Page:Philosophical Review Volume 1.djvu/235

Rh of the denial of a proposition is equivalent to its affirmation; 5, that the denial of any proposition is equivalent to the denial of its conjunction with any other proposition, together with the denial of its conjunction with the contradictory of that other proposition. V. ($$\S \;$$8) These results can be put into more familiar forms. We have two fundamental types of synthesis, — conjunctive and disjunctive. Each of these types has four varieties involving x, y, or their contradictories, viz. conjunctives xy, xy, xy, xy; disjunctives xy, xy, xy, xy. In our view there is no essential difference between the disjunctive, hypothetical, and alternative forms. This is shown symbolically. VI. ($$\S \;$$9) Other Interpretations of the Disjunctive, Hypothetical, and Alternative Mode of Synthesis. VII. Other Modes of Synthesis than not and and, e.g. if and or ($$\S \;$$10). VIII. ($$\S \;$$11) The Primary Analysis of Propositions. The molecular proposition contains two sorts of elements, a subjective and a predicative term. The usual analysis of the predicate term into copula and predicate term is a verbal device, devoid of logical significance. IX. ($$\S \;$$12) Synthesis of Propositions as modified by their Analysis: (1) of propositions containing a common individual derivative subject name; (2) of singular propositions containing a common predication, but different subjects; (3) of propositions which refer to the same aggregate subjects. X. ($$\S \;$$13) Foregoing Principles applied to the Logic of Relatives. XI. Criticism of the preceding analysis. If the above analysis is correct, it will establish the point that all the familiar methods of formal logic and the less familiar results of relative logic depend, not on the peculiar relation of subject and predication, but on the proportional synthesis involved in the quantitative element of the universal or particular judgment.

In the second volume of the above periodical H. had tried to formulate the psychophysic law so as to embrace more than one variable, e.g. the three variables in the determinations of the color sensations of trichromatic eyes. In the present article H. shows there is a close correspondence between the curve for color differences experimentally found by König, and the curve calculated from the extended pp. formula on the assumption of the three elementary fundamental colors. This verification of the formula gives a basis for the determination of the fundamental colors which are found to be provisionally, carmine red,