Philosophische Schriften [Gerhardt] Bd. 8, p. 198.
[1317]. The influence of the mathematics of Leibnitz upon his philosophy appears chiefly in connection with his law of continuity and his prolonged efforts to establish a Logical Calculus.... To find a Logical Calculus (implying a universal philosophical language or system of signs) is an attempt to apply in theological and philosophical investigations an analytic method analogous to that which had proved so successful in Geometry and Physics. It seemed to Leibnitz that if all the complex and apparently disconnected ideas which make up our knowledge could be analysed into their simple elements, and if these elements could each be represented by a definite sign, we should have a kind of “alphabet of human thoughts.” By the combination of these signs (letters of the alphabet of thought) a system of true knowledge would be built up, in which reality would be more and more adequately represented or symbolized.... In many cases the analysis may result in an infinite series of elements; but the principles of the Infinitesimal Calculus in mathematics have shown that this does not necessarily render calculation impossible or inaccurate. Thus it seemed to Leibnitz that a synthetic calculus, based upon a thorough analysis, would be the most effective instrument of knowledge that could be devised. “I feel,” he says, “that controversies can never be finished, nor silence imposed upon the Sects, unless we give up complicated reasonings in favor of simple calculations, words of vague and uncertain meaning in favor of fixed symbols.” Thus it will appear that “every paralogism is nothing but an error of calculation.” “When controversies arise, there will be no more necessity of disputation between two philosophers than between two accountants. Nothing will be needed but that they should take pen in hand, sit down with their counting-tables, and (having summoned a friend, if they like) say to one another: Let us calculate”—Latta, Robert.
Leibnitz, The Monadology, etc. (Oxford, 1898), p. 85.
[1318]. Pure mathematics was discovered by Boole in a work which he called “The Laws of Thought“.... His work was concerned with formal logic, and this is the same thing as mathematics.—Russell, Bertrand.
International Monthly, 1901, p. 83.
[1319]. Mathematics is but the higher development of Symbolic Logic.—Whetham, W. C. D.
Recent Development of Physical Science (Philadelphia, 1904), p. 34.
[1320]. Symbolic Logic has been disowned by many logicians on the plea that its interest is mathematical, and by many mathematicians on the plea that its interest is logical.—Whitehead, A. N.
Universal Algebra (Cambridge, 1898), Preface, p. 6.
[1321]. ... the two great components of the critical movement, though distinct in origin and following separate paths, are found to converge at last in the thesis: Symbolic Logic is Mathematics, Mathematics is Symbolic Logic, the twain are one.—Keyser, C. J.