It applies only to the One True Proposition that is available to mankind at the present time: “Jesus Christ is Lord.” Its denial is the definition of Falsehood. Other propositions do not have truth values of True or False, therefore this “law” cannot apply to them.
All other propositions are neither-true-nor-false.
3. The law of Excluded Middle
The law of excluded middle is the principle that for any proposition, either that proposition is true, or its negation is true. Thus for two-valued logic, the law is stated that a Proposition can have only One of Two possible Truth values: either TRUE or FALSE.
1- The definitions of the words True and False are assumed to be known. It is rarely pointed out that philosophers have not come to an agreement about what those words mean! Until they decide, these statements barely rise above the level of utopian aspirations.
2- There are no objects in nature that are wholly other. All created entities have something in common no matter how different they seem to be, and thus cannot be described by propositions that are complete contraries of each other.
3- Several insurmountable objections make it clear that the “law” of Excluded Middle does NOT apply to the reality with which we deal in our daily lives.
See page 37- Neither True Nor False.
* Laws of Logic are not true but useful. The notion that a valid deduction leads to truth is not justified. Being logical does not guarantee that a person’s deduction is true.
* God is not bound by “laws” of logic. Logic is of no relevance when one is in the presence of nothing but the Truth.
* Laws of Logic are similar to the “laws” of science or mathematics: temporarily VALID, Necessary & Useful for pauciscient beings, but not eternal.
Quotes on the Nature of Logic
Logic and mathematics are not true inherently, however cogent or extensive. They are ideal constructions based on ideal axioms…
George Santayana; (1863-1952); Scepticism and Animal Faith; 1923/1955; p262
The task of logic is not to determine what is true. Because, being only a ‘theory of inference’, it explicates the ways in which one reasons conclusively from given sentences, irrespective of their truth or falsity.
Willem Kuyk; Complementarity in Mathematics; 1977; p21
The propositions of logic are tautologies. The propositions of logic therefore say nothing. Theories which make a proposition of logic appear substantial are always false.
…the propositions of logic do not stand in any representational relation to reality.
Ludwig Wittgenstein; (1889-1951); Tractatus Logico-Philosophicus; 1921; s6.1, 6.11, 6.111, 4.462
Logic, too, rests on assumptions that do not correspond to anything in the real world, e.g., on the assumption of the equality of things, the identity of the same thing at different points of time; but this science arose from the opposite belief– that there were indeed such things in the real world. So it is with mathematics, which would certainly not have originated if it had been known from the beginning that there is no exactly straight line in nature, no real circle, no absolute measure.
F. Nietzsche; (1844-1900); Human, All Too Human; 1878; s1, p11
… the propositions of logic are tautologous, they say nothing at all about the objects we want to talk about.Hans Hahn; (1879-1934); Logic, Mathematics and Knowledge of Nature; 1933
[Hahn’s theme] is that logic is not about the world … it is about transforming one way of speaking to another equivalent way of speaking … that logical “truth” is not a species of truth: it is a mere artifact of the representational system.
Warren Goldfarb; The Philosophy of Mathematics in Early Positivism; p220 in Origins of Logical Positivism; vXVI of Minnesota Studies in the Philosophy of Science; Ronald N. Giere; ed.; 1996
I hope I have made clear that intuitionism … denounces logic as a source of truth.
L. E. J. Brouwer; (1881-1966); Consciousness, Philosophy, and Mathematics; 1940
The laws of logic are purely formal… They are principles of procedure, the parliamentary rules of intelligent thought and speech. … Those who suppose that there is, for example, a logic which everyone would agree to if he understood it and understood himself, are more optimistic than those versed in the history of logical discussion have a right to be. The fact is that there are several logics, markedly different, each self-consistent in its own terms and such that whoever using it, if he avoids false premises, will never reach false conclusions.
C. I. Lewis; (1883-1964); A Pragmatic Conception of the a priori; 1923
The intuitionistic logic is but one of many non-classical logics. Several other such “logics” were defined first by Łukasiewicz and Post and later by other logicians. Some of them were invented for purely formal reasons, but several others, e.g. modal logic, possess intrinsic philosophical value.
