Combining Texts

All the ideas for 'works', 'Methodological Reflections on Current Linguistic Theory' and 'Review of Frege's 'Grundlagen''

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3 ideas

5. Theory of Logic / G. Quantification / 2. Domain of Quantification
17743 De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan, by Walicki]
     Full Idea: In 1846 De Morgan introduced the enormously influential notion of a possibly arbitrary and stipulated 'universe of discourse'. It replaced Boole's original - and metaphysically a bit suspect - universe of 'all things'.
     From: report of Augustus De Morgan (works [1846]) by Michal Walicki - Introduction to Mathematical Logic History D.1.1
     A reaction: This not only brings formal logic under control, but also reflects normal talk, because there is always an explicit or implicit domain of discourse when we talk. Of virtually any conversation, you can say what it is 'about'.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
9992 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!).
19. Language / C. Assigning Meanings / 2. Semantics
15788 Syntax and semantics are indeterminate, and modern 'semantics' is a bogus subject [Quine, by Lycan]
     Full Idea: Quine has argued tirelessly that syntax and 'semantics' are indeterminate, and linguistic semantics of the sort that is currently in favor is a pseudoscience and a pipe dream.
     From: report of Willard Quine (Methodological Reflections on Current Linguistic Theory [1972]) by William Lycan - The Trouble with Possible Worlds 02
     A reaction: I think the defence of such things is that they may not integrate into science very well (or even integrate at all), but semantics is intended to integrate into philosophy, and is motivated by philosophical concerns. Quine may be right!