One of the initial obstacles to the study of the theory of value is the fact that practically every author whom the student consults on the subject characterizes value and valuation differently, and seems to trace them ultimately to a different source. For example, one writer will formulate a theory of value in terms of pain and pleasure (1); another, in terms of feeling (16, p.22); another, in terms of desires or wants (3, p.1); still others, in terms of “requiredness” (8, p.63), of interest (11, p.115), of striving (4, pp.1–29); and so on.

This study purports to demonstrate the possibility of applying logical analysis in the field of jurisprudence, and the usefulness of this method for exhibiting some essential features of the law.

logical analysis applies to language systems. To carry out the logical analysis of a language, is to construct a simplified model language “in close connection with” the given language, and to study the conditions of validity of the sentences of this model language. The given language is subjected to a kind of purifying chemical process. To deal with this simplified language seems to be a detour; it is, however, the most direct way to an ultimate insight into the logical structure of the given language.

If we may rely for our evidence on simple observation, it would appear that the tendency of random or unguided activity in external nature is opposed to the development of complex organization and favorable to structural simplicity—in the sense of uniformity in the distribution of elements. This anti-organizing trend of purely physical processes is illustrated in ordinary large-scale mixing and stirring operations, as well as in the automatic increase of entropy with time in systems subject to the laws of thermodynamics (material or molecular systems in general). It is common experience that complex systems which are the seat of physical activity tend to become simpler when left to themselves, i.e., they lose organization. Recently Eddington has given the whole matter an admirably clear expression: “Entropy may most conveniently be described as the measure of disorganization of a system. ... We can see chance creeping in where formerly it was excluded.” Unless counteracted by directive action the casual or random element in nature tends to increase. If things are left to chance, not only does organization of any high degree of complexity fail to develop, but what organization there is tends to lapse or disappear. Hence in those cases, such as living organisms, where the existence and activity of the system depend on a special and complex organization, it appears necessary to assume the continued operation of a stable directive influence or factor which pervades the whole system and excludes or compensates casual factors as far as possible. The presence of this factor is what makes possible the development and maintenance of the organization required for vital activity.

Only those whose work and interests have led them to notice it, will have realised, in all probability, the remarkable extent to which the term organization has gained currency, or acquired new and special emphasis, throughout the entire range of scientific and sociological literature during the last ten or twenty years.

In biology and bio-chemistry organization has been discussed or used as a technical term, mostly since 1930 by at least thirty well-known authors; amongst the more prominent are Huxley, Wilson, Woodger, Cannon, Waddington, McDougall, Needham, Block, Hopkins and Sherrington. Under this magic term some authors refer to the physico-chemical nature of the cell or cytoplasm, and usually with special reference to selective or directive catalysis; others to the general constitution or structure of the organism and almost indistinguishable from general morphology and physiology; others to embryological development as such (i.e. progressive differentiation under specific chemical stimuli); others more especially to “relations” between cells, organs and structural parts, often in an abstract sense; others refer more particularly to a hypothetical integrating and/or co-ordinating factor (“entelechy', ”field“, ”formative force“, ”telepathic hierarchial monads“, ”diffused Maxwell's Demon“, and so forth): a few refer to re-constitution from dissociated cells (so-called ”re-organization“) as observed in experiments with Sponges and Hydroids.

The purpose of this paper may be found in the following quotation. “Whenever an argument can be made to lead to a descending infinitude of natural numbers the hypothesis upon which the argument rests becomes untenable. This method of proof is called the method of infinite descent; .... It would be interesting and valuable to compare this method with the method of mathematical induction.”