Yquotes.com

 

A single observation that is inconsistent with some generalization points to the falsehood of the generalization, and thereby 'points to itself'.
--
Chapter 4, Evidence, p. 34

 

Ian Hacking

» Ian Hacking - all quotes »

Similar quotes

 

The word generalization in literature usually means covering too much territory too thinly to be persuasive, let alone convincing. In science, however, a generalization means a principle that has been found to hold true in every special case. ... The principle of leverage is a scientific generalization.

 

Buckminster Fuller

 

An extra-terrestrial philosopher, who had watched a single youth up to the age of twenty-one and had never come across any other human being, might conclude that it is the nature of human beings to grow continually taller and wiser in an indefinite progress towards perfection; and this generalization would be just as well founded as the generalization which evolutionists base upon the previous history of this planet.

 

Bertrand Russell

 

Prediction can never be absolutely valid and therefore science can never prove some generalization or even test a single descriptive statement and in that way arrive at final truth.

 

Gregory Bateson

 

Whoever participates in universal Knowledge will regard two apparently contradictory truths as he would two points situated on one and the same circumference that links them together by its continuity and so reduces them to unity; in the measure in which these points are distant from and thus opposed to one another there will be contradiction and this contradiction will reach its maximum when the two points are situated at the extremities of a diameter of the circle; but this extreme opposition or contradiction only appears as a result of isolating the points under consideration from the circle and ignoring the existence of the latter.

 

Frithjof Schuon

 

It is remarkable that this generalization of plane geometry to surface geometry is identical with that generalization of geometry which originated from the analysis of the axiom of parallels. ...the construction of non-Euclidean geometries could have been equally well based upon the elimination of other axioms. It was perhaps due to an intuitive feeling for theoretical fruitfulness that the criticism always centered around the axiom of parallels. For in this way the axiomatic basis was created for that extension of geometry in which the metric appears as an independent variable. Once the significance of the metric as the characteristic feature of the plane has been recognized from the viewpoint of Gauss' plane theory, it is easy to point out, conversely, its connection with the axiom of parallels. The property of the straight line as being the shortest connection between two points can be transferred to curved surfaces, and leads to the concept of straightest line; on the surface of the sphere the great circles play the role of the shortest line of connection... analogous to that of the straight line on the plane. Yet while the great circles as "straight lines" share the most important property with those of the plane, they are distinct from the latter with respect to the axiom of the parallels: all great circles of the sphere intersect and therefore there are no parallels among these "straight lines". ...If this idea is carried through, and all axioms are formulated on the understanding that by "straight lines" are meant the great circles of the sphere and by "plane" is meant the surface of the sphere, it turns out that this system of elements satisfies the system of axioms within two dimensions which is nearly identical in all of it statements with the axiomatic system of Euclidean geometry; the only exception is the formulation of the axiom of the parallels. The geometry of the spherical surface can be viewed as the realization of a two-dimensional non-Euclidean geometry: the denial of the axiom of the parallels singles out that generalization of geometry which occurs in the transition from the plane to the curve surface.

 

Hans Reichenbach