Combining Texts

All the ideas for 'fragments/reports', 'On the Frame of Reference' and 'Whitehead and the Rise of Modern Logic'

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4 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13639 Quine says higher-order items are intensional, and lack a clearly defined identity relation [Quine, by Shapiro]
     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.
     From: report of Willard Quine (Whitehead and the Rise of Modern Logic [1941]) by Stewart Shapiro - Foundations without Foundationalism 1.3
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
10009 Substitutional quantification is just a variant of Tarski's account [Wallace, by Baldwin]
     Full Idea: In a famous paper, Wallace argued that all interpretations of quantifiers (including the substitutional interpretation) are, in the end, variants of that proposed by Tarski (in 1936).
     From: report of Wallace, J (On the Frame of Reference [1970]) by Thomas Baldwin - Interpretations of Quantifiers
     A reaction: A significant-looking pointer. We must look elsewhere for Tarski's account, which will presumably subsume the objectual interpretation as well. The ontology of Tarski's account of truth is an enduring controversy.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
21557 Russell confused use and mention, and reduced classes to properties, not to language [Quine, by Lackey]
     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.
     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
     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.
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
     Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
     From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?