Such a theory is a mental construct. Hence, in our terms it is a systemic value. Since, however, anything can be considered in all three value dimensions, a value theory can also be regarded as an extrinsic and as an intrinsic value. In the former case, it is seen as a tool functioning in the space-time world among similar such tools, or a member of the expositional class of value theories. In the latter case, it is regarded as unique and incomparable, and some person as fully involved with it.

A value theory regarded as a systemic value cannot be either a good or bad value theory, but it either is theory of value or is not. It is if it fulfills the definition of value theory, and it is not if it lacks an element of that definition. We must therefore first of all define a value theory and determine the criterion or criteria. A value theory, obviously, must be a theory of value, that is to say, it must be theory which accounts for the value world, which in turn is the totality of all the value phenomena. Hence, the one criterion that makes or breaks a value theory is that of universal applicability to values. A theory not universally applicable to values is not, according to this criterion, a value theory.

As the proof of the pudding is in the eating, so the proof of a value theory is in the application. There is an elegant way and there is a less elegant way of making this proof. The elegant way is to investigate the level of abstraction. Since a theory is the more applicable the more abstract it is, the most abstract theory is the most applicable. The "best" theory, then, will be a purely formal one and, indeed, no value theory that is not formal will, by this test, by a value theory.

But this elegant test is only available to minds trained in philosophy and science. The less elegant way is to enumerate all the value phenomena to which a value theory is applicable and cross off from membership in the systemic class of value theories any which does not account for all of the enumerated value phenomena. If there is only one value phenomenon which a value theory A does not account for while a value theory B does, then value theory A is not a value theory in the systemic sense of the word.

In our case, there is indeed one value feature which is new in our theory as against any other value theory: that of systemic value, both in conception and application.⁷

A value theory can also be regarded as an extrinsic value. As such it is one of the tools for the understanding of the value world. In this case, again, universal applicability can be used as a criterion; that value theory will be the better value theory which is applicable to more value phenomena. In extrinsic valuation the degrees of value of the things valued are being taken into consideration, and therefore a value theory lacking some of the criteria of a good value theory will not, for that matter, be disqualified as a value theory, as is the case in systemic valuation. Thus there can be better or worse value theories. The extrinsic valuation of value theories, in other words, will admit more theories with the name of value theories into the class of value theories.

A value theory may, finally, have an intrinsic value. In this case all that counts is the involvement of the valuer in the theory. Here we must distinguish two cases. The involvement may be positive or negative, that is to say, either an intrinsic valuation or an intrinsic disvaluation of the theory -- either S^I or S_I. In the first case, we have the personal appreciation of the theory. It is based on the appropriate valuation of the theory as a theory, that is, its systemic features, and the valuer gives himself to the theory as a rational being, and is as such fully involved. In the second case, the personal involvement is not based on these objective criteria but the personal needs of the valuer. Thus, the creator of a value theory may be so much in love with it that he is blind to all other theories. This, of course, would imply that his own theory is incapable of dealing as a theory, that is to say, systematically and rationally, with other theories, and hence the creator must deal with them unsystematically and irrationally -- epithetically rather than analytically. The same is true for the advocate of any value theory who is so much taken by this theory that he does not consider any other. Such an attitude again, and for the same reason, proves the insufficiency of the theory held.⁸

Value in general thus is to specific values, or interests, as color in general is to specific colors. In the degree that a person is more or less sensitive to color in general, his preference for this or that specific color is more or less valid and significant. Similarly, in the degree that a person is more or less sensitive to value in general, his preference for this or that value is more or less valid and significant.¹⁰

The meaning of a thing is, logically, the set of properties by which the thing is characterized. This set of properties is called, logically, the "content" of the thing's concept or the intension of the thing's concept.

Formal axiology is based on the logical nature of meaning, namely intension, and on the structure of intension as a set of properties. It applies set theory to this set of properties. Set theory is a certain kind of mathematics that deals with the relationship of sets and subsets in general and of finite and infinite sets in particular.

Since mathematics is objective and a priori, formal axiology is an objective and a priori science, and a test based on it is an objective test based on an objective standard.

Just as each class of things must be measured by the kind of measure appropriate to it -- the circumference of a tree cannot be measured by a meter rod but only by a tape -- so each class of things must be measured by the intension appropriate to it. Pears cannot be measured by the intension of "apple", and apples not by that of "tree". But any kind of intension is a set of predicates as any kind of length measure is a set of centimeters (or inches, etc.).

