Thursday 24 October 2013


              God and Logic


Gordon H. Clark



In thinking about God, Calvinists almost immediately repeat the Shorter Catechism and say, "God is a spirit, infinite, eternal, and unchangeable." Perhaps we do not pause to clarify our ideas of spirit, but hurry on to the attributes of "wisdom, holiness, justice, goodness, and truth." But pause: Spirit, Wisdom, Truth. Psalm 31:5 addresses God as "0 Lord God of truth." John 17:3 says, "This is life eternal, that they might know thee, the only true God...." 1 John 5:6 says, "the Spirit is truth." Such verses as these indicate that God is a rational, thinking being whose thought exhibits the structure of Aristotelian logic.
If anyone objects to Aristotelian logic in this connection––and presumably he does not want to replace it with the Boolean–Russellian symbolic logic––let him ask and answer whether it is true for God that if all dogs have teeth, some dogs––spaniels––have teeth? Do those who contrast this "merely human logic" with a divine logic mean that for God all dogs may have teeth while spaniels do not? Similarly, with "merely human" arithmetic: two plus two is four for man, but is it eleven for God? Ever since St. Bernard distrusted Abelard, it has been a mark of piety in some quarters to disparage "mere human reason"; and at the present time existentialistic, neo-orthodox authors object to "straight-line" inference and insist that faith must "curb" logic. Thus they not only refuse to make logic an axiom, but reserve the right to repudiate it. In opposition to the latter view, the following argument will continue to insist on the necessity of logic; and with respect to the contention that Scripture cannot he axiomatic because logic must be, it will be necessary to spell out in greater detail the meaning of Scriptural revelation.
Now, since in this context verbal revelation is a revelation from God, the discussion will begin with the relation between God and logic. Afterward will come the relation between logic and the Scripture. And finally the discussion will turn to logic in man.

Logic and God
It will be best to begin by calling attention to some of the characteristics the Scriptures attribute to God. Nothing startling is involved in remarking that God is omniscient. This is a commonplace of Christian theology. But, further, God is eternally omniscient. He has not learned his knowledge. And since God exists of himself, independent of everything else, indeed the Creator of everything else, he must himself be the source of his own knowledge. This important point has had a history.
At the beginning of the Christian era, Philo, the Jewish scholar of Alexandria, made an adjustment in Platonic philosophy to bring it into accord with the theology of the Old Testament. Plato had based his system on three original, independent principles: the World of Ideas, the Demiurge, and chaotic space. Although the three were equally eternal and independent of each other, the Demiurge fashioned chaotic space into this visible world by using the Ideas as his model. Hence in Plato the World of Ideas is not only independent of but even in a sense superior to the maker of heaven and earth. He is morally obligated, and in fact willingly submits, to the Ideas of justice, man, equality, and number.
Philo, however, says, "God has been ranked according to the one and the unit; or rather even the unit has been ranked according to the one God, for all number, like time, is younger than the cosmos, while God is older than the cosmos and its creator."
This means that God is the source and determiner of all truth. Christians generally, even uneducated Christians, understand that water, milk, alcohol, and gasoline freeze at different temperatures because God created them that way. God could have made an intoxicating fluid freeze at zero Fahrenheit and he could have made the cow's product freeze at forty. But he decided otherwise. Therefore behind the act of creation there is an eternal decree. It was God's eternal purpose to have such liquids, and therefore we can say that the particularities of nature were determined before there was any nature.
Similarly in all other varieties of truth, God must be accounted sovereign. It is his decree that makes one proposition true and another false. Whether the proposition be physical, psychological, moral, or theological, it is God who made it that way. A proposition is true because God thinks it so.
Perhaps for a certain formal completeness, a sample of Scriptural documentation might be appropriate. Psalm 147:5 says, "God is our Lord, and of great power; his understanding is infinite." If we cannot strictly conclude from this verse that God's power is the origin of his understanding, at least there is no doubt that omniscience is asserted. 1 Samuel 2:3 says "the Lord is a God of knowledge." Ephesians 1:8 speaks of God's wisdom and prudence. In Romans 16:27 we have the phrase, "God only wise," and in 1 Timothy 1:17 the similar phrase, "the only wise God."
Further references and an excellent exposition of them may be found in Stephen Charnock, The Existence and Attributes of God, chapters VIII and IX. From this distinguished author a few lines must he included here.
God knows himself because his knowledge with his will is the cause of all other things; ... he is the first truth, and therefore is the first object of his understanding.... As he is all knowledge, so he hath in himself the most excellent object of knowledge.... No object is so intelligible to God as God is to himself... for his understanding is his essence, himself. God knows his own decree and will, and therefore must know all things.... God must know what he hath decreed to come to pass.... God must know because he willed them ... he therefore knows them because he knows what he willed. The knowledge of God cannot arise from the things themselves, for then the knowledge of God would have a cause without him.... As God sees things possible in the glass of his own power, so he sees things future in the glass of his own will.
A great deal of Charnock's material has as its purpose the listing of the objects of God's knowledge. Here, however, the quotations were made to point out that God's knowledge depends on his will and on nothing external to him. Thus we may repeat with Philo that God is not to be ranked under the idea of unity, or of goodness, or of truth; but rather unity, goodness, and truth are to be ranked under the decree of God.

