We see how much richer the new logic is than the classic logic; the symbols are multiplied and allow of varied combinations _which are no longer limited in number_. Has one the right to give this extension to the meaning of the word _logic_? It would be useless to examine this question and to seek with Russell a mere quarrel about words. Grant him what he demands; but be not astonished if certain verities declared irreducible to logic in the old sense of the word find themselves now reducible to logic in the new sense--something very different.
A great number of new notions have been introduced, and these are not simply combinations of the old. Russell knows this, and not only at the beginning of the first chapter, 'The Logic of Propositions,' but at the beginning of the second and third, 'The Logic of Classes' and 'The Logic of Relations,' he introduces new words that he declares indefinable.
And this is not all; he likewise introduces principles he declares indemonstrable. But these indemonstrable principles are appeals to intuition, synthetic judgments _a priori_. We regard them as intuitive when we meet them more or less explicitly enunciated in mathematical treatises; have they changed character because the meaning of the word logic has been enlarged and we now find them in a book entitled _Treatise on Logic_? _They have not changed nature; they have only changed place._
