Combining Texts

All the ideas for 'poems', 'Classes and Attributes' 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
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.
8. Modes of Existence / B. Properties / 11. Properties as Sets
9783 While no two classes coincide in membership, there are distinct but coextensive attributes [Cartwright,R]
     Full Idea: Attributes and classes are said to be distinguished by the fact that whereas no two classes coincide in membership, there are supposed to be distinct but coextensive attributes.
     From: Richard Cartwright (Classes and Attributes [1967], §2)
     A reaction: This spells out the standard problem of renates and cordates, that creatures with hearts and with kidneys are precisely coextensive, but that these properties are different. Cartwright then attacks the distinction.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
6017 Nomos is king [Pindar]
     Full Idea: Nomos is king.
     From: Pindar (poems [c.478 BCE], S 169), quoted by Thomas Nagel - The Philosophical Culture
     A reaction: This seems to be the earliest recorded shot in the nomos-physis wars (the debate among sophists about moral relativism). It sounds as if it carries the full relativist burden - that all that matters is what has been locally decreed.