Combining Texts

All the ideas for 'fragments/reports', 'Material Constitution' and 'Higher-Order Logic'

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18 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10301 The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588 First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298 Some say that second-order logic is mathematics, not logic [Shapiro]
10299 If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290 Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10294 Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
16065 Constitution is identity (being in the same place), or it isn't (having different possibilities) [Wasserman]
16067 Constitution is not identity, because it is an asymmetric dependence relation [Wasserman]
16069 There are three main objections to seeing constitution as different from identity [Wasserman]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
16068 The weight of a wall is not the weight of its parts, since that would involve double-counting [Wasserman]
9. Objects / F. Identity among Objects / 3. Relative Identity
16074 Relative identity may reject transitivity, but that suggests that it isn't about 'identity' [Wasserman]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]