December 3 J, 1909] 



SCIENCE 



951 



token of life, that it came to be thouj^ht of 

 as a thing that is dead. - And I suspect that 

 even to-day there may be found scientific 

 men of eminence who are not aware of the 

 fact that in our time logic, as a field of 

 research, affords a spectacle of teeming 

 activity quite as intense as may be wit- 

 nessed in physics, for example, or in as- 

 tronomy or biology— men, it may be, who 

 have yet to learn that, owing to modern 

 logistic research, it would be as radical an 

 error to identifj' the modern significance of 

 the term logic with that of the Aristotelian 

 system as to identify the modem meaning 

 of the term geometry with that of Euclid's 

 "Elements" or to identify modern juris- 

 prudence with the code of Lycurgus or the 

 "Pandects" of Justinian. By the logis- 

 tical movement I mean the movement that 

 began— somewhat prematurely, however, as 

 the event was destined to show— in the 

 logical .speculations and investigations of 

 Jungius (1587-1657), Leibniz (1646-1716) 

 and Lambert (1728-1777) ; awaited the 

 powerful impulse imparted by Boole's .sym- 

 bolical "Investigation of the Laws of 

 Thought" (1854); and, under the leader- 

 ship of C. S. Peirce in our own country, of 

 Schroder in Germany, of Peano and his 

 numerous collaborators in Italy, of Cou- 

 turat, brilliant expounder and advocate of 

 the subject in France, and of Rassell, 

 Whitehead and McColl in England, has at 

 length produced that imposing body of 

 doctrine now known throughout the scien- 

 tific portions of the world under the char- 

 acteristic name of symbolic logic. 



In its present form and state of develop- 

 ment this science is constituted of three 

 distinct but interconnected branches: the 

 logic of classes, which, though it corre- 

 sponds to the traditional system of Aris- 

 totle, Is far from being identical with it; 

 the logic of propositions; and the logic of 

 relations, which was originated by Charles 



S. Peirce, was much elaborated, refined and 

 clarified by Schroder in the third volume 

 of his "Vorlesungen iiber die Algebra der 

 Logik," 1895, but owes its present form and 

 conception mainly to the various contribu- 

 tions of Bertrand Russell in recent volumes 

 of the Revue des Mathemaliqiies (formerly 

 the Revista di Matematica) and elsewhere. 

 For the purpose in hand the thing to be 

 noted is the discovery of the fact that for 

 the }wtional basis of the triple organon it 

 was necessary and sufficient to assume, 

 without definition, a very few notions — 

 called the primitive ideas; or con.stants, of 

 logic— in order that in terms of them all 

 other notions entering logic should be de- 

 finable ; and that it was nece.esary and suffi- 

 cient, for the propositional basis, to assume, 

 without proof, a somewhat larger yet very 

 small number of propositions— called the 

 primitive propositions, or the premises, of 

 logic— in order that by means of them all 

 other propositions of the science should be 

 capable of demonstration. This is not all, 

 however ; for it has been found— and here we 

 encounter the thesis of modern logistic, the 

 common culmination and result of the two 

 movements hitherto sketched, and so a joint 

 achievement of the logician and the mathe- 

 matician, though hardly foreseen by either 

 of them— it has been found, I say, that the 

 basis of logic Is the basis of mathematics 

 also— that, in other words, given the primi- 

 tives of logic, mathematics requires none of 

 its o^vn but that in terms of the logical 

 primitives all mathematical ideas and all 

 mathematical propositions admit respect- 

 ively of precise definition and of rigoroas 

 demonstration. Accordingly, if a scientific 

 edifice may properly be regarded as consist- 

 ing of both foundation and superstructure, 

 it becomes evident, the thesis once estab- 

 lished, that, in.stead of logic and mathe- 

 matics being, as hitherto supposed, radi- 

 cally distinct sciences, the latter is strictly 



