Combining Texts

All the ideas for 'Science and Method', 'works' and 'Review of Frege's 'Grundlagen''

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3 ideas

1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
Hermeneutics of tradition is sympathetic, hermeneutics of suspicion is hostile [Ricoeur, by Mautner]
     Full Idea: Ricoeur distinguishes a hermeneutics of tradition (e.g. Gadamar), which interprets sympathetically looking for hidden messages, and a hermeneutics of suspicion (e.g. Nietzsche, Freud) which sees hidden drives and interests.
     From: report of Paul Ricoeur (works [1970]) by Thomas Mautner - Penguin Dictionary of Philosophy p.249
     A reaction: Obviously the answer is somewhere between the two. Nietzsche's suspicion can be wonderful, but Freud's can seem silly (e.g. on Leonardo). On the whole I am on the 'tradition' side, because great thinkers can rise above their culture (on a good day).
6. Mathematics / A. Nature of Mathematics / 2. Geometry
One geometry cannot be more true than another [Poincaré]
     Full Idea: One geometry cannot be more true than another; it can only be more convenient.
     From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics
     A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor]
     Full Idea: The author entirely overlooks the fact that the 'extension of a concept' in general may be quantitatively completely indeterminate. Only in certain cases is the 'extension of a concept' quantitatively determinate.
     From: George Cantor (Review of Frege's 'Grundlagen' [1885], 1932:440), quoted by William W. Tait - Frege versus Cantor and Dedekind
     A reaction: Cantor presumably has in mind various infinite sets. Tait is drawing our attention to the fact that this objection long precedes Russell's paradox, which made the objection more formal (a language Frege could understand!).