Combining Texts

All the ideas for 'fragments/reports', 'Whitehead and the Rise of Modern Logic' and 'Demonstratives'

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5 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
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
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.
19. Language / C. Assigning Meanings / 10. Two-Dimensional Semantics
Indexicals have a 'character' (the standing meaning), and a 'content' (truth-conditions for one context) [Kaplan, by Macià/Garcia-Carpentiro]
     Full Idea: Kaplan distinguished two different semantic features of indexical expressions: a 'character' that captures the standing meaning of the expression, and a 'content' that consists of their truth-conditional contribution in particular contexts.
     From: report of David Kaplan (Demonstratives [1989]) by Macià/Garcia-Carpentiro - Introduction to 'Two-Dimensional Semantics' 1
     A reaction: This seems so clearly right that there isn't much to dispute. You can't understand the word 'I' or 'now' if you don't understand both its general purpose, and what it is doing in a particular utterance. But will this generalise to other semantics?
'Content' gives the standard modal profile, and 'character' gives rules for a context [Kaplan, by Schroeter]
     Full Idea: Kaplan sees two aspects of meaning, the 'content', reflecting a thing's modal profile, which is modelled by standard possible worlds semantics, and 'character', giving rules for different contexts. Proper names have constant character; indexicals vary.
     From: report of David Kaplan (Demonstratives [1989]) by Laura Schroeter - Two-Dimensional Semantics 1.1.1
     A reaction: This gives rise to 2-D matrices for representing meaning, and the possible worlds are used twice, for evaluating meaning and then for evaluating context of use. I've always been struck by the two-dimensional semantics of passwords.
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
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?