Logic Is God
It is to be hoped that these remarks on the relation between God and truth will be seen as pertinent to the discussion of logic. In any case, the subject of logic can be more clearly introduced by one more Scriptural reference. The well–known prologue to John's Gospel may be paraphrased, "In the beginning was Logic, and Logic was with God, and Logic was God.... In logic was life and the life was the light of men."
This paraphrase––in fact, this translation––may not only sound strange to devout ears, it may even sound obnoxious and offensive. But the shock only measures the devout person's distance from the language and thought of the Greek New Testament. Why it is offensive to call Christ Logic, when it does not offend to call him a word, is hard to explain. But such is often the case. Even Augustine, because he insisted that God is truth, has been subjected to the anti–intellectualistic accusation of "reducing" God to a proposition. At any rate, the strong intellectualism of the word Logos is seen in its several possible translations: to wit, computation, (financial) accounts, esteem, proportion and (mathematical) ratio, explanation, theory or argument, principle or law, reason, formula, debate, narrative, speech, deliberation, discussion, oracle, sentence, and wisdom.
Any translation of John 1:1 that obscures this emphasis on mind or reason is a bad translation. And if anyone complains that the idea of ratio or debate obscures the personality of the second person of the Trinity, he should alter his concept of personality. In the beginning, then, was Logic.
That Logic is the light of men is a proposition that could well introduce the section after next on the relation of logic to man. But the thought that Logic is God will bring us to the conclusion of the present section. Not only do the followers of St. Bernard entertain suspicions about logic, but even more systematic theologians are wary of any proposal that would make an abstract principle superior to God. The present argument, in consonance with both Philo and Charnock, does not do so. The law of contradiction is not to be taken as an axiom prior to or independent of God. The law is God thinking.
For this reason also the law of contradiction is not subsequent to God. If one should say that logic is dependent on God's thinking, it is dependent only in the sense that it is the characteristic of God's thinking. It is not subsequent temporally, for God is eternal and there was never a time when God existed without thinking logically. One must not suppose that God's will existed as an inert substance before he willed to think.
As there is no temporal priority, so also there is no logical or analytical priority. Not only was Logic the beginning, but Logic was God. If this unusual translation of John's Prologue still disturbs someone, he might yet allow that God is his thinking. God is not a passive or potential substratum; he is actuality or activity. This is the philosophical terminology to express the Biblical idea that God is a living God. Hence logic is to be considered as the activity of God's willing.
Although Aristotle's theology is no better (and perhaps worse) than his epistemology, he used a phrase to describe God, which, with a slight change, may prove helpful. He defined God as "thought-thinking-thought." Aristotle developed the meaning of this phrase so as to deny divine omniscience. But if we are clear that the thought which thought thinks includes thought about a world to be created-in Aristotle God has no knowledge of things inferior to him––the Aristotelian definition of God as "thought-thinking-thought" may help us to understand that logic, the law of contradiction, is neither prior to nor subsequent to God's activity.
This conclusion may disturb some analytical thinkers. They may wish to separate logic and God. Doing so, they would complain that the present construction merges two axioms into one. And if two, one of them must be prior; in which case we would have to accept God without logic, or logic without God; and the other one afterward. But this is not the presupposition here proposed. God and logic are one and the same first principle, for John wrote that Logic was God.
At the moment this much must suffice to indicate the relation of God to logic. We now pass to what at the beginning seemed to he the more pertinent question of logic and Scripture.

