The functional validity of a working hypothesis is not a priori certain, because often it is initially based on intuition. However, logical deductions from such a hypothesis provide expectations (so called prognoses) as to the circumstances under which certain phenomena will appear in nature. Such a postulate or working hypothesis can then be substantiated by additional observations or by experiments especially arranged to test details. The value of the hypothesis is strengthened if the observed facts fit the expectation within the limits of permissible error.
Reinout Willem van BemmelenRelated topics
additional appear certain error fit functional hypothesis intuition nature postulate prognosis under validity value working circumstances factsRelated quotes
The fact that I myself, at the moment of painting, do not understand my own pictures, does not mean that these pictures have no meaning; on the contrary, their meaning is so profound, complex, coherent, and involuntary that it escapes the most simple analysis of logical intuition. To describe my pictures in everyday language, to explain them, it is necessary to submit them to special analyses and preferably with the most ambitiously objective scientific rigour possible. Then all explanation arises a posteriori; once the picture already exists as phenomenon.
Salvador Dalí
Any test that turns on what is offensive to the community's standards is too loose, too capricious, too destructive of freedom of expression to be squared with the First Amendment. Under that test, juries can censor, suppress, and punish what they don't like, provided the matter relates to "sexual impurity" or has a tendency "to excite lustful thoughts". This is community censorship in one of its worst forms. It creates a regime where in the battle between the literati and the Philistines, the Philistines are certain to win.
William O. Douglas
I am not [...] asserting that humans are either genial or aggressive by inborn biological necessity. Obviously, both kindness and violence lie within the bounds of our nature because we perpetrate both, in spades. I only advance a structural claim that social stability rules nearly all the time and must be based on an overwhelmingly predominant (but tragically ignored) frequency of genial acts, and that geniality is therefore our usual and preferred response nearly all the time. [...] [T]he center of human nature is rooted in ten thousand ordinary acts of kindness that define our days.
Stephen Jay Gould
The method of successive approximations is often applied to proving existence of solutions to various classes of functional equations; moreover, the proof of convergence of these approximations leans on the fact that the equation under study may be majorised by another equation of a simple kind. Similar proofs may be encountered in the theory of infinitely many simultaneous linear equations and in the theory of integral and differential equations. Consideration of semiordered spaces and operations between them enables us to easily develop a complete theory of such functional equations in abstract form.
Leonid Kantorovich
When we seek a textbook case for the proper operation of science, the correction of certain error offers far more promise than the establishment of probable truth. Confirmed hunches, of course, are more upbeat than discredited hypotheses. Since the worst traditions of "popular” writing falsely equate instruction with sweetness and light, our promotional literature abounds with insipid tales in the heroic mode, although tough stories of disappointment and loss give deeper insight into a methodology that the celebrated philosopher Karl Popper once labeled as "conjecture and refutation.”.
Stephen Jay Gould
