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Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. these fundamental principles are called the axioms of geometry.
-David Hilbert
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Geometry, Like Arithmetic, Requires For Its Logical

David Hilbert
Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. these fundamental principles are called the axioms of geometry.
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As soon as science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms. we call such a system of thought a theory. the theory finds the justification for its existence in the fact that it correlates a large number of single observations, and it is just here that the 'truth' of the theory lies.
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To make positive change requires lasting commitment, lasting commitment requires measurable targets, measurable targets requires detailed action plans, detailed action plans requires a goal you desire, desire requires a positive attitude to change your life, and the option to change your life requires work. byron pulsifer, from nothing ventured, nothing gained if you deny yourself commitment, what can you do with your life?
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While the game of deadlocks and bottle-necks goes on, another more serious game is also being played. it is governed by two axioms. one is that there can be no peace without a general surrender of sovereignty: the other is that no country capable of defending its sovereignty ever surrenders it. if one keeps these axioms in mind one can generally see the relevant facts in international affairs through the smoke-screen with which the newspapers surround them.
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The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms.
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A science is something which is constructed from truth on workable axioms. there are 55 axioms in scientology which are very demonstrably true, and on these can be constructed a great deal.
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I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect. . . geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.
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