Generalize Quotes (9 quotes)
Another characteristic of mathematical thought is that it can have no success where it cannot generalize.
Before you generalize, formalize, and axiomatize there must be mathematical substance.
Every science begins by accumulating observations, and presently generalizes these empirically; but only when it reaches the stage at which its empirical generalizations are included in a rational generalization does it become developed science.
Having discovered by observation and comparison that certain objects agree in certain respects, we generalise the qualities in which they coincide,that is, from a certain number of individual instances we infer a general law; we perform an act of Induction. This induction is erroneously viewed as analytic; it is purely a synthetic process.
Induction is the process of generalizing from our known and limited experience, and framing wider rules for the future than we have been able to test fully. At its simplest, then, an induction is a habit or an adaptationthe habit of expecting tomorrows weather to be like todays, the adaptation to the unwritten conventions of community life.
Man is made for science; he reasons from effects to causes, and from causes to effects; but he does not always reason without error. In reasoning, therefore, from appearances which are particular, care must be taken how we generalize; we should be cautious not to attribute to nature, laws which may perhaps be only of our own invention.
No generalizing beyond the data, no theory. No theory, no insight. And if no insight, why do research.
Random search for data on ... off-chance is hardly scientific. A questionnaire on 'Intellectual Immoralities' was circulated by a well-known institution. 'Intellectual Immorality No. 4' read: 'Generalizing beyond one's data'. [Wilder Dwight] Bancroft asked whether it would not be more correct to word question no. 4 'Not generalizing beyond one's data.'
The book [Future of an Illusion] testifies to the fact that the genius of experimental science is not necessarily joined with the genius of logic or generalizing power.