Foundations of Mathematics Vol . 1 ( 1934 ) Paul
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چکیده
§ 1. The Problem of consistency in axiomatics as a logical decision problem. The state of research in the field of foundations of mathematics, to which our presentation is related, is characterized by three kinds of investigations: 1. the development of the axiomatic method, especially with the help of the foundations of geometry, 2. the founding of analysis by today’s rigorous methods through the reduction of the theory of magnitudes to the theory of numbers and sets of numbers, 3. investigations in the foundations of number theory and set theory.
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Foundations of Mathematics Vol . 1 ( 1934 )
2. Elementary number theory.—Finite inferring and its limits. The question raised at the end of the previous paragraph, whether we couldn’t found arithmetic directly by a method independent of axiomatics and make a special proof of consistency superfluous, gives us reason to recall that the method of rigorous axiomatics, especially existential inference, presupposing a fixed domain of individua...
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