From the imputation of confounding axioms with assumed concepts Euclid himself, however, is free. Euclid incorporated the former among his postulates while he separated the latter as common concepts-a proceeding which even on the part of his commentators was no longer understood, and likewise with modern mathematicians, unfortunately for science, has met with little imitation. As a matter of fact, the abstract methods of mathematical science know no axioms at all.
Hermann GrassmannRelated topics
abstract common confounding euclid free imputation likewise longer matter met proceeding science whileRelated quotes
It is a matter of course and of absolute necessity to the conduct of business, that any discretionary businessman must be free to deal or not to deal in any given case; to limit or withhold the equipment under his control, without reservation. Business discretion and business strategy, in fact, has no other means by to work out its aims. So that, in effect, all business sagacity reduces itself in the last analysis to judicious use of sabotage.
Thorstein Veblen
Science sometimes improves hypotheses and sometimes disproves them. But proof would be another matter and perhaps never occurs except in the realms of totally abstract tautology. We can sometimes say that if such and such abstract suppositions or postulates are given, then such and such abstract suppositions or postulates are given, then such and such must follow absolutely. But the truth about what can be perceived or arrived at by induction from perception is something else again.
Gregory Bateson
I find it expressed in various passages of Scripture that the fact that God knows things while in a state of possibility, when their existence belongs to the future, does not change the nature of the possible in any way; that nature remains unchanged; and the knowledge of the realisation of one of several possibilities does not yet effect that realisation. This is likewise one of the fundamental principles of the Law of Moses concerning which there is no doubt nor any dispute.
Maimonides
Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.
David Hilbert
Some of the colonizers do understand and quickly retreat, while some, because they are stupid, continue colonizing others, increasing the suffering, deaths, injuries, defeat and humiliation. The people colonized by Abyssinia will be free. Eritrea will be free, and they cannot refuse to let them be free. Western Somalia will be free, and they cannot refuse to grant it freedom. The numerous Abo will be free because this is history, and no one can prevent the sunshine from reaching us.
Siad Barre