The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.

... two men could be just alike in all their dispositions to verbal behavior under all possible sensory stimulations, and yet themeanings or ideas expressed in their identically triggered and identically sounding utterances could diverge radically, for the two men, in a wide range of cases.

For me the problem of induction is a problem about the world: a problem of how we, as we are now (by our present scientific lights), in a world we never made, should stand better than random, or coin-tossing chances changes of coming out right when we predict by inductions. . . .

One man's observation is another man's closed book or flight of fancy.

Linguistically, and hence conceptually, the things in sharpest focus are the things that are public enough to be talked of publicly, common and conspicuous enough to be talked of often, and near enough to sense to be quickly identified and learned by name; it is to these that words apply first and foremost.

The strategy of semantic ascent is that it carries the discussion into a domain where both parties are better agreed on the objects (viz., words) and on the main terms connecting them. Words, or their inscriptions, unlike points, miles, classes and the rest, are tangible objects of the size so popular in the marketplace, where men of unlike conceptual schemes communicate at their best. The strategy is one of ascending to a common part of two fundamentally disparate conceptual schemes, the better to discuss the disparate foundations. No wonder it helps in philosophy.

Unlike Descartes, we own and use our beliefs of the moment, even in the midst of philosophizing, until by what is vaguely called scientific method we change them here and there for the better. Within our own total evolving doctrine, we can judge truth as earnestly and absolutely as can be, subject to correction, but that goes without saying.