293 resultados para philosophical foundations


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Contains the proceedings of the Royal Society of Edinburgh, the Wernerian Natural History Society, etc

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Mode of access: Internet.

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Mode of access: Internet.

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Published in 1922 as volume I of "A short history of the American people."

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The Church-Turing Thesis is widely regarded as true, because of evidence that there is only one genuine notion of computation. By contrast, there are nowadays many different formal logics, and different corresponding foundational frameworks. Which ones can deliver a theory of computability? This question sets up a difficult challenge: the meanings of basic mathematical terms (like "set", "function", and "number") are not stable across frameworks. While it is easy to compare what different frameworks say, it is not so easy to compare what they mean. We argue for some minimal conditions that must be met if two frameworks are to be compared; if frameworks are radical enough, comparison becomes hopeless. Our aim is to clarify the dialectical situation in this bourgeoning area of research, shedding light on the nature of non-classical logic and the notion of computation alike.

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"The manuscript of this work is in the library of the American philosophical society. It is a copy made by Mr. Duponceau, and forms no. xxvii of a collection made by him and recorded in a folio account book, of which it occupies pp. 114-119."--Pilling, Bibl. of the Algonquin languages, p. 227.

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Translation of Dictionnaire philosophique.