If a thing possesses the whole set of properties given in the intension it is call a good such thing. It corresponds to the full measure of its value, or it corresponds fully to the measure of its value, the intension. If it does not possess them all, it is not so good a thing, or a bad thing -- as a chair, which lacks a seat or a back or both. Words such as good or bad, then, are nothing but words of measuring meaning, logically no different from words such as meter, dozen, score and other measuring words. Sometime such value words are actually used to measure number, as when we say "the town is lousy with tourists", meaning that there are very many tourists in town. We use lousy, which is a value word meaning "very bad", to signify "very many".

The measure of the value of the thing thus is the logical intension of the thing; and a thing is the better the more elements of the intension can be matched with the set of properties possessed by the thing. In general, the possession of all the intensional properties makes the thing good, of half of them so-so or average, of more than half fair, and of less than half bad. Valuation arranges an re-arranges the properties of things. It sees things fluidly rather than solidly, dynamically rather than statically.

The more expert we are at knowing certain things the more properties we know these things to have. The taste of a glass of Burgundy, for example, has been shown by experts to contain 158 properties. This means that there are 2¹⁵⁸ = 3.6 x 10⁴⁶ possibilities of taste in a glass of Burgundy, an astronomical figure, considering the number of all particles in the universe is only of the range of magnitude 10⁷⁹.

Thus, the application of the combinatorial calculus to intensions brings about the exact measurement of value. Value sensitivity may then be exactly defined. It is the capacity of matching a set of predicates one has in mind with a set of properties one recognizes in an actual thing or situation. It is a capacity of conceptual-perceptual matching -- a capacity of qualitative measuring. Formal axiology, thus, is the quantification of qualities.

Since, in formal axiology, the intension or logical meaning of a thing's concept is the value standard of the thing, and this standard is objective, namely the definition of the thing in question -- which is arrived at by the development of human speech and society throughout history -- the correct answers for a test based on the system of formal axiology are known from the system of axiology itself, that is from the mechanism of value thinking. In this respect an axiological test is similar to a mathematical test, in which the correct answers are known from the system of mathematics, and the person's answers are measured against the correct ones. Actually, the capacity of valuation is a talent similar to the mathematical or musical.

The items of the test have their precise axiological order and the ranking by a person has a measurable relationship to that order. His scores from the test are the measures of this relationship, that is, of the subject's deviation from the axiological order. This order is due to the fact that the items are illustrations of formulae arising from the mathematical statement of the value dimensions.

The validation of such a test is verification rather than standardization. The standards are the correct answers given in the system. The statistical validation has to verify whether the theory corresponds to practice, that is, whether, in actuality, the majority of people do value as the theory predicts; in particular, whether in the majority of actual value judgments the items of the test follow in the axiological order of the test.

The test is extremely sensitive and shows up very subtle deviations from the norm. These deviations have their basis in the person's own value pattern. The pattern expresses itself in specific values, interests or preferences, but the test does not measure the latter; it measures the underlying value pattern. The test does not intend to measure the energy or drive a person has. Two persons with identical axiological endowment may have different ranges of action, depending on their innate energy. It is not a test of professional skill or ability. Two persons with the same professional ability, say, as accountants, may have very different scores. This means that one will have a better and one a worse, general value capacity than the other; and this, in turn, may influence their handling of their respective jobs. But it would indicate, even more strongly, two different ways of handling their respective lives; and of handling their jobs differently only in the total matrix of their lives. Thus, the test is not primarily one applicable to special groups, but to individuals. Its standardization by group performance reflects deeper axiological differences than social classification. Thus, a group of hippies and a group of medical pathologists will exhibit different collective patterns; but the reason is not their different social functions but the different value patterns that underlie these functions. Better scores are usually -- though not necessarily -- made by persons in professions demanding empathy with people or things than by persons in professions indifferent to the full range of valuation.

The capacity of valuation, as was mentioned, is a talent similar to the musical or the mathematical. While there are groups of musicians, however, and of mathematicians, there is no special group or profession of people sensitive to values. Rather, this talent is found in all groups and all professions, as well as in all ages, and both sexes. High and low scores, therefore, are distributed among all groups, and usually, in any large enough group the scores follow the normal frequency curve. The specific value differences of the groups, as well as of the individuals, appear as result of the configurations of these scores.