Logic and Scripture
There is a minor misunderstanding that can easily he disposed of before discussing the relation of logic to the Scriptures. Someone with a lively historical sense might wonder why Scripture and revelation are equated, when God's direct speech to Moses, Samuel, and the prophets is even more clearly revelation.
This observation became possible simply because of previous brevity. Of course God's speech to Moses was revelation, in fact, revelation par excellence, if you wish. But we are not Moses. Therefore, if the problem is to explain how we know in this age, one cannot use the personal experience of Moses. Today we have the Scripture. As the Westminster Confession says, "It pleased the Lord ... to reveal himself ... and afterwards ... to commit the same wholly unto writing, which maketh the holy scripture to he most necessary, those former ways of God's revealing his will unto his people being now ceased." What God said to Moses is written in the Bible; the words are identical; the revelation is the same.
In this may be anticipated the relation of logic to the Scripture. First of all, Scripture, the written words of the Bible, is the mind of God. What is said in Scripture is God's thought.
In contemporary religious polemics, the Biblical view of the Bible, the historic position of the Reformation, or––what is the same thing––the doctrine of plenary and verbal inspiration is castigated as Bibliolatry. The liberals accuse the Lutheran's and Calvinists of worshipping a book instead of worshipping God. Apparently they think that we genuflect to the Bible on the pulpit, and they deride us for kissing the ring of a paper pope.
This caricature stems from their materialistic turn of mind––a materialism that may not be apparent in other discussions––but which comes to the surface when they direct their fire against fundamentalism. They think of the Bible as a material book with paper contents and a leather binding. That the contents are the thoughts of God, expressed in God's own words, is a position to which they are so invincibly antagonistic that they cannot even admit it to be the position of a fundamentalist.
Nevertheless we maintain that the Bible expresses the mind of God. Conceptually it is the mind of God, or, more accurately, a part of God's mind. For this reason the Apostle Paul, referring to the revelation given him, and in fact given to the Corinthians through him, is able to say, "We have the mind of Christ." Also in Philippians 2:5 he exhorts them, "Let this mind be in you which was also in Christ Jesus." To the same purpose is his modest claim in 1 Corinthians 7:40, "I think also that I have the Spirit of God."
The Bible, then, is the mind or thought of God. It is not a physical fetish, like a crucifix. And I doubt that there has ever been even one hillbilly fundamentalist ignorant enough to pray to a black book with red edges. Similarly, the charge that the Bible is a paper pope misses the mark for the same reason. The Bible consists of thoughts, not paper; and the thoughts are the thoughts of the omniscient, infallible God, not those of Innocent III.
On this basis––that is, on the basis that Scripture is the mind of God––the relation to logic can easily be made clear. As might be expected, if God has spoken, he has spoken logically. The Scripture therefore should and does exhibit logical organization.
For example, Romans 4:2 is an enthymematic hypothetical destructive syllogism. Romans 5:13 is a hypothetical constructive syllogism. 1 Corinthians 15:15-18 is a sorites. Obviously, examples of standard logical forms such as these could be listed at great length.
There is, of course, much in Scripture that is not syllogistic. The historical sections are largely narrative; yet every declarative sentence is a logical unit. These sentences are truths; as such they are objects of knowledge. Each of them has, or perhaps we should say, each of them is a predicate attached to a subject. Only so can they convey meaning.
Even in the single words themselves, as is most clearly seen in the cases of nouns and verbs, logic is embedded. If Scripture says, David was King of Israel, it does not mean that David was president of Babylon; and surely it does not mean that Churchill was prime minister of China. That is to say, the words David,King, and Israel have definite meanings.
The old libel that Scripture is a wax nose and that interpretation is infinitely elastic is clearly wrong. If there were no limits to interpretation, we might interpret the libel itself as an acceptance of verbal and plenary inspiration. But since the libel cannot be so interpreted, neither can the Virgin Birth be interpreted as a myth nor the Resurrection as a symbol of spring. No doubt there are some things hard to be understood which the unlearned wrest to their own destruction, but the difficulties are no greater than those found in Aristotle or Plotinus, and against these philosophers no such libel is ever directed. Furthermore, only some things are hard. For the rest, Protestants have insisted on the perspicuity of Scripture.
Nor need we waste time repeating Aristotle's explanation of ambiguous words. The fact that a word must mean one thing and not its contradictory is the evidence of the law of contradiction in all rational language.
This exhibition of the logic embedded in Scripture explains why Scripture rather than the law of contradiction is selected as the axiom. Should we assume merely the law of contradiction, we would he no better off than Kant was. His notion that knowledge requires a priori categories deserves great respect. Once for all, in a positive way––the complement of Hume's negative and unintentional way––Kant demonstrated the necessity of axioms, presuppositions, or a priori equipment. But this sine qua non is not sufficient to produce knowledge. Therefore the law of contradiction as such and by itself is not made the axiom of this argument.
For a similar reason, God as distinct from Scripture is not made the axiom of this argument. Undoubtedly this twist will seem strange to many theologians. It will seem particularly strange after the previous emphasis on the mind of God as the origin of all truth. Must not God be the axiom? For example, the first article of the Augsburg Confession gives the doctrine of God, and the doctrine of the Scripture hardly appears anywhere in the whole document. In the French Confession of 1559, the first article is on God; the Scripture is discussed in the next five. The Belgic Confession has the same order. The Scotch Confession of 1560 begins with God and gets to the Scripture only in article nineteen. The Thirty-Nine Articles begin with the Trinity, and Scripture comes in articles six and following. If God is sovereign, it seems very reasonable to put him first in the system.
But several other creeds, and especially the Westminster Confession, state the doctrine of Scripture at the very start. The explanation is quite simple: our knowledge of God comes from the Bible. We may assert that every proposition is true because God thinks it so, and we may follow Charnock in all his great detail, but the whole is based on Scripture. Suppose this were not so. Then "God" as an axiom, apart from Scripture, is just a name. We must specify which God. The best known system in which "God" was made the axiom is Spinoza's. For him all theorems are deduced from Deus sive Natura. But it is the Natura that identifies Spinoza's God. Different gods might be made axioms of other systems. Hence the important thing is not to presuppose God, but to define the mind of the God presupposed. Therefore the Scripture is offered here as the axiom. This gives definiteness and content, without which axioms are useless.
Thus it is that God, Scripture, and logic are tied together. The Pietists should not complain that emphasis on logic is a deification of an abstraction, or of human reason divorced from God. Emphasis on logic is strictly in accord with John's Prologue and is nothing other than a recognition of the nature of God.
Does it not seem peculiar, in this connection, that a theologian can be so greatly attached to the doctrine of the Atonement, or a Pietist to the idea of sanctification, which nonetheless is explained only in some parts of Scripture, and yet be hostile to or suspicious of rationality and logic which every verse of Scripture exhibits?

Logic in Man
With this understanding of God's mind, the next step is the creation of man in God's image. The nonrational animals were not created in his image; but God breathed his spirit into the earthly form, and Adam became a type of soul superior to the animals.
To be precise, one should not speak of the image of God in man. Man is not something in which somewhere God's image can be found along with other things. Man is the image. This, of course, does not refer to man's body. The body is an instrument or tool man uses. He himself is God's breath, the spirit God breathed into the clay, the mind, the thinking ego. Therefore, man is rational in the likeness of God's rationality. His mind is structured as Aristotelian logic described it. That is why we believe that spaniels have teeth.
In addition to the well-known verses in chapter one, Genesis 5:1 and 9:6 both repeat the idea. 1 Corinthians 11:7 says, "man ... is the image and glory of God." See also Colossians 3:10 and James 3:9. Other verses, not so explicit, nonetheless add to our information. Compare Hebrews 1:3, Hebrews 2:6-8, and Psalm 8. But the conclusive consideration is that throughout the Bible as a whole the rational God gives man an intelligible message.
It is strange that anyone who thinks he is a Christian should deprecate logic. Such a person does not of course intend to deprecate the mind of God; but he thinks that logic in man is sinful, even more sinful than other parts of man's fallen nature. This, however, makes no sense. The law of contradiction cannot be sinful. Quite the contrary, it is our violations of the law of contradiction that are sinful. Yet the strictures which some devotional writers place on "merely human" logic are amazing. Can such pious stupidity really mean that a syllogism which is valid for us is invalid for God? If two plus two is four in our arithmetic, does God have a different arithmetic in which two and two makes three or perhaps five?
The fact that the Son of God is God's reason––for Christ is the wisdom of God as well as the power of God––plus the fact that the image in man is so-called "human reason," suffices to show that this so-called "human reason" is not so much human as divine.
Of course, the Scripture says that God's thoughts are not our thoughts and his ways are not our ways. But is it good exegesis to say that this means his logic, his arithmetic, his truth are not ours? If this were so, what would the consequences be? It would mean not only that our additions and subtractions are all wrong, but also that all our thoughts––in history as well as in arithmetic––are all wrong. If for example, we think that David was King of Israel, and God's thoughts are not ours, then it follows that God does not think David was King of Israel. David in God's mind was perchance prime minister of Babylon.
To avoid this irrationalism, which of course is a denial of the divine image, we must insist that truth is the same for God and man. Naturally, we may not know the truth about some matters. But if we know anything at all, what we must know must he identical with what God knows. God knows all truth, and unless we know something God knows, our ideas are untrue. It is absolutely essential therefore to insist that there is an area of coincidence between God's mind and our mind.

