Page:Philosophical Review Volume 1.djvu/234



[ABBREVIATIONS. — ''Am.J. Ps. = American Journal of Psychology; Ar.f. G. Ph. = Archiv für Geschichte der Philosophie; Int. J. E. = International Journal of Ethics; Phil. Mon. = Philosophische Monatshefte; Phil. Stud. = Philosophische Studien; Rev. Ph. = Revue Philosophique; R. I. d. Fil.= Rivista Italiana di Filosofia; V. f. W. Ph. = Vierteljahrschrift für Wissenschaftliche Philosophie; Z. f. Ph. = Zeitschrift für Philosophie und philosophische Kritik; Z. f. Ps. u. Phys. d. Sinn. = Zeitschrift für Psychologie und Physiologie der Sinnesorgane''. — Other titles are self-explanatory.]

I. Begins by attempting to enumerate briefly the principles common to every species of symbolic calculus: (1) the representation of symbols, (2) the convention of permanence of import, (3) the possibility of equivalence, (4) the method of substitution, (5) the prepositional import of equivalence, (6) the inferential relation between equivalence, (7) the distinction between universal and particular symbols, (8) the applicational interpretation of universals, (9) the force of the bracket, and (10) the postulate of homogeneity. II. ($$\S \;$$2) The Synthesis of Propositions. A. The inferential mode of synthesis has been prominent in traditional synthesis, but a more general view of synthesis is here taken, in which inference will be shown to be dependent on and subordinate to pure synthesis. B. The conception of a proposition in general is indicated by the article not. III. ($$\S \;$$5) All that formal logic can do in the way of synthesis of propositions is contained in the laws regulating the use of the words and and not, i.e. logic is limited to a development of the conceptions of pure synthesis and pure negation. The fundamental laws or axioms that regulate these operations must now be given. IV. The Fundamental Laws of Prepositional Synthesis ($$\S \;$$6). 1. The Commutative Law: xy = yx. 2. The Associative Law: xy.z = x.yz. 3. The Law of Tautology: xx = x. 4. The Law of Reciprocity: x = x. 5. The Law of Dichotomy: x = xy xy. 1 says that the order of pure synthesis is indifferent; 2, that the mode of grouping in pure synthesis is indifferent; 3, that the mere repetition of a proposition does not in any way add to its force or alter it; 4, that the denial Rh