Tuesday, October 10, 2006

Quine Quotes

I picked up a copy of Set Theory and Its Logic by one Willard Van Orman Quine. Few good quotes thus far (emphasis mine):

If the sentence represented by 'F x' happens to contain a quantifier capable of binding the y of 'F y', then an evasive relettering of the quantification is to be understood...


I think evasive relettering is a much more user-friendly term than α-conversion.

From the preface to the First Edition (emphasis still mine):

Because the axiomatic systems of set theory in the literature are largely uincompatiblewith one another and no one of them clearly deserves to be singled out as standard, it seems prudent to teach a panorama of alternatives. This can encourage research that may some day issue in a set theory that is clearly best. But the writer who would pursue this liberal policy has his problems. He cannot very well begin by offering the panoramic view, for the beginning reader will appreciate neither the material that the various systems are meant to organize nor the cconsiderationsthat could favor one system in any respect over another. Better to begin by orienting the reader with a preliminary informal survey of the subject matter. But here again there is trouble. If such a survey is to get beyond trivialities, it must resort to serious and sophisticated reasoning such as could quickly veer into the antinomies and so discredit itself if not shunted off them in one of two ways: by abandoning the informal approach in favor of the axiomatic after all, or just by slyly diverting the reader's attention from dangerous questions until the formal orientation is accomplished. The latter course calls for artistry of a kind that is distasteful to a science teacher, and anyway it is powerless with readers who hear about the antinomies from someone else. Once they have heard about them, they can no longer submit to the discipline of complex informal arguments in abstract set theory; for they can no longer tell which intuitive arguments count. It is not for nothing, after all, that set theorists resort to the axiomatic method. Intuition here is bankrupt, and to keep the reader innocent of this fact through half a book is a sorry business even when it can be done.

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