Combining Texts

All the ideas for 'fragments/reports', 'On Second-Order Logic' and 'Things and Their Parts'

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16 ideas

4. Formal Logic / G. Formal Mereology / 1. Mereology
13331 Part and whole contribute asymmetrically to one another, so must differ [Fine,K]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10833 Many concepts can only be expressed by second-order logic [Boolos]
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
13332 Hierarchical set membership models objects better than the subset or aggregate relations do [Fine,K]
9. Objects / C. Structure of Objects / 3. Matter of an Object
13333 The matter is a relatively unstructured version of the object, like a set without membership structure [Fine,K]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
13326 A 'temporary' part is a part at one time, but may not be at another, like a carburetor [Fine,K]
13327 A 'timeless' part just is a part, not a part at some time; some atoms are timeless parts of a water molecule [Fine,K]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
13329 An 'aggregative' sum is spread in time, and exists whenever a component exists [Fine,K]
13330 An 'compound' sum is not spread in time, and only exists when all the components exists [Fine,K]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
13328 Two sorts of whole have 'rigid embodiment' (timeless parts) or 'variable embodiment' (temporary parts) [Fine,K]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]