Combining Texts

Ideas for 'Wiener Logik', 'The Logical Form of Action Sentences' and 'The Principles of Mathematics'

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2 ideas

5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
14149 The Achilles Paradox concerns the one-one correlation of infinite classes [Russell]
     Full Idea: When the Achilles Paradox is translated into arithmetical language, it is seen to be concerned with the one-one correlation of two infinite classes.
     From: Bertrand Russell (The Principles of Mathematics [1903], §321)
     A reaction: Dedekind's view of infinity (Idea 9826) shows why this results in a horrible tangle.
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
15895 Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine]
     Full Idea: Burali-Forti didn't discover any paradoxes, though his work suggested a paradox to Russell.
     From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Shaughan Lavine - Understanding the Infinite I