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1, 2, 3, ... the letters of alphabet and some special symbols like "+", "⇒", "(", ")", etc.), give a finite number of propositions expressed in those symbols, which were to be taken as "foundations" (the axioms), and some
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In standard mathematics, an operation is finitary by definition. Therefore, these terms are usually only used in the context of
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in the argument will necessarily be finite since the proof is finite, but the number of axioms from which these are
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thought is based on a finite number of principles and all the reasonings follow essentially one rule: the
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the theorems of mathematics could be deduced. That aim is known as
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using only the stated rules (which make mathematics look like a
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which would model the way humans make conclusions. From these,
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Stanford
Encyclopedia of Philosophy entry on Infinitary Logic
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regardless of the semantic interpretation of the symbols
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Qualifies an operation with a finite number of arguments
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The stress on finiteness came from the idea that human
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of symbolic propositions starting from a finite set of
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58:"Finitary"
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