Ideas from 'Whitehead and the Rise of Modern Logic' by Willard Quine [1941], by Theme Structure
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13639
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Quine says higher-order items are intensional, and lack a clearly defined identity relation
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Full Idea:
Quine (in 1941) attacked 'Principia Mathematica' because the items in the range of higher-order variables (attributes etc) are intensional and thus do not have a clearly defined identity relation.
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From:
report of Willard Quine (Whitehead and the Rise of Modern Logic [1941]) by Stewart Shapiro - Foundations without Foundationalism 1.3
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
21557
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Russell confused use and mention, and reduced classes to properties, not to language
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Full Idea:
Quine (1941) said that Russell had confused use and mention, and thus thought he had reduced classes to linguistic entities, while in fact he reduced them only to Platonic properties.
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From:
report of Willard Quine (Whitehead and the Rise of Modern Logic [1941]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.133
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A reaction:
This is cited as the 'orthodox critical interpretation' of Russell and Whitehead. Confusion of use and mention was a favourite charge of Quine's.
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