We tend to believe the premises because we can see that their consequences are true, instead of believing the consequences because we know the premises to be true. But the inferring of premises from consequences is the essence of induction; thus the method in investigating the principles of mathematics is really an inductive method, and is substantially the same as the method of discovering general laws in any other science.
Bertrand RussellRelated topics
believing believe discovering essence general induction inferring investigating mathematics method premises science see thus laws consequencesRelated quotes
With reference to practical social doctrines, our method permits and commands the same independence. Sociology thus understood will be neither individualistic, communistic, nor socialistic in the sense commonly given these words. On principle, it will ignore these theories, in which it could not recognize any scientific value, since they tend not to describe or interpret, but to reform, social organization.
Émile Durkheim
Intermediate between mathematics, statistics, and economics, we find a new discipline which, for lack of a better name, may be called econometrics. Econometrics has as its aim to subject abstract laws of theoretical political economy or "pure" economics to experimental and numerical verification, and thus to turn pure economics, as far as possible, into a science in the strict sense of the word.
Ragnar Frisch
One might ask why the teachers do not notice the difficulty children have in learning BASIC. The answer is simple: Most teachers do not expect high performance from most students, especially in a domain of work that appears to be as "mathematical" and "formal" as programming. Thus the culture's general perception of mathematics as inaccessible bolsters the maintenance of BASIC, which in turn confirms these perceptions.
Seymour Papert
The endeavor of scientific research to see events in their more general connection in order to determine their laws, is a legitimate and useful occupation. Any protest against such efforts, in the name of freefom from restrictive conditions, would be fruitless if science did not naïvely identify the abstractions called rules and laws with the actually efficacious forces, and confuse the probability that B will follow A with the actual effort make B follow A.
Max Horkheimer
Magic is that which it is; it is by itself, like the mathematics; for it is the exact and absolute science of Nature and its laws.
Magic is the science of the Ancient Magi: and the Christian religion, which has imposed silence on the lying oracles, and put an end to the prestiges of the false Gods, itself reveres those Magi who came from the East, guided by a Star, to adore the Saviour of the world in His cradle.
Albert Pike
