Combining Texts

All the ideas for 'fragments/reports', 'Transworld Heir Lines' and 'Review of Chihara 'Struct. Accnt of Maths''

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13 ideas

5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Logicians like their entities to exhibit a maximum degree of purity [Kaplan]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set theory is the standard background for modern mathematics [Burgess]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess]
There is no one relation for the real number 2, as relations differ in different models [Burgess]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
If set theory is used to define 'structure', we can't define set theory structurally [Burgess]
Abstract algebra concerns relations between models, not common features of all the models [Burgess]
How can mathematical relations be either internal, or external, or intrinsic? [Burgess]
9. Objects / C. Structure of Objects / 7. Substratum
Models nicely separate particulars from their clothing, and logicians often accept that metaphysically [Kaplan]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
The simplest solution to transworld identification is to adopt bare particulars [Kaplan]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Unusual people may have no counterparts, or several [Kaplan]
Essence is a transworld heir line, rather than a collection of properties [Kaplan]
19. Language / A. Nature of Meaning / 8. Synonymy
Sentences might have the same sense when logically equivalent - or never have the same sense [Kaplan]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]