#david pole

Hill 70 | Loos | 26 Sep 1915

The truths of Logic and Mathematics are represented as dwelling in a region of their own. Lifted out of the flux of contingency, they subsist timelessly, visible only to the eye of pure reason. Yet no sooner have we relegated them to this height than we find ourselves obliged to recall them; we have to bring them down again. For what use can these existencies be, with all their purity, if they remain permanently laid up in a heaven and never descend?--if we never meet them at dinner or in the drawing-room, where the affairs of common life are carried on.

Logic marks the limits of the language-game; and it follows that logical statements are in a certain sense empty. They are, as we say, merely formal. If we are told say, that a chess-player will never move his king's bishop except to a white square, that is no prediction about the course of the game. It tells us no more than that he will observe the rules; it lays down what he must do so long as he is playing chess and not some other game with the same pieces. The statement that every object is either cubical or not cubical is equally uninformative; and yet, here too, we may appeal to it, and to similar statements, to impugn other people's linguistic practice or to justify our own.