Logic and Language
This point brings us to the central issue of language. Language did not develop from, nor was its purpose restricted to, the physical needs of earthly life. God gave Adam a mind to understand the divine law, and he gave him language to enable him to speak to God. From the beginning, language was intended for worship. In the Te Deum, by means of language, and in spite of the fact that it is sung to music, we pay "metaphysical compliments" to God. The debate about the adequacy of language to express the truth of God is a false issue. Words are mere symbols or signs. Any sign would he adequate. The real issue is: Does a man have the idea to symbolize? If he can think of God, then he can use the sound GodDeus Theos, or Elohim. The word makes no difference, and the sign is ipso facto literal and adequate.
The Christian view is that God created Adam as a rational mind. The structure of Adam's mind was the same as God's. God thinks that asserting the consequent is a fallacy; and Adam's mind was formed on the principles of identity and contradiction. This Christian view of God, man, and language does not fit into any empirical philosophy. It is rather a type of a priori rationalism. Man's mind is not initially a blank. It is structured. In fact, an unstructured blank is no mind at all. Nor could any such sheet of white paper extract any universal law of logic from finite experience. No universal and necessary proposition can he deduced from sensory observation. Universality and necessity can only he a priori.
This is not to say that all truth can he deduced from logic alone. The seventeenth-century rationalists gave themselves an impossible task. Even if the ontological argument he valid, it is impossible to deduce Cur Deus Homo, the Trinity, or the final resurrection. The axioms to which the a priori forms of logic must be applied are the propositions God revealed to Adam and the later prophets.

Conclusion
Logic is irreplaceable. It is not an arbitrary tautology, a useful framework among others. Various systems of cataloging books in libraries are possible, and several are equally convenient. They are all arbitrary. History can be designated by 800 as easily as by 400. But there is no substitute for the law of contradiction. If dog is the equivalent of not-dog, and if 2 = 3 = 4, not only do zoology and mathematics disappear, Victor Hugo and Johann Wolfgang Goethe also disappear. These two men are particularly appropriate examples, for they are both, especially Goethe, romanticists. Even so, without logic, Goethe could not have attacked the logic of John's Gospel (I, l224-1237).
Geschrieben steht: "Im anfang war das Wort!" Hier stock
ich schon! Wer hilft mir weiter fort?
Mir hilft der Geist! Auf einmal seh' ich Rath und schreib'
getrost: "Im Anfang war die Thai!"
But Goethe can express his rejection of the divine Logos of John 1:1, and express his acceptance of romantic experience, only by using the logic he despises.
To repeat, even if it seems wearisome: Logic is fixed, universal, necessary, and irreplaceable. Irrationality contradicts the Biblical teaching from beginning to end. The God of Abraham, Isaac, and Jacob is not insane. God is a rational being, the architecture of whose mind is logic.


 The Structure of The Logic

The Logic has a uniquely Hegelian structure in which the whole is built up from triads: triads each component of which itself is a triad and so on ad infinitum. Consequently, although Hegel wrote The Science of Logic and The Shorter Logic in a kind of narrative which begins with Pure Being and proceeds step-by-step, page after page to The Absolute Idea as the apex of the lot, it is very difficult to read like this. You need to know where you are.
For a start, you need to first understand the overall triad, which I will call (taking a slight liberty with Hegel's structure) Being - Notion - Absolute Idea.
(Actually towards the end of the Logic, the third parts start falling off so that the Logic does not spill over into a new book, but comes to a stop with the Absolute Idea. As presented in The Science of Logic, the Absolute Idea is the culmination of the Doctrine of the Notion. The Science of Logic is presented as Being - Essence - Notion).

