Symbolical Logic

Abstract

IN my recent letter on Symbolical Logic (see NATURE, vol. xxiii, p. 578) I said that Prof. Peirce's symbol of inclusion, as, defined by him in his “Logic of Relatives”, was equivalent to the words “is not greater than”. This however is not quite correct; for though Prof. Peirce speaks of this symbol as equivalent to the words “is as small as”, he also speaks of it as denoting “inclusion”, and bis illustration f —< m may be read, The class f is included in the class m. In my notation the analogous composite symbol f : m may be read, The statement f implies the statement m. If for f in my notation we read He belongs to the class f, and for m we read He belongs to the class m, then my f : m will coincide in meaning with Prof. Peirce's f —< m; but this does not alter the fact that my f differs in meaning from his f, that my: differs from his —<, and my m from his m. Mr. Venn, in his recent paper in the Proceedings of the Cambridge Philosophical Society, speaks of these distinguishing features of my method as unimportant, and he regards my definitions of my elementary symbols as “arbitrary restrictions of the full generality of our symbolic language”. But Mr. Venn overlooks the fact that all accurate definitions are more or less arbitrary restrictions of language, and he also seems to me, in this particular case, to mistake vagueness for generality. Philosophical investigations that begin with Let x = anything commonly end with x = anything, a result which, whatever may be thought of its generality, does not add much to our knowledge.