Generality Quotes
Conventions of generality and mathematical elegance may be just as much barriers to the attainment and diffusion of knowledge as may contentment with particularity and literary vagueness... It may well be that the slovenly and literary borderland between economics and sociology will be the most fruitful building ground during the years to come and that mathematical economics will remain too flawless in its perfection to be very fruitful.
Kenneth Boulding
The generality of men are so bound within the sphere of their circumstances that they have not even the courage to get out of them through their ideas, and if we see a few whom, in a way, speculation over great things makes incapable of mean ones, we find still more with whom the practice of small things takes away the feeling for great ones.
Luc de Clapiers, Marquis de Vauvenargues
Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.
Richard Courant
What all this amounts to, then, is that the Rule of Law requires that administrative discretion in coercive action (i.e., in interfering with the person and property of the private citizen) must always be subject to review by an independent court which is not an instrument of, or even privy to, the aims of current governmental policy; that its review must in all such instances extend to the substance of the administrative act and not merely to the question whether it was infra or ultra vires; and that, if such a court finds that the rights of private citizens have been infringed, it will assess damages just as if the right of this person had been violated by another private citizen. This, in addition to the familiar requirements of generality, equality, and certainty of the law is really the crux of the matter, the decisive point on which it depends whether the Rule of Law prevails or not.
Friedrich Hayek
Had it merely called to our attention the existence and exact nature of certain fundamental gaps in economic theory, the Theory of Economic Behavior by von Neumann and Morgenstern would have been a book of outstanding importance. But it does more than that. It is essentially constructive: where existing theory is considered to be inadequate, the authors put in its place a highly novel analytical apparatus designed to cope with the problem.
It would be doing the authors an injustice to say that theirs is a contribution to economics only. The scope of the book is much broader. The techniques applied by the authors in tackling economic problems are of sufficient generality to be valid in political science, sociology, or even military strategy. The applicability to games proper (chess and poker) is obvious from the title. Moreover, the book is of considerable interest from a purely mathematical point of view.
Leonid Hurwicz
Natural historians tend to avoid tendentious preaching in this philosophical mode (although I often fall victim to such temptations in these essays). Our favored style of doubting is empirical: if I wish to question your proposed generality, I will search for a counterexample in flesh and blood. Such counterexamples exist in abundance, for they form a staple in a standard genre of writing in natural history - the "wonderment of oddity” or "strange ways of the beaver” tradition.
Stephen Jay Gould
Time's arrow of "just history” marks each moment of time with a distinctive brand. But we cannot, in our quest to understand history, be satisfied only with a mark to recognize each moment and a guide to order events in temporal sequence. Uniqueness is the essence of history, but we also crave some underlying generality, some principles of order transcending the distinction of moments-lest we be driven mad by Borges's vision of a new picture every two thousand pages in a book without end. We also need, in short, the immanence of time's cycle.
Stephen Jay Gould
Logical analysis applied to mental phenomenon shows that there is but one law of mind, namely that ideas tend to spread continuously and to affect certain others which stand to them in a peculiar relation of affectibility. In this spreading they lose intensity, and especially the power of affecting others, but gain generality and become welded with other ideas.
Charles Sanders Peirce
Art is simultaneously particular and general. This is a real dichotomy. The great thing about proportion, one aspect of art, is that it is both extremes at once. The level of quality of a work can usually be established by the extent of the polarity between its generality and particularity. Or, to state the idea a little too simply, the better the work, the more diverse its aspects. The nature of the general aspects and the particular ones changes from artist to artist and especially from time to time, since the changes are due to broad changes in philosophy. This change is the essential change in art, determining its purpose and appearance.
Donald Judd
With the publication of J. M. Keynes's General Theory in 1936 and the mathematical formalizations of his theory by J. R. Hicks (1937) and others, the language of macro-economic theory became systems of simultaneous equations. These are general equilibrium systems of interdependence in the sense that the relationships describe an entire national economy, not just a particular industry or sector. The systems are usually not completely closed; they depend on exogenous parameters including instruments controlled by policy-makers. Seeking definite relationships of economic outcomes to policies and other exogenous variables, qualitative and quantitative, these models sacrifice detail and generality, limiting the number of variables and equations by aggregations over agents, commodities, assets, and time.
James Tobin