The Story of Philosophy

by Will Durant

Only mathematical formulas have necessity—they alone are inherently and unchangeably true; and this merely because such formulae are tautological—the predicate is already contained in the subject; “3 X 3 = 9” is an eternal and necessary truth only because “3 X 3” and “9” are one and the same thing differently expressed; the predicate adds nothing to the subject. Science, then, must limit itself strictly to mathematics and direct experiment; it cannot trust to unverified deduction from “laws.” “When we run through libraries, persuaded of these principles,” writes our uncanny sceptic, “what havoc must we make! If we take in our hands any volume of school metaphysics, for instance, let us ask, ‘Does it contain any abstract reasoning concerning quantity or number?’ No. ‘Does it contain any experimental reasoning concerning matter of fact and existence?’ No. Commit it then to the flames, for it can contain nothing but sophistry and illusion.”