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.

Unscientific man is beset by a deplorable desire to have been right. The scientist is distinguished by a desire to be right.

An indirect quotation we can usually expect to rate only as better or worse, more or less faithful, and we cannot even hope for astrict standard of more and less; what is involved is evaluation, relative to special purposes, of an essentially dramatic act.

Meaning is what essence becomes when it is divorced from the object of reference and wedded to the word.

Yields falsehood when preceded by its quotation.

Confusion of sign and object is original sin coeval with the word.

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.