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"The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function."
C
Consistency"A silly ass … wrote a paper to prove me inconsistent. … Inconsistency is the bugbear of fools! I wouldnt give a damn for a fellow who couldnt change his mind with a change of conditions."
In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory is consistent if there is no formula such that both and its negation are elements of the set of consequences of . Let be a set of closed sentences and the set of closed sentences provable from under some formal deductive system. The set of axioms is consistent when there is no formula su
"The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function."
"The theoretical view of the actual universe, if it is in correspondence to our reasoning, is the following. The curvature of space is variable in time and place, according to the distribution of matter, but we may roughly approximate it by means of a spherical space. ...this view is logically consistent, and from the standpoint of the general theory of relativity [is most obvious] lies nearest at hand; whether, from the standpoint of present astronomical knowledge, it is tenable, will not be discussed here. In order to arrive at this consistent view, we admittedly had to introduce an extension of the field equations of gravitation, which is not justified by our actual knowledge of gravitation. It is to be emphasized, however, that a positive curvature of space is given by our results, even if the supplementary term [] is not introduced. The term is necessary only for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocity of the stars."
"Do I contradict myself? Very well then I contradict myself, (I am large, I contain multitudes.)"
"Consistency is contrary to nature, contrary to life. The only completely consistent people are the dead."
"Consistency is a virtue for trains: what we want from a philosopher is insights, whether he comes by them consistently or not."
"The classic example of an is that of plane geometry formulated by Euclid... It forms the model of all rigorous mathematical schemes. The axioms are the initial assumptions... From them, logical deductions can proceed under stipulated rules of reasoning... analogous to the scientists laws of Nature, whilst the axioms play the role of s. We are not free to pick any axioms... They must be logically consistent..."