Being - Notion - Absolute Idea

The world first appears in thought as "one damn thing after another", immediate perception. Laws and tendencies, form and content, cause and effect, etc., are all present in this world which presents itself to us, but these moments are not yet disclosed, they lie "behind" Being.
Some say that these "mediated" aspects are part of the subject and are imposed upon the object. But this is not true; they are part of the object which has yet to show itself; otherwise, how could they ever come into subjective consciousness (innate ideas, faith?). And even if they did, how could they be "true" unless we accept that apart from existing in consciousness they also exist in the objective world, and our subjective concepts correspond to the object.
This immediate perception, or the world "in-itself", we call Being.
Human practice and individual consciousness may be said to "reconstruct" the world in the form of the mental images we have of it. These "mental images" are not just "snap-shots" of the various objects and processes, but the laws and concepts such as form, likeness, causality, means and end, genus and species, etc., etc., by which we both recognise and understand reality and reproduce it in our practice.
This "reconstruction" of the world has the form of concepts, concepts which are not immediately given in perception, but are the product of a long period of historical development. This conceptual image of the world is an "Other" of the world, a copy or negative of the world, which is not identical with the world, but approximates it in an opposite or negative form. It is not immediate, but mediated. That is, it is a world built up not from bits and pieces coming one after another, but from general concepts. We could call it a theoretical version of reality.
This conceptual form of the world "for itself", we call the Notion.
When we act in the world as humans (rather than simply as lumps of hydrocarbon) we act both as part of the world, immediate actors and agents, driven by unconscious urges and the ordinary forces of Nature, and, as an Other, as conscious, social individuals expressing our theoretical Notion of the world by consciously negating it, translating an idea of the world as it ought to be andcould be, and putting it into the world, changing the world to bring it into line with our more or less well-founded Notion of it.
Practice is action of a material subject in the world, according to its Notion. It is the return of the Notion to Being, the unity of Being and its opposite, the Notion.
There is always a "gap" between what we set out to do and what we actually do, between our theoretical idea and our practical idea. To the extent that our Notion of the world, is an adequate reconstruction of the world of Being, then the negation of Being by the Notion approximates what Hegel calls the Absolute Idea - the world fully conscious of itself and acting with absolute self-consciousness.
This ultimate of absolute self-conscious practice we call the Absolute Idea.
The Absolute Idea is nothing but everything that leads up to it. Consequently, there is nothing for Hegel to say when he gets to this chapter of the Science of Logic, but give a kind of general summary of what has gone before.
The Absolute Idea is the Subject which has become identical with the Object, and is in this sense just a return to the beginning - but at a higher level.

Being - Essence - Notion

Between Being (Book I) - immediate perception, and the Notion (Book III) - the conception of immediate perception in terms of notions, lies Essence (Book II). Essence is to do with how something of which we do not yet have a Notion enters consciousness - how we first form a notion of something. Being is about Notion-less perception; Essence is about the genesis or Becoming of the Notion; the Notion is about the development or concretisation of a concept.
We can only begin to grasp something new in terms of the concepts we already have. These past notions have their source in Being, but they are "out of step" with the new. New Being meets with itself in past Being. The result is a contradictory development of perception in which the inadequacy of past notions is brought out in the form of internal contradictions which arise as we penetrate deeper into immediate perception.
As Hegel puts it in The Science of Logic:
It may be said that cognition begins in general with ignorance, for one does not learn to know something with which one is already acquainted. Conversely, it also begins with the known; this is a tautological proposition; that with which it begins, which therefore it actually cognises, is ipso facto something known; what is not as yet known and is to be known only later is still an unknown. So far, then, it must be said that cognition, once it has begun, always proceeds from the known to the unknown. [Science of Logic, Analytic Cognition]
The Notion represents an Other to the world of immediate perception, which approximates to the object but in an opposite or negative form. The thing is "posited" in Being, but confronts a "negative" in the form of past Being contained in theoretical form (prejudice) in the Notion. The interpenetration of Being and Notion is called Essence - a contradictory process which leads to the identification of Being and the Notion, the modification of the Notion brought about by the successive resolution of internal contradictions, the struggle to understand what we are doing.

The triad

The above demonstrates the "triad" of Hegel which runs through almost every sentence of the Science of Logic. Most people who are about to study Hegel, will have heard of "thesis - antithesis - synthesis". Actually, Hegel never used this expression. This may be because the expression tends to imply a reference to what I call "propositional algebra". Also, "thesis" and "antithesis", like "positive" and "negative" imply a specific kind of opposition, namely polarity, in which the "thesis" and "anti-thesis" can have no separate existence and a kind of symmetry which limits the concept unduly. Nevertheless, I think "thesis - antithesis - synthesis" fairly well sums up the form of Hegel's triad and we should not be ashamed to use it.
It would be quite contrary to the spirit of Hegel to attempt here to give a "definition" of the triad. You will learn as you study the triad in its multifarious forms and development in Hegel's Logic. But the purpose of this article is to aid your reading, so you will forgive a brief and inadequate description.
At first something is put forward, is posited, presents itself. It presents itself also by way of negating something else, its negation, that which it is not. That which it is not may be what it was, it'sform as opposed to its content, a pre-conception of it, or merely its negative pole - the "anti-thesis". This "other side" is essentially connected with the thesis, the thesis already contains implicitly the antithesis, as an inner contradiction within itself. A new and higher concept arises on the basis of conceiving both the thesis and antithesis in this way as identical with each other. Thus a new thesis is posited, .... and so on.
Examples are superfluous. The whole of the Logic, and hopefully the explanations to follow here, demonstrate this dynamic. In reading the Logic, you should look back and forward as you begin each new chapter and section, and try to keep a bearing on where you are in terms of triads. You should feel free to skip back and forth so as to ensure that you grasp a particular triad before going too far "into it". But at the same time, don't expect to fully understand a concept until you have read through it, and followed exactly how its own internal contradictions build up and pass over into the next concept.

System and Method

According to Engels, the progressive content in Hegel is his "method" as opposed to his "system" which constitutes an idealistically perfected structure. If we develop a habit of trying to adhere to Hegel's system or structure (and the same applies to Marxism) in our theoretical work, we run the danger of pushing reality into a straitjacket, of justifying what exists, of adapting to and rationalising reality, rather than criticising and revolutionising reality.
"Whoever placed the chief emphasis on the Hegelian system could be fairly conservative in both spheres [politics and religion]; whoever regarded the dialectical method as the main thing could belong to the most extreme opposition, both in politics and religion." [Ludwig Feuerbach, etc. Part I]
Systematicity is a property of the objective world. The adequacy of countless concepts of systematicity in Nature has been proved by practice. However, with Marx, the concept of system in philosophy was transformed from an absolute to a relative. As marvelous a creation as is Hegel's system of the Absolute Idea, it is absurd to suppose that we can build up a systematic Notion of the world by perfecting such a system, or at least that a single writer can do so within the scope of a single book.
"The proof must be derived from history itself ... This conception [historical materialism], however, puts an end to philosophy in the realm of history, just as the dialectical conception of nature makes all [systems of] natural philosophy both unnecessary and impossible. It is no longer a question anywhere of inventing interconnections from out of our brains, but of discovering them in the facts. For philosophy, which has been expelled from nature and history, there remains only the realm of pure thought, so far as it is left: the theory of the laws of the thought process itself, logic and dialectics". [Ludwig Feuerbach, etc. Part IV]
Method and System are concepts indicating aspects of a theory, roughly analogous to tool and result: For instance, Marx used a specific method in his critique of political economy, the dialectical materialist method; the product was a system of concepts - commodity, value, surplus value, abstract labour, alienation, etc., etc. - the system of Marxist political economy.
How are we to learn from the practice of the great thinkers of the past? How can we copy their way of working in different circumstances and in confronting different aspects of the world?
All systems of concepts reflecting the general laws of motion of different aspects or "levels" of movement are inter-related and inter-connected, but distinct and different. At the most general level of abstraction we may share the same method, but in considering different aspects of the world, we shall find different systems of concepts applicable. Thus in a sense the method is that aspect of a theory which is absolute, less specific and more "transferable"; while system denotes that aspect of a practice which is relative, more specific, less "transportable". The method is the inner structure, the system the outer form; the method is manifested in the system, but the method must be true to the system. The method is the "germ" of the system.
I do not believe it is any more possible to grasp Hegel's method without labouring through his system, than it is to grasp the method of natural science without studying a science. Hegel's Logic is hard reading and the reader will find a road map useful if she/he is going to appreciate the countryside. Consequently, in what follows I shall unashamedly give emphasis to Hegel's system and only point out in passing and at the end aspects of his method, which is after all, most adequately demonstrated in his result, the system.
It is the job of you, the reader, to study Hegel's Logic and learn to understand his method.

Tuesday 22 October 2013

 The Myth Logic

                   “But I Already Know This!”

I_already_know_2.png
A few days ago, I emailed a friend of mine who saw Maharaji for the first time at the Woodstock event on August 25. Knowing she had thoroughly enjoyed the evening and had started to find out more by watching The Keys a few days later, I was curious to know if she had any questions.
She didn’t. But she did have an interesting observation about herself. As she watched The Keys, she explained, a recurring thought kept running through her mind.
But I already know this.”
I’ve heard the same thing from many people over the years — especially friends of mine who are just starting to explore Maharaji’s offer.
This time, maybe because Maharaji had just come to my hometown, it gave me extra pause. Why, I wondered, was it so common for people to respond to Maharaji’s message with the potentially dismissive “But I already know that”?
Could it be they weren’t quite open? Or not sufficiently humble? Too full of concepts? Well, that describes all of us — Maharaji’s students, too. The real reason is simpler.
The real reason why so many people respond to Maharaji’s message with “I already know that” is because they do. Indeed, this is one of the recurring themes at the core of his message. If it seems familiar to you, that’s because it is.
This is where things really get interesting. Indeed, if there is a place where the “path” begins, this is it.
A good teacher does not invent anything new. He (or she) does not recycle old truths. A teacher turns theory into practice. Makes the potential kinetic. Activates the process where seeking comes to an end and finding begins.
For most of us, the essence of who we are has long been forgotten — like we’ve all gotten a bad case of amnesia. We know the time, but not the timeless. We know our phone number, but not our heart. We know where we want to be tomorrow, but not where we are today.
Big difference.
Bottom line, Maharaji’s waking people up to the most ancient thing within them — the essence of what makes life worth living. And not only that. He’s also providing the tools and inspiration to maintain steady contact with this glorious place of being. How cool is that?
The second reason why some people respond to Maharaji’s message with the “I already know this” mantra is because it’s very likely they’ve heard his message before. Maharaji’s not the only one talking this talk. What he’s saying has been preached, written about, sung, danced, sculpted, painted, whispered, dreamed, and yodeled since the beginning of time.
Strip away the jargon of any path and you’ll find his message at the core. What you are looking for is within you!
What, then, is the value of Maharaji and Knowledge, when his message is as old as the hills — and the time before hills? Simply this: He helps people make it real. He helps them apply it in daily life.
He has an extraordinary gift for helping people close the gap between theory and practice — helping them understand, in their bones, that this is it — that the promised land is beneath our very feet right now — if only we would keep our promise to ourselves.
He’s a wake-up call — not with a bugle, but a breath.
Illustration by Sara Shaffer.
Source: www.wopg.org

        The Logic oF the Magic is That The                                                                             Real Magic is U

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When I was 10-years-old I wanted to be a magician.
I had read Harry Houdini’s biography and seen the movie “Houdini” starring the late Tony Curtis. I knew everything about the life of that great magician and escape artist who had performed worldwide in the early 1900s.
In our town’s library I got some books on children’s magic tricks and, with my dad’s help, I ordered some by mail from a magic shop in New York City.
Boy, those tricks were great: the guillotine chop-off-the-forefinger trick, the deck of cards made of nothing but jacks, the wobbling pencil... just to name a few. Of course, I had a small black white-tipped magic wand.
Practicing the tricks diligently, I collared my parents — “Pick a card, any card” — and bored my two older brothers, who’d humor me for a few minutes before heading out on their summer adventures over the hot and humid Jersey Shore.
I called myself The Great Houvoserous. I took the “Hou” from Houdini, and I think that I thought that “voserous” sounded deep and important and serious, like a real magician’s name.
I carried my magic tricks and wand in an old small black suitcase that I had dug out of the attic — it probably had been my grandmother’s at one time — and on each side I painted in white three-inch-high-by-one-inch-wide letters: The Great Houvoserous.
For my magic shows, performed on the small cement front porch of our three-bedroom ranch house, I’d lasso any of the 6-, 7-, and 8-year-old kids I could find and then persuade them to watch my show in the hot, sticky summer afternoon. I’d charge them a nickel each.
With my tricks laid out on an aluminum TV-dinner table covered with a black cloth, my wand at my ready, I’d launch into my act.
“I will put my finger into this guillotine,” I’d tell my audience of little skeptics, “and chop it off. But if I say the magic word, Alakazan, my finger will not be chopped off! Watch!”
Throwing down the guillotine — “Alakazan!” — my finger stayed intact.
“Do it again!” they’d scream.
Hesitatingly, I would proceed to chop off my finger one more time, well aware of the magician’s adage: don’t do the same trick twice in the same show because someone might discover the secret.
“Alakazan!” I’d cry while throwing down the little guillotine blade.
“We see it!” they’d say, pointing to the little mechanism inside the guillotine that lifted the blade so you would not cut off your finger.
They weren’t impressed, either, by the wobbly pencil, and my card tricks needed polishing.
My young audience demanded their nickels back.
I coughed up the 30 cents feeling a little disappointed, disillusioned. My career as a magician wasn’t taking off like I had dreamed it would. I held a few more shows, but soon stopped.
Over the years I've kept my interest in magicians, especially those adept at card tricks done by sleight of hand. To this day, 50 years later, I’ll pick up a deck of cards and practice a few of those tricks.
The real magic, I was lucky to learn, is with us at all times, giving us life. It’s exciting and it’s fresh: every moment. Fresh now, and now, and now.
In his kindness, Prem Rawat pointed out this magic of life to me — giving me an incredible sense of wonder.
“Do you like to see magic?” he asks. “Because if you do, there is an incredible magician. And the magic show that this magician puts on — every day — is simply spectacular.”
“The magic is you. You. Out of dirt, dust, nothing, life has been breathed into you. A breath comes, life comes. You are alive. This is the magician’s magic. Very fascinating magic,” he says, “the magic of this breath coming in and out, in and out, in and out… every day that you are alive, every day that you breathe, every day that you exist.”
“I want you to know the magic,” he concludes. “Believing is okay. Knowing is best. This is why I am here, to tell you how important it is for you to live this life consciously, so you can be who you are. So then you can have the eyes to admire the magic of this magician.”
Illustration by Sara Shaffer.\
Source : www.wopg.org

 2)              Hard

Although it is very simple to separate things into opposites, it is much more difficult to disallow something from having an opposite. By definition a hard egg is not a soft egg. By definition the opposite of a hard egg is a soft egg. If you can see the egg is hard, it’s probably not soft. Then again, all eggs have hard shells.
Difficulty is likened to hardness. If a brick is hard, it’s going to be difficult to look at. Hard water is soft to touch, feel and rub in your eyes but has more tiny hard bits than soft water. If a man has a hard face, it’s not because no one can work out what expression it’s showing, it’s because if you smashed a plank on it the plank would splinter leaving nary a splinter. Maybe he looked at bricks for too long. All the same in genera hardness is an oversimplification. Why is it that a hard case can have a soft inner? Wouldn’t you just call that an “average” case? If you think watching TV is hard then you’re looked at like some kind of infantile mutant who has grown far beyond the correct height or weight.
What seems strange to me is that because we’re all so different, it is definitely true that everything is hard. The relativistic application of the word means that on average, everything is hard to someone. I guess that’s got to be one of the main reasons that Capitalism works. We can’t be bothered working out how to replace spark plugs or buy new toilet paper so we get others to do it all. The opposite of hardness therefore lies rooted in Socialism, an ideology that purports to even the hardness playing field by creating all as close to equal as possible. In this scenario, things are less hard on average because we’re all brought up to be equals. Ironic that humanity wants to make things hard; socialism is too hard to execute without corruption.

  Logics : 


                Why

“Mr. Cummingham, if we were to leave this school and find there were no birds in the sky, what would we say to our parents?”
“The answer to that actually happens to be what today is all about. We’re going to answer a question that doesn't  present itself as such.”
“Sir we’re only in grade four. Do you really thing that we’ll be able to even gradually comprehend the vast labyrinth of potential philosophy?”
“You may. I think that it’s important to remember kids, while you’re eating oranges, something, somewhere, isn’t caring why.”
Mr. Cummingham took the pen that was lying closest to the whiteboard. Though it was clearly on its last 20% pen-streakiness, it was just enough to avoid the frustrating trip to the school stationary department. He wiped off the contemporary latin definitions, the notes from the history lesson on science fiction, the graph of (x vs. x)=x, the drawing of the cat, the last teacher’s name (“Carlisle”), the picture of the whiteboard and the list of alphabatical numericals.
Drawing a deep, knowing breath, he drew a large but even square with the almost-black ink excreting from the semester old nib. Above the square he drew a solid question mark, one he went over four times in the hope of physically displaying his point. The children were quick to respond to the basic representation of logic.
“Oh right so you’re meant to tick the box if yes, tick it if no right? You said this wasn’t a question!”
“Ah but you fail to see my point. You have two options in this form correct?”
“Yeah!”
“No! Wrong! You have three! The first is to ignore your preconceptions about this box. This box could simply BE as the dust in your trousers IS. The second option is you tick, affirming your opinion on its existence yet ignoring the vast possibilities of what it could have been. The last is that you place the letter “y” inside the box.”
Cummingam put a large Y in the box and walked out of the classroom, humming about his surname in a cockney tone.  The children learnt that although “Y” is pronounced “Why”, yes is not an affirmation of a question. It merely leads one to ask why.

