Combining Texts

All the ideas for 'fragments/reports', 'On Second-Order Logic' and 'Properties'

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25 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
4036 What matters is not how many entities we postulate, but how many kinds of entities [Armstrong, by Mellor/Oliver]
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]
8. Modes of Existence / B. Properties / 2. Need for Properties
15754 Without properties we would be unable to express the laws of nature [Armstrong]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
4034 Whