An Abstract Definition of the GoodAuthor(s): John G. GillReviewed work(s):Source: Ethics, Vol. 80, No. 2 (Jan., 1970), pp. 112-122Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/2379875 .Accessed: 30/10/2012 07:25

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AN ABSTRACT DEFINITION OF THE GOOD

JOHN G. GILL

I. THE PROBLEM

When Plato lectured "On the Good," many expected to hear about the recog- nized goods-wealth, health, strength, or happiness. Instead, the Master talked about mathematics. So the hear- ers were disappointed. Aristotle says, ''some people despised the whole thing, while others criticized it."'

The disillusion would be duplicated today. The crowd wants solutions, not problems. If satisfaction fails to come quickly, there is no answer. Throw out the question. David Hume, high on the current popularity poll, contrasts the precision of geometry with the vague- ness of ethics, without being led to any serious attempt to make moral ideals meet mathematical standards. "The great advantage of the mathematical sciences above the moral consists in this, that the ideas of the former, being sensible, are always clear and deter- minate, the smallest distinction be- tween them is immediately perceptible, and the same terms are still expressive of the same ideas, without ambiguity or variation. An oval is never mistaken for a circle, nor an hyperbola for an ellipsis. The isosceles and scalenum are distinguished by boundaries more ex- act than vice and virtue, right and wrong."2 Whether we accept Hume's words as ultimate authority or stimu- lating challenge, no demon compels us to stay where Hume left us. Our own character and ideals determine our re- sponse. Hume has observed keenly, but he has not enacted a universal law.

This paper contends that a clear definition of good is possible if the

work meets certain standards. Follow- ing the example of mathematics, it must break away from special cases. The definition must have no empirical conditions to prevent it from being universally generalized.

II. AXIOMS AND PRIMITIVE TERMS

We take for granted the rules of logic. These apply both to natural sci- ence and to human affairs. Every field of inquiry assumes logic. Logic con- tains principles by which we must think if we think at all. The usual concepts and rules of logic are considered postu- lates for our purpose. In particular, we require four axioms.

Postulate One: An inconsistency cannot be affirmed. An affirmation claims that something is true or valu- able. A contradiction cannot be either. Whatever sentence is represented by p, it is false that p and not-p can be asserted. In logical terms, the assertion of p and not-p is false: NKpNp. If an inconsistency were true, everything would follow, and truth itself have no meaning. Affirmation implies consis- tency.

Postulate Two: A concept and its complement exhaust the universe of discourse. This rule makes possible in- direct proofs. Euclid demonstrates that the number of primes is infinite, relying on this postulate. The number is finite or infinite. If it is finite, there is a largest one. Using this unknown "largest prime" and familiar rules of arithmetic, he constructs a still larger prime-one larger than the largest. Thus he shows a contradiction in the

112

AN ABSTRACT DEFINITION OF THE GOOD 113

assumption that the number is finite. Considering the number finite, leads to contradiction. Therefore, the num- ber of primes is infinite.3

Postulate Two is no longer con- sidered a necessary "Law of Thought." Its universal application, especially to infinite series, is questioned by mathe- matical intuitionists. Construction of three-valued and even n-valued logics, shows that Postulate Two can some- times be dispensed with.4 Yet reduction ad absurdum remains a powerful tool. With Postulate Two, we apply to un- derstanding a concept, negative knowl- edge obtained through study of its com- plement. Large difficulties can be over- come by its use. Most mathematicians find reduction ad absurdum indispens- able.

In defining the good, Postulate Two expresses the resolve to carry through the analysis. Ordinary logic classifies propositions as true or false. Postulate Two generalizes the demand that the basis of decision, the fundamentum divisionis, be clear. It says that there is no barrier to completing a classifica- tion. Classes can be exclusive and ex- haustive. Scientific procedure requires this sort of rigor.

Postulate Three is the axiom of de- cidability: Between any two elements, it is possible to decide. Postulate Three suggests that complex evaluations can be broken down to atomic decisions. In a different context it repeats the resolve to carry analysis to its conclusion. If the criterion is clear, any relevant ele- ment can be classified.

Postulate Four adds: A decision hav- ing been made, the objects can be ordered. If all atomic instances are de- cidable, molecular units can be ar- ranged in a sequence.5 Since each ele- ment is "good" or "not-good," com-

plexes can be placed with good on top, evil on the bottom. "Better than" an asymmetric, nonreflexive transitive, or- dering relation, yields a lattice.

Definition of the good, in addition to four postulates, requires five primi- tive terms, These must be the simplest discoverable, which can be used to de- fine the concept. They appear with their everyday connotations. The def- inition starts from ordinary speech. The primitives are restricted as they assume their place in the theory. Their nar- rower meanings must not conflict with common usage. In effect, the system itself defines them. The five primitives are: affirmation, negation, life, indi- vidual, and society.

Adding to ordinary rules of logic four axioms and five primitive terms gives us the technical apparatus neces- sary for a definition of the good.

III. EXTENSION OF GOOD

A common catalog of goods includes: health, wealth, happiness, fame, and power. Most desirable objects can be classified under one of these headings. The arrangement may vary. A person frustrated in some experience might exclude this or that. The list expresses the values of most people.

Rabbi Liebman, as a student, wrote up what he considered the goods of life. He proudly exhibited his work to a respected teacher. The older man smiled, canceled the whole page, re- placing it with one phrase: "Peace of mind." "You have forgotten," the teacher said, "the one ingredient lack- ing which each possession becomes a hideous torment, and your list as a whole an intolerable burden."6

Interpreting our catalog fairly, how- ever, shows "peace of mind" subsumed under at least two headings. Health

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must include psychological well-being. This cannot be very different from the good of which the teacher spoke. Peace of mind is also part of happiness which, as the teacher suggested, is impossible without it.

A romantic might attack our head- ings for not mentioning "love." But, except in storybooks of the last cen- tury, love cannot stand alone. Given health, wealth, happiness, fame, and power, a modicum of love can be taken for granted. Love, without these quali- ties, could not be considered good.

Conventional religion would add im- mortality. But immortality, as com- monly understood, is a quantitative term. We do not need to surround our goods with "as much . . . as possible." Neither do we need to follow them with, " . . . for as long as possible." Given health, wealth, happiness, fame, and power, duration is implied. With- out these, immortality is a fair descrip- tion of hell.

If our respondent follows the more spiritual strain in Chrisianity, he will consider immortality, not as duration, but as fullness. A moment completely lived is infinite.7 If this is his meaning, then he has taught us something. He brings a dimension of depth to our understanding of happiness. This con- tributes far more than adding another heading under which goods are class- ified, but leaves the original catalog complete.

A moralist might substitute "ap- proval of God" for the human approval implied by "fame." To include the con- tent of all thoughtful positions we write "approval" for "fame." This intention- ally leaves open the question as to whether the approval is human or di- vine. We value the approval of those we consider significant. The essential is the

approval itself. Our goods are complete, then, with: health, wealth, happiness, approval, and power.

While other lists might be drawn up, these five headings certainly con- tain the good. We have, at least, boxed our subject. Can we then close in on it? Can we shorten the list without losing its truth? Can any headings be elimi- nated or included in others?

Examining health, remembering that it includes the psychological, we see that health represents a fundamental good. Other objects lose their appeal if health is lacking. Almost everyone desires physical health. Most want mental health as well. If there are any who do not care to be healthy, they may be considered twisted souls who are very sick indeed. Health, however, cannot be a defining characteristic of good. Health is not a complete concept, and cannot be well formed in our theory.

By Postulate Two: A concept and its complement exhaust the universe of discourse. Disease is the opposite of health. But disease cannot be a true contradictory. Both health and disease appear to be only parts of ideas. Disease is related to death, to which in all extreme cases it leads. Pure sickness would be death. The contradictory of death is life, one of our primitives. Death can be defined as the comple- ment of life, and the classification can be made exclusive and exhaustive. Everything in the universe is either alive or dead. Our list of goods is strengthened if, instead of health, we write life.

The next item is incomplete in much the same way as health. The opposite of wealth is poverty, and the two can be made exclusive by placing a figure on annual income as "the poverty line."

AN ABSTRACT DEFINITION OF THE GOOD 115

But like health and disease, wealth and poverty are not exhaustive. Wealth, by itself, represents only so much paper or metal. The meaning of wealth is power. Total poverty would be com- plete impotence. Power is another heading on our list.

Bernard Bosanquet has pointed out that beauty and ugliness are not op- posites.8 On the contrary, they are closely related. Pleasure and pain, hap- piness and misery, also require each other. We are hardly ever conscious of one without the other. Each of the pairs represents experience. The contradic- tory of each is no experience at all, but plain dullness. Dullness itself is only part of a concept and is closely kin to death. Complete dullness would be the absence of experience which is death. The complement of death, once again is life.

Careful examination of our five headings shows that each of them, insofar as it is good, represents life. Each has for its opposite, death. We have only one pair of contradictories, life and death. Life is one of our ac- cepted primitives. Death is defined as the negation of life. They are exclusive and exhaustive. Together they describe a universe of discourse which is the Universe itself. They also reveal an interesting structure.

Death includes inert, unconscious matter. Opposed to it is the highly com- plex substance - protoplasm - which forms the basis of all living beings. Life is structured and creative. It occurs in many forms, from the simple bac- terium, or amoeba, to the jellyfish, the oyster, the salmon, the elk, the ape, and the man. Life in its myriad present manifestations is still not exhausted. It also includes all past forms in which it has appeared-the trilobite, the pte-

raspis, the pterodactyl, the brontosau- rus, and the mastodon. To get the full meaning of life, we also include future forms, perhaps infinite in number.

Here the concept life reveals a signif- icance which we may not have con- sidered. Essential to life is possibility. The complement of inert matter counts capacities as well as achievements. Death is an end of possibilities. Life includes the past, the present, and all that the future may be. Life contains "Point Omega" which the brilliant priest and scientist, Pierre Teilhard de Chardin, postulated as the still un- known high-water mark of evolution.9

If a concept and its complement ex- haust the universe of discourse, then the contradictory of death goes far beyond mere achievements. It means possibilities as well. This is obviously more than we consciously include in the word life, but far from contradict- ing everyday usage, it brings out an implied sense. Part of the meaning of life is possibility. Among the possibili- ties are consciousness and growth. The primitive word life is defined by its place in the system. Compared with this fuller sense of life, the facile notion "the good is individual survival" ap- pears a truncated version of a more profound and exciting idea.

Extensionally, the good is an en- riched and deepened concept of life, counting as part of its meaning-possi- bility. All of our list of goods are in- cluded in this idea of life.

IV. INTENSIONAL MEANING OF GOOD

In looking for the intension of good, we return to our fivefold conventional classification. Seeking an idea which would draw together the positive con- tent of each heading, we found the meaning of good in the primitive term

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life, as reinterpreted in the theory. Now we ask what these five headings have in common. What is the intension of good? What is there that distinguishes health, wealth, happiness, approval, and power?

In accepting this list and ruling out other claimants, we asked of each: "Is this desirable?" The natural basis for counting any object good is its desira- bility. This clue leads to the meaning of good. Every child takes for granted that what he wants is good. The good is the desirable. The notion of the good as the desirable is intuitively satisfying. The objects we want appear good to us. No matter who the speaker, it seems to express a truth for him to say: "The good for me is that which I desire."

This prima facie definition conforms closely to ordinary speech. Beyond any doubt it expresses an important charac- teristic of the good. The good for me is that which I desire represents at least a surface view. Many thoughtful people have not gone beyond this. However, certain limitations make it unsuitable for a definition. The most obvious dif- ficulty lies in the word "desire." Being subjective, it can never yield an objec- tive test. We have no way to compare desires. We cannot measure how much anybody desires anything. While the first-glance definition conveys an ele- ment of truth, it also carries a flimsy, fairy godmother quality. It makes the object of every wish good while we wish for it.

If, for the subjective word "desire" we substitute the word "choose," we can relate our definition to an objective criterion, decidedly strengthening it. The good for me is that which I choose, makes the act of selection, rather than the feeling, the fundamentum divisionis. It separates objects of deliberate selec- tion from momentary wishes. Our re-

vision identifies the good with the object of choice.

We can further increase precision without losing the force of our intuitive definition by substituting the logical word affirm for the informal, less clearly demarked word "choose." To affirm means to accept as valid, to consider true or valuable. The defini- tion now contains a tautological ele- ment. It suggests: "The good for me is that which I accept as good." Since the act of affirming makes the object af- firmed to be good, the defining charac- ter is found, not in the object, but in the affirmation. The good for me is that which I affirm.

This settles some old debates, with one danger. It risks treating philoso- phers as computers treat engineers. Engineers design computers. Comput- ers do engineers out of jobs. Over the head of each philosopher, hangs the sword of Damocles. A thoroughgoing definition of the good threatens value theorists with technological obsoles- cence.

For eight centuries, the ancient schools tried to settle the question, "What is good?" Aristippus said: "Pleasure is the chief good, pain its opposite. . . . Corporeal pleasures are superior to mental ones, and corporeal sufferings worse than mental ones."

Antisthenes the Cynic remarked: "I would rather go mad than feel plea- sure." He found his good in despising the luxuries of Hellenic society.'0

The Megarian believed that exact- ness of measure and careful definition were the first considerations. He af- firmed measurement. To him, the ra- tional represented the good."

The long debate between Epicurean, Stoic, and Sceptic, while illuminating many points, brought the issue no near- er resolution. The schools agreed that

AN ABSTRACT DEFINITION OF THE GOOD 117

inner repose, peace of mind, was good. They disputed as to where to find it. Epicureans sought it in calm joy, in quietness and beauty, in rejecting the fears and hopes of religion, and in public service. Stoics valued inner cour- age, freedom from desires, freedom from arbitrary authority, submission to Nature and to Nature's God.12

Sceptics cultivated their riddles: "All generalities are false, including this one."

"What is truth?" "Why this more than that?" Their point of view they summed up

in one word, "Perhaps." Then correct- ing themselves, "Perhaps not." They sought escape from annoyances and disputes created by abstract ideas. Sometimes they found immediate ex- perimental knowledge. For this they are called Empiricists and are honored today.'3

The schools of Greek and Roman philosophers, and the medieval Scholas- tics who followed them, never succeed- ed in convincing each other. Their work lacked the permanent achievement of their contemporaries, the mathemati- cians. They remained divided. They developed consequences of various def- initions of good, but could not resolve differences between the schools. They failed to find principles strong enough to convince all serious students. 14 Now we understand. Each was right in his way. The good for me is that which I affirm. Affirmation determines the good. Beginning at the wrong end, they tried to select the object first. They should have started with their own choices.

V. LOGICAL DEVELOPMENT

My good is relative to me, yours to you. Man's good is related to himself. In more general form, the good for an

individual is that which he affirms. Ap- pearing as a propositional function, the definition connects two of our primitive terms, affirmation and individual. It remains tautological, but carries inter- esting implications. It is a fruitful def- inition. The theory already restricts the meaning of its primitive terms.

The good for an individual is that which he affirms, implies that the in- dividual can affirm. Not every organic unit meets this requirement. Our defini- tion, relative to the individual, assumes that the individual is able to decide. He must have well-formed desires. His affirmations must proceed from a single point. To be an agent requires unity. For the word good to have meaning, the concept of individual is restricted. It presupposes organization and cen- tral direction. The extension of the primitive term individual is narrowed. Its intension increased.

Where knowledge is cut up, in am- nesia or schizophrenia, we have a di- vided personality. We cannot speak of "good" any more than we can speak strictly of individual. We have two or more persons moving a single body. The nerves and blood vessels are inte- grated, the mind is not. An individual must be a harmony, a unity of desires, for the good to be meaningful. This fol- lows from the definition.

The ordering of affirmations extends through time. The individual must con- tinue to affirm his choice for his good to be significant. Principles by which affirmations are made or altered be- come second-order concepts. The good has enduring meaning insofar as the individuals have continuing principles and have decided how they will choose. The good can have no content under conflicting principles, because a con- tradiction implies everything and noth- ing. This conforms to experience. It

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also follows from the definition: The good for an individual is that which he affirms.

The definition can now be clarified by application of Postulate One: An inconsistency cannot be affirmed. This severely cuts down its extension. Many acts that at first glance appeared to be affirmations are eliminated. This oper- ates like a definition in geometry.

A triangle is a plane figure bounded by three straight lines. A surface is that which has length and breadth only. Modern geometers add, "it is a plane if it has a curvature of zero." Nothing in nature meets this standard. A line is breadthless length.'5 Breadthless length cannot be drawn or even imagined. Hume was wrong about the "sensibil- ity" of mathematics. The power of mathematical concepts lies in the fact that they are not experienced. They do not conform to nature. "Man can only understand what he has constructed according to the laws of thought."1 Mathematical structures, because they follow ideas rather than objects, serve as standards to which nature can be compared. The line, the plane, and the triangle, are found in their definitions. They are never seen, but only sug- gested by their diagrams. The sharper the pencil, the more firmly the ruler is held, the nearer we come to drawing a straight line.

Few concepts outside mathematics have achieved the clarity of a triangle, a hyperbola, or an ellipse. Fewer still have been tested for consistency. Prob- ably, up to now, ethics and sociology have been dealing with "apparent goods" and have not made the first step toward a science of values.'7 Until a concept is proved self-consistent, we do not know whether it can be affirmed.

Alexander Meiklejohn, in a too little- known essay, pointed out that most

human tragedies grow out of man's failure to find out what things really are. For centuries men bowed before bricks and stones. They sacrificed their firstborn children and their dearest treasures. Because they did not know what things were, they threw away objects of priceless worth.18 Nowhere is the lack of reality more costly than in a superficial and untested idea of good.

Postulate Two clarifies our defini- tion: A concept and its complement ex- haust the universe of discourse. This expresses the determination to create classes which are exclusive and exhaus- tive. A self-contradictory notion like a round square cannot exist. Attempting to find it leads to frustration. Self-con- sistency is a necessary criterion of the good. In it we have a standard. Seeming goods can be tested and some of them eliminated. The self-contradictory be- longs to the class of not-good, that is to say, evil. Here an interesting parallel to Thomism appears. Thomists insist that evil does not exist, but is real. To them, evil has a negative being, like darkness, a wound, or a scar. Evil is compared to the noise an orchestra makes when the players fail to follow the conductor. Evil is a missing harmony.19 We may add precision to their insight. A contra- diction is real, but a contradictory ob- ject cannot exist. Men place their hopes in it only to go wrong, and to be dis- appointed.

Postulate Three: Between any two elements, it is possible to decide, in add- ing decidability expresses the resolve to break molecules down into parts. In complex situations no simple judgment is adequate. The decisions with which we are confronted will not be made easy by a postulate. In Postulate Two we provided that our classes should be exclusive and exhaustive. Postulate

AN ABSTRACT DEFINITION OF THE GOOD 119

Three goes further. The analysis is not complete until the atoms are distin- guished. Once recognized, elements are classifiable. They are good, or if not good, then evil.

Postulate Four adds: A decision hav- ing been made, the objects can be or- dered. With the elements classified, a partially ordered system, or lattice, can be constructed. We can build such a lattice because "better than" turns out to be a typical asymmetric, nonreflex- ive, transitive, ordering relation.

The levels of values appeared at first glance to be arbitrary. On the surface, we could choose anything for first, sec- ond, or third. Values appeared as con- fused as human desires. Now we see that the good is not subject to our vary- ing whims. The arrangement is struc- tured. Some elements can be meaning- fully affirmed. Others cannot. Some sit- uations are better than others. Postulate Four asserts the possibility of an order- ing of values.

If the good for an individual is that which he affirms, what becomes of our definition when we universalize it? The logical operation Universal Generaliza- tion (U.G.) can be performed on any propositional function which is not "flagged"-that is, subject to particular limiting conditions. What holds for a triangle, applies to any triangle, pro- vided the description has been com- pletely general. By U.G. it is asserted of all triangles.20 Our definition contains no empirical limitations.

The good for an individual is that for which he affirms. With U.G. this be- comes: The good for all individuals is that which each affirms. We cannot gen- eralize the remaining "each" without risking the fallacy of composition, in- ferring from the accepted fact of indi- vidual desires, some possible universal agreement.

Even as it stands, the proposition is interesting. The good for all individuals is that which each affirms can be recog- nized as a form of the Golden Rule: "What you desire for yourself should be your rule in treating others." That this formula should appear in all ad- vanced religions,2" takes on a new and obvious explanation. Only a familiar logical step separates this advanced in- sight of ethics from an intuitive defini- tion. The good for me is that which I affirm, becomes: The good for all indi- viduals is that which each affirms. The demonstration can be written as a one- step theorem:

The good for an individual is that which he affirms.

The good for all individuals is that which each affirms.

While we cannot give meaning to the phrase "the good of society" by general- izing what we have learned about indi- viduals, another approach is open. The argument which connected the good for me is that which I affirm with the good for all individuals is that which each affirms shows that if societies do have desires or make affirmations, then: The good of all societies is that which each affirms. The steps which connect the premise for an individual with a state- ment about all individuals can be re- peated. If the good for this society is intuitively seen to be that which it af- firms, then the good for all societies is that which each affirms.

We speak of nations desiring colo- nies, of corporations wanting higher profits, of labor unions demanding wage increases and fringe benefits. Whether these phrases make sense, or merely display varieties of the pathetic fallacy, depends on an analysis of meanings and implications, and on comparison of the

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results with the facts of experience. That attributing desires to societies is not entirely fantastic is shown by the rule that groups do fight to survive.

If societies affirm, it can be shown that they affirm life. Life would now in- clude the life of society. For reasons given above, this must count the past history, the present state, and the future possibilities of society.

If societies have desires or make af- firmations, then it follows that not every assemblage is a society. The primitive term society is restricted by the defini- tion of the good. The theory postulates a society far more integrated than ex- perience generally indicates. We are driven to recognize the truth of Plato's dictum: "All existing cities are not one, but two, the rich and the poor."22 In- sofar as a collection of people is able to make decisions: The good of all soci- eties is that which each affirms.

VI. BASIC THEOREM AND DEFINITION

We have found that the objects men consider good can be classified under: health, wealth, happiness, approval, or power. Other arrangements might serve, but this expresses the accepted meaning of good. Analyzing each of the head- ings, we found a single idea which cov- ered them all, though no existing word was adequate. Life when interpreted to include past achievements and future possibilities expressed the concept most nearly.

Turning again to our catalog of goods, we asked what the recognized goods had in common. We found a first- glance answer. The good is the desir- able. The good for me is that which I desire. By substituting increasingly pre- cise terms and universally generalizing the result, we reached a relative defini- tion of the good: The good for all indi- viduals is that which each affirms. Sub-

stituting our synonym for the good, we obtain a basic theorem: Life is that which each individual affirms.

To speak of all living beings affirm- ing life, at first glance appears absurd, as if a chestnut tree desired water, or a crab chose sand. The same absurdity would have struck a seventeenth-cen- tury philosopher, if a modern physicist had told him of invisible light or inaud- ible sound. These would have appeared contradictory. However, freeing light and sound from their matrix of sense has let us deal with wavelengths be- yond the visible spectrum or the audi- tory range. The extension exposes many interconnections. The concepts deal more powerfully with reality. They re- veal hidden structures. The theorem: Life is that which each individual af- firms, clarifies the terms it uses.

Since a single negative example suf- fices to disprove a theory, questions of suicide and war must be faced. Some individuals choose suicide. Almost all human beings, and some animals, dear- ly love war. Suicide involves us in the Freudian "death wish." To what extent is suicide a choice? Could suicide be a perverted affirmation of life's possibil- ities, involving total rejection of some form of "mere existence?"

War may not be the negative example it first appears. The slogans of recent wars raise the question. "Make the world safe for democracy," and, "this is a war to end all war," or "the defense of the free world" and even "national aggrandizement," may be distorted manifestations of life-affirmation.23

The theorem: Life is that which each individual affirms, corresponds closely to Dr. Albert Schweitzer's observation: "I am life that wills to live, surrounded by life that also wills to live." From this, he derives the basic principle of his ethics: "Reverence for life." Dr.

AN ABSTRACT DEFINITION OF THE GOOD 121

Schweitzer's argument moves from his own "Cwill to live" through a mystical experience of universal life-will.24 We reach the same point from postulates, omitting the mystical step. Considering life as including its possibilities, we have come to the conclusion: Life is that which each individual affirms.

We can now define the good. If the good for all individuals is that which each affirms, and life is that which each individual affirms, then the good is life- affirmation.

VII. CONCLUSION

The argument shows why so-called "normative theory" as the game is usu- ally played, is unlikely to produce sci- entific results. Questionnaires which try to find out what people value are often phrased in different words or different contexts to get beyond the merely "ap- proved" response. Each answer is writ- ten down. The researcher goes on to the next question or the next respondent. We see that this procedure cannot get beyond "apparent good," and hence can not be called science. It finds what the individual thinks he affirms, remain-

ing ignorant of whether the object can be affirmed or not.

Socrates had a better way. He also asked people what they considered good. Then he cross-questioned them to find whether their opinions were self- consistent and therefore made sense. Even then he did not stop until he had found whether the affirmations were consistent with other objects which the individual thought he chose. Only if the answers passed the tests of self-con- sistency and consistency with each other, could the respondent be consid-. ered as holding a scientific view. The criterion was set. No opinions met Soc- rates' standard, not even his own.

Our inquiry has shown that the good can be defined. If, in the primitive term life, possibilities and consciousness are included, then The good is life affirma- tion. We have seen that "good" yields an ordering. Complex situations can be arranged from the best to the worst. The resultant lattice, when the detailed work has been done, will be, in the mathematical sense of the words, a val- ue theory. CENTRAL MICHIGAN UNIVERSITY

NOTES

1. Sir David Ross, ed., The Works of Aristotle, vol. 12, Select Fragments (Oxford, 1952), p. 115. This and other reports of Plato's lecture are from Aristotle's lost work, On the Good.

2. David Hume, The Philosophical Works, 4 vols. (1882; reprint ed. London, 1964), vol. 4, An Enquiry concerning Human Understanding, p. 50.

3. Euclid, The Elements, trans. with commen- tary by Sir Thomas L. Heath (New York, 1956), 2:412-13. IX Prop. 20. Summaries are to be found in almost any advanced algebra.

4. A. Heyting, Intuitionism (Amsterdam, 1966), p. 99 et passim. See also: Gerhard Gentzen, Recherches sur la deduction logique, trans. with commentary R. Feys and Jean Ladriere (Paris, 1955), pp. ix, 19, 48. The principle ApNp is re- jected as a fundamental axiom, but added to the system later, where it applies. (See J. B. Rosser and A. R. Turquette, Many-valued Logics [Am- sterdam, 1958], p. 10 et passim, for rejection of this postulate.)

5. Patrick Suppes, Introduction to Logic (New York, 1957), pp. 220-23. See also Garrett Birkoff and Saunders MacLane, A Survey of Modern Alge- bra, rev. ed. (New York, 1953), pp. 348-55. Con- temporary lattice theory constitutes a rapidly growing field.

6. Joshua Loth Liebman, Peace of Mind (New York, 1946), pp. 3-4.

7. Expressed in poetry by William Blake in Poetry and Prose, ed. Keynes (New York, 1935), p. 118:

To see a World in a Grain of Sand And Heaven in a Wild Flower, Hold Infinity in the palm of your hand And Eternity in an hour.

It is also found in John 17:3, and in modern theologians. Tillich considers that participation in eternity is not life hereafter. Bultmann finds the demythologized meaning of eternal life in an aspect of "now" (see Alexander J. McKelway, The Sys- tematic Theology of Paul Tillich [New York,

122 ETHICS

19661, p. 245; Rudolf Bultmann, Jesus Christ and Mythology [New York, 1958], pp. 33-34).

8. Bosanquet's view, suggested in a number of his lectures, is capable of much greater develop- ment (see The Principle of Individuality and Value [London, 1927], p. 5; The Value and Destiny of the Individual. [London, 1923], p. 176; and, commenting on Croce, A History of Aesthetic [New York, 1957], pp. 417-19, Science and Phi- losophy [New York, 1927], p. 423; or, in relation to Hartmann, History, pp. 433-34).

9. Pierre Tielhard de Chardin, The Phenomenon of Man, with introduction by Sir Julian Huxley (New York, 1959), pp. 257ff.

10. Charles M. Bakewell, ed., Source Book in Ancient Philosophy (New York, 1907), pp. 144, 146.

11. F. Ueberweg, A History of Philosophy (New York, 1894), 1:89.

12. Whitney J. Oates, ed., The Stoic and Epi- curean Philosophers (New York, 1940), pp. xix, xxiv.

13. Philip P. Hallie, ed., Scepticism, Man and God, the writings of Sextus Empiricus, trans. from the Greek by Sanford G. Etheridge (Middletown, Conn., 1964), pp. 78-82.