The test items and scales were tested in various countries, especially the United States, where the following studies were made: empirical indices of reliability, indices of construct validity, and empirical indices of concurrent validity. Among the first were: Test retest stability of individual scores; correspondence of group mean scores; freedom from influence of sex, age, marital status, and educational background; central tendencies of response to each item. Among the second were: Relationships with the following tests: Rorschach, Minnesota Multiphasic Personality Inventory, Raven, Domino Sacks Incomplete Phrases, Allport-Vernon-Lindzey's Study of Values, Leary's System for the "Interpersonal Diagnosis of Personality" (in an adaptation by Austin); Felker's "Philosophic Mindedness (PM) Scales," and others. Among the third are the following empirical studies: Differentiation of normals from underachieving high school students; differentiation of normals from juvenile delinquents; influence of professor's values on changes in students' values; differentiation of successful from unsuccessful college students; relationships with grades in college courses on marriage and family, philosophy, and sociology; relationships with peer-rankings of college students for a hypothetical leadership role; relationships with peer-rankings of college students for a hypothetical counseling role; differentiation of successful from unsuccessful graduate school students; relationships with grades in graduate school courses of philosophy of education and social ethics; and others.

The fundamental studies in every country are those which test the validity of the items. This is implicitly a validation of the scales. Since the test is a theoretical construction it was important to see whether the theory corresponded to practice and whether, with sufficiently large samples, the items would be located by the test persons close to their position on the theoretical value scale. The first such experiment, with the first version of the test was made with 225 volunteers in 1966, of mean age 25 years, 67 of whom were male, 158 female, 99 were undergraduate and 126 graduate students. The results are shown in the following chart which gives the correlation between the theoretical and the actual position of each item. As is seen, in the chart of Mean Position of Items, Part 1, Dif is 22 and in Part 11 it is 34. This means a mean deviation of 22 + 4 divided by 2 = 28.5. This result may be measured in two ways, by the theoretical possible range of deviation, *Dif = 162 of the inverted order; and by the random order in which the 18 items arrange themselves. To this end 18 pieces, of equal weight and form, numbered 1-18, were thoroughly mixed and together thrown in the same direction. The number of each item was then registered on the scoring form according to its distance from the thrower, with the closest item in position 1, the next closest in position 2, etc., and the most distant in position 18. The results were the following Random Distribution scoring forms, for four random throws. The random deviations seem to be between 90 (though this is extreme and rarely observed) as lower and 125 as upper limit; or a mean of 102.5. We shall use this mean, though it makes our result slightly worse, rather than the usually observed mean of 100 + 125 divided by 2 = 112.5.

Measuring the mean deviation of the sample, 28.5, as percentage of the theoretically possible deviation of 162, we have 28.5 x 100 divided by 162 = 17.59 percent of a possible 100 percent, or a correctness of 100 percent - 17.59 percent = 82.41 percent. Measuring the sample against the random distribution we have 28.5 x 100 divided by 105 = 27.1 percent, and a correctness of 100 percent - 27.1 percent = 72.9 percent. These are the correlations between theory and practice of the first version of the test used.

*Differentiation Score (Dif) - This score measures the subject's Value Sensitivity, that is, his capacity of differentiating the value elements in situations. Differentiation Scores vary in practice between 0 and 150. The score represents the value errors of the subject. Theoretically, the maximum of errors is 162, when namely, the subject numbers the items in the inverse order, instead of I to 18, from 18 to 1. The differences in this case add up to 2(17 + 15 + 13 .... 3 +1) = 2 x 92 = 2 x 81 = 162.

It was found that the coincidence of mean position of items with the theory of the test is so close as to produce in the sample a test of excellent value capacities, with a CQ 55 - 22 (excellent - very good), BQa 46 - 18 (excellent - good), and BQr 1.2 - 0.8 (excellent - excellent). A more detailed description is provided in The Manual of Interpretation.

The items with the largest deviations were subsequently corrected in order to make the verbal formulation more adequate to the formula as well as to the total context of the formulae. Thus, in the first test, item e was changed from "Mud" to "A rubbish heap" (in Spanish it had the correct formulation from the beginning,''Basura"); item g from 'Tear out a fly's wings" to "Blow up an airline in flight," etc.