Page:Mind (New Series) Volume 12.djvu/195

RECENT WORK ON THE PHILOSOPHY OF LEIBNIZ. 181 giving different meanings to the symbols, a given symbolic pro- position may be interpreted as a true proposition in any one of these sciences a procedure of which there are innumerable in- stances in mathematics. The most ambitious and the most chimerical of Leibniz's schemes was the Encyclopaedia. This was to contain the whole body of human knowledge, historical and scientific, arranged in a logical order, and following a demonstrative method. It w 7 as to begin with simple and primitive terms, and Euclid's Elements were to be its model ; finally, a small number of principles would suffice for the foundation, and thus the sciences would be abridged as they grew (p. 152). This task, even Leibniz had to admit, sur- passed the powers of a single man, and for its fulfilment he wished to found an "Imperial German Society"; all his plans for the foundation of Academies are connected with the Encyclopaedia (p. 127 and Appendix iv). Originally, theology and law ^occupied the place of honour in the Encyclopaedia ; but after 1679 logic was to be immediately succeeded by mathematics and physics (p. 129). Two causes, we are told (p. 175), prevented the accom- plishment of the work the lack of time, and the failure to find collaborators. Surely we may add the inherent impossibility of the task ; for here Leibniz's panlogism, his belief in the possibility of deducing everything a priori from a small number of premisses, led him to conceive all truth as an ordered chain of deduction in a sense which is essentially false. In Pure Mathematics, where alone this ideal is applicable, the task which he attempted has been at last accomplished; but elsewhere, premisses which are essentially empirical i.e. concerned with existence at particular times appear to be logically and ultimately essential. The Encyclopaedia required what Leibniz called Scientia Generalis, i.e. a general method applicable to all the sciences ; this was, in fact, the whole of his Logic (p. 176). M. Couturat studies it fully in a long chapter (chap. vi.). Leibniz makes two divisions in the art of reasoning. We may reason, he says, from principles to consequences, from causes to effects ; or again, we may go from given consequences to the principles required, from known effects to unknown causes (p. 177). The other division is into the logic of certainties and the logic of probabilities (p. 239). Both these divisions seem ob- jectionable. If a principle can be inferred from a consequence, it must follow from the consequence, and is therefore a consequence of the consequence. As for causes and effects, it is of course possible, speaking generally, to argue either from effects to causes or from causes to effects, and this seemed relevant to Leibniz be- cause he regarded causes as logically prior to effects (p. 222). But when it is recognised that cause and effect are on the same logical level, this twofold direction of temporal implications ceases to have a fundamental logical importance. As for probability, it is, Leibniz says, the logic of the real ; if we could calculate the