14. Regles pour la direction de l'esprit, Ren6 Descartes, Oeuvres et lettres, Pl6iade ed. n.d. (Bruges, 1952), regle 2, p. 40:

En vWrite, si nous observons bien cette regle, il y aura fort peu de choses dont nous pourrons entreprendre l'etude. Dans les sciences, en effet, il n'y a peut-etre pas une question, sur laquelle les savants n'aient Re en desaccord. Or, chaque fois que sur le meme sujet deux d'entre eux sont d'un avis different, il est certain que l'un des deux au moins se trompe; et meme aucun d'eux semble-t-il, ne possede la science: car, si les raisons de l'un etaient certaines et evidentes, il pourrait les ex- poser a l'autre de telle maniere qu'il finirait par le convaincre i son tour. Nous voyons donc que sur tout ce qui ne donne lieu qu'a des opinions probables, il est impossible d'acquerir une con- naissance parfaite, parce que nous ne pouvons sans prisomption esperer de nous-memes plus que les autres n'ont fait, en sorte que, si notre raisonne- ment est juste, il ne reste de toutes les sciences de'a connues que l'arithmetique et la geometrie, auxquelles l'observation de cette regle nous ram~ne.

15. The Elements, pp. 153-54, definitions 2, 5, 19. 16. Compare the Hume quotation with which

this paper opened with Ernst Cassirer, The Phi- losophy of Symbolic Forms, with introduction by Charles W. Hendel (New Haven, Conn., 1953), 1:3: "Reason only possesses insight into that which reason itself constructs according to its own plan." See also vol. 3, p. 429: "As examples we need only mention such concepts as those of the 'rigid body,' the 'ideal gas,' the 'incompressible liquid,' the 'per-

fect circular process,' etc. It is only through the intellectual metamorphosis which they undergo in this method that the contents of immediate ob- servation first become possible for physical judg- ments." Cassirer speaks of these as "value limits toward which the series as a whole converges."

17. However, interesting work is being done by Professor Robert S. Hartman in The Structure of Value, with preface by Paul Weiss (Carbondale, Ill., 1966). Hartman's essay, "The Measurement of Value, Set Theory as Value Theory" delivered at the Fourteenth International Congress of Phi- losophy, Vienna, 1968, will doubtless be published with the Proceedings of the Congress. Hartman's argument that value theory can be effectively analyzed mathematically must be treated with re- spect.

18. Alexander Meiklejohn, Philosophy (Chicago, 1926), pp. 31-32: "If I find an object to be a brick, I can use it for building. If I find an object to be beautiful and sacred then I can bow down before it in adoration and worship. And the deepest tragedies of life occur when men, being mistaken about objects, bow down before bricks and stones, or use for meanest purposes things of transcendent value. To base my life and action upon views of the world which belie its real nature is to make of my life a futility and a delusion."

19. For a recent presentation of this view, traced to St. Augustine, see John Hick, Evil and the God of Love (New York, 1966), pp. 53-54. See also Jacques Maritain, God and the Permission of Evil (Milwaukee, 1966), pp. 33-35.

20. Suppes, pp. 60-62; John M. Anderson and Henry W. Johnstone, Jr., Natural Deduction, the Logical Basis of Axiom Systems (Belmont, Calif., 1962), pp. 162-70.

21. Christianity: Matt. 7:12, Luke 6:31. Juda- ism: Tobit 4:15, or Talmud, Shabath fol. 31 col. 1. in Maurice H. Harry, comp., Hebraic Litera- ture (New York, 1943), p. 4. Hinduism: Bhagavad Gita (ca. A.D. 1) trans. Nikhilananda, N. Y. 1944, p. 171. Also, in Lin Yu'tang, ed., The Wisdom of China and India (New York), p. 831, Tsekung asked: Is there a single word that can serve as a principle of conduct for life?

Confucius replied, "Perhaps the word reciproc- ity will do. Do not do unto others what you do not want others to do unto you."

22. The Republic of Plato, trans. Francis M. Cornford (New York, 1964), p. 113.

23. For a powerful treatment of these seem- ingly inverted drives, see Herbert Marcuse, Eros and Civilization (New York, 1955), esp. p. 46. "The perversions suggest the ultimate identity of Eros and death instinct."

24. Albert Schweitzer, The Philosophy of Civili- zation (New York, 1949), esp. pp. 307-15.