Andrzej Mostowski; (1913-1975); Thirty Years of Foundational Studies; 1966; p17
… Aristotelian logic yields only the laws of correct or valid thinking; it does not satisfy our demand for truth.
Edgar S. Brightman; (1884-1953); An Introduction to Philosophy; 1951; p45
The principles of rationality – in logic … are ideals; and ideals are things which do not exist as empirical facts.
The whole development of the last quarter century goes to enforce the fact that no deductive system, logic itself included, can justly claim to be demonstration of certain truth from indispensible first principles.
C. I. Lewis; (1883-1964); The Structure of Logic and its Relation to Other Systems; 1921; p513
… all of logic is independent of a definition of truth…
Gabriele Lolli; (1942-); Logical completeness, Truth, and Proofs; p119; in Truth in Mathematics; Dales & Oliveri; eds.; 1998
Logic and truth, as a matter of fact, have very little to do with each other. Logic is concerned merely with the fidelity and accuracy with which a certain process is performed, a process which can be performed … with any assumption. You can be as logical about griffins and basilisks as about sheep and pigs. On the assumption that a man has two ears, it is good logic that three men have six ears, but on the assumption that a man has four ears, it is equally good logic that three men have twelve. … Logic has again and again been expended, and expended most brilliantly and effectively, on things that do not exist at all. … The relations of logic to truth depend, then, not upon its perfection as logic, but upon certain pre-logical faculties and certain pre-logical discoveries… Logic, then, is not necessarily an instrument for finding truth… Briefly, you can only find truth with logic if you have already found truth without it.
G. K. Chesterton; Daily News; Feb 25; 1905
… we cannot maintain that the propositions of logic are true, for “truth” is defined for assertions in terms of the rules of method but not for these rules themselves.
Felix Kaufmann; (1895-1949); Truth and Logic; 1940
The question why and with what right we acknowledge a law of logic to be true, logic can answer only by reducing it to another law of logic. Where that is not possible, logic can give no answer.Gottlob Frege; (1848-1925); Basic Laws of Arithmetic; 1893
Logic is not a reliable instrument for uncovering truths and can deduce no truths that are not obtainable just as well in some other way.
Morris Kline; (1908-1992); Mathematics: The Loss of Certainty; 1981; p236
An omniscient being, indeed, would at once know everything
that is implicitly contained in the assertion of a few propositions.
An omniscient being
has no need
for logic and mathematics.
Hans Hahn; (1879-1934);
Logic, Mathematics and Knowledge of Nature;
The power of logic and mathematics to surprise us depends, like their usefulness, on the limitations of our reason. A being whose intellect was infinitely powerful would take no interest in logic and mathematics. For he would be able to see at a glance everything that his definitions implied, and, accordingly, could never learn anything from logical inference which he was not fully conscious of already. But our intellects are not of this order.
A. J. Ayer; (1883-1964); Language, Truth and Logic; 1946; p85
An omniscient being would thus require neither logic nor mathematics since the relations between all entities would, to him, be self-evident. … once all meaning and all relationships were fully disclosed, these disciplines would be superfluous.
Edward Kasner; (1878-1955); & James R. Newman; (1907-1966);
Mathematics and the Imagination; 1940; p361
An omniscient being needs no logic, and contrary to Plato we can say:
God never does mathematics.
Hence, logic is not a theory about the behaviour of the world – on the contrary, a logical proposition states nothing at all about the world – but a set of directions for making certain transformations within the symbolism we employ. And once we take this view of logic, a much-discussed problem dissolves of its own accord – the problem of the seemingly mysterious parallelism between the course of our thought and that of the world, the seemingly pre-established harmony between thought and world, which would enable us to discover something about the world by thought. This is impossible in each and every case. Thought can only transform propositions tautologically and in so doing bring them into a form which we find easier to survey, or extract statements from them which had been asserted along with them and are more suitable for checking than the original propositions.
Hans Hahn; (1879-1934);
The Significance of the Scientific World View,
Especially for Mathematics and Physics; 1930;
in Empiricism, Logic and Mathematics; 1980; p23-24; Brian McGuinness; ed.
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