Quotessence
Home / Quotes / A Quotes

A Quotes

Browse famous quotes beginning with A. This page is a child index of the full Popular Quotes A-Z directory.

All A Quotes

“A proof represents a logical process which has come to a definitive conclusion in a finite number of stages. However, a logical machine following definite rules need never come to a conclusion. It may go on grinding through different stages without ever coming to a stop, either by describing a pattern of activity of continually increasing complexity, or by going into a repetitive process like the end of a chess game in which there is a continuing cycle of perpetual check. This occurs in the case of some of the paradoxes of Cantor and Russell. Let us consider the class of all classes which are not members of themselves. Is this class a member of itself? If it is, it is certainly not a member of itself; and if it is not, it is equally certainly a member of itself. A machine to answer this question would give the successive temporary answers: “yes,” “no,” “yes,” “no,” and so on, and would never come to equilibrium. Bertrand Russell’s solution of his own paradoxes was to affix to every statement a quantity, the so-called type, which serves to distinguish between what seems to be formally the same statement, according to the character of the objects with which it concerns itself—whether these are “things,” in the simplest sense, classes of “things,” classes of classes of “things,” etc. The method by which we resolve the paradoxes is also to attach a parameter to each statement, this parameter being the time at which it is asserted. In both cases, we introduce what we may call a parameter of uniformization, to resolve an ambiguity which is simply due to its neglect.”

“A proper autobiography is a death-bed confession. A true man finds so much work to do that he has no time to contemplate his yesterdays; for to-day and to-morrow are here, with their impatient tasks. The world is so busy, too, that it cannot afford to study any man's unfinished work; for the end may prove it a failure, and the world needs masterpieces.”

“A proper community, we should remember also, is a commonwealth: a place, a resource, an economy. It answers the needs, practical as well as social and spiritual, of its members - among them the need to need one another. The answer to the present alignment of political power with wealth is the restoration of the identity of community and economy. (pg. 63, "Racism and the Economy")”

“A proper record shop reminds us why we got into this in the first place - a place to be reminded of old friends, still in their spots on the shelves, a source of unexpected magic and lucid memories - a place that reminds us that music is more than dumb file sharing and the management of dead data by faceless sociopathic corporations, but a storehouse of dreams, both possible and impossible.”