36 research outputs found

    A new look at analogical reasoning

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    Axioms in Mathematical Practice

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    Dedekind's Abstract Concepts: Models and Mappings

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    From Weber to van der Waerden

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    Fregean Logical Graphs

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    In \u201cGedankengef\ufcge\u201d Frege says that any two sentences of the form \u201cA and B\u201d and \u201cB and A\u201d have the same sense. In a 1906 letter to Husserl he says that sentences with the same sense should be represented in a perfect notation by one and the same formula. Frege\u2019s own notation, just like any linear notation for sentential logic, is not perfect in this sense, because in it \u201cA and B\u201d and \u201cB and A\u201d are represented by distinct formulas, as is any pair of logically equivalent compound conditionals. A notation for the sentential calculus that meets Frege\u2019s worries about conjunction, and indeed about any symmetric relation that there may be occasion to symbolize, is Peirce\u2019s Alpha graphs
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