                 Addicted to Logic


There are two types of computer users: those who are addicted to a computer game and those who have a life. At the moment, I count myself in the second group, but I confess to several computer-game infatuations in my sordid past. Every addict surely knows the anguish of hearing an unexpected knock on the door, just when you are at a critical moment of the game. What should you do? Answer the door, or lie low and finish the game? Now, players of the computer game Minesweeper can open the door with a clear conscience. They can say they were just practicing their logical reasoning skills.
At the January meeting of the Mathematical Association of America in San Antonio, Patti Frazer Lock of St. Lawrence University explained how Minesweeper gives her students a better sense of what proofs are all about. "Students accept that when you play a game, you have to play by certain rules and take only what those rules give you," Lock says. The same is true in mathematics, but her students' earlier math courses leave them with conflicting ideas of what the rules are. So she starts out her sophomore courses with a look at Minesweeper, where the rules are clear.
Example of a starting position
The game, which comes as an accessory on any Windows 3.1- or Windows 95/98-based computer, is played on a gray, rectangular grid of squares. Concealed within the grid are a number of "land mines," and the object of the game is to "flag" each square that contains a mine without ever "stepping on" one. If you step on a mined square, of course, you lose. When you step on a safe square, the computer reveals how many mines—between 1 and 8—are adjacent to that cell. Or, if there are none, the computer automatically uncovers all the squares around it, because they are all safe as well. That's the way the game normally begin—with a little island of safe cells surrounded by a sea of unknown hazards, as in the picture below.
After her students have played a few games for practice, Lock gives them a position like this one and asks them to tell which squares are definitely safe and which are definitely mined. Typically, the discussion will begin with D6.
ALICE: It has to be mined, because there are so many 1s around it.
BOB: No, it doesn't. What if D7 were mined instead? That would explain the 1s on E6 and E7.
CLARA: Doh! Look at E5, dude! It has a 1, and D6 is the only square next to it that we don't know is safe. So D6 has to have a mine.
Clara is right, of course, but all three comments represent typical stages of mathematical discovery. Alice has made a correct conjecture based on plausible evidence, but without a convincing proof. Bob has tried to disprove Alice's conjecture by offering an alternative possibility, which mathematicians call a counterexample. Finally, Clara has settled the discussion with an argument based on the rules of the game and the known information.
The position after square D6 is flagged.Click to Enlarge Image
Now that we know D6 is mined, we can "flag" it. This conclusion leads to further consequences.
DAVID: D7 is safe, because it's next to E6 and we know E6 has only one mine next to it.
ERNEST: So C6 is safe, too!
FRANCES: And B4, B5, and B6!
BOB: Wait a minute, you're going too fast for me. Why are B4, B5, and B6 safe?
FRANCES: Because C5 has a 1, and there's a mine next to it at D6. So that means all the other squares next to C5 are safe.
Working their way around, the students conclude that B3 is mined; B2, C2, D2 are safe; E2 is mined; and F2, far from where the action began, is safe.
"Often the students will say, 'Wow, I would never have guessed you could say anything about that cell,'" Lock says. "This teaches them several things. The idea that mathematicians have hypotheses, which are just the rules of the game, and they try to push them as far as they can. The idea that you can use one result to prove a later result. And they really come to believe that it's good to write things down carefully."
Serious Minesweeper addicts soon discover and learn to use facts about whole classes of positions. Here is one, which I call the "Corner-Turning Theorem": If a rectangular island of safety ends with two 1s side by side (e.g., B7 and C7 in the following example) then you can "turn the corner" and determine the status of every square on the long side of the rectangle. Thus, all the squares A1 to A8 can be predicted. (For starters, A6 through A8 are safe because there is a mine at B8 or C8, which must be the only one adjacent to B7.)
An island of safety with two 1s on the right.
Mathematicians love finding patterns like this. Amazingly, the students love it, too. "I've had them not want to leave the classroom at the end of the hour," Lock says.
Lock borrowed the idea of Minesweeper as a pedagogical tool from Allan Struthers of Michigan Technological University in Houghton, who wrote about it in the June 1995 issue ofPrimus. Struthers explains, "Putting a flag on a square is a theorem—you know there's a bomb there." The same reasoning techniques that students develop for Minesweeper, such as counterexamples and proofs by contradiction, can be used when they prove other theorems later in the course.
The man who wrote the code for Minesweeper never intended it as a teaching tool or even as a novelty. A similar computer game had existed before, in which the goal was simply to find a clear path from one corner to the other. Robert Donner of Microsoft wrote a program for that game one Saturday afternoon, but his friends assumed the goal was to find all the mines, not just a clear path. So Donner rewrote the program accordingly, adding a few cute graphical touches. A few years later, Minesweeper was on every new operating system Microsoft sold.

Donner says that the most frequently asked question about Minesweeper is, "What's the best time?" He doesn't keep records—with one noteworthy exception. "The only official time I remember is when Bill Gates sent me a message stating he just completed beginner level in 4 seconds, and left the game sitting on a machine if I wanted to verify it." Even the richest businessman in the world, it seems, can be addicted to logic.