The time of revision is past. The book is dated, and its dates are 1953 and 1961.
p 14
The three main mediaeval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially the same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names of logicism, intuitionism, and formalism.
Modern empiricism has been conditioned in large by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truths which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall agree, are ill-founded.
[...] for all its a priori reasonableness, a boundary between analytic and synthetic statements has not been drawn. That there is such a distinction to be drawn at all is an unempirical dogma of empiricists, a metaphysical article of faith.
I am now urging [...] that even in taking the statement as unit we have drawn our grid too finely. The unit of empirical significance is the whole of science.
The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges.
p 43
Revision even of the logical law of the excluded middle has been proposed as a means of simplifying quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle?
p 44
As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. [...] For my part I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing the physical objects and the gods differ only in degree and not in kind.
p 45
Moreover, the abstract entities which are the substance of mathematics—ultimately classes and classes of classes and so on up—are another posit in the same spirit. Etymologically these are myths on the same footing with physical objects and gods [...]
[...] there is considerable agreement among modern linguists that the idea of an idea, the idea of the mental counterpart of a linguistic form, is worse than worthless.
p 49
The grammarian and the lexicographer are concerned with meaning to an equal degree, be it zero or otherwise; the grammarian wants to know what forms are significant, or have meaning, while the lexicographer wants to know what forms are synonymous, or alike in meaning.
Whereas the theory of types avoids the contradictions by excluding unstratified formulas from the language altogether, we might gain the same end by continuing to countenance unstratified formulas but simply limiting R3 explicitly to stratified formulas.
The primitive notation undergoing the foregoing development of logic was threefold, comprising the notations of membership, alternative denial, and universal quantification. Now it is worth noting that this choice of primitives was neither necessary nor minimal. We could have done with just two: the notations of inclusion and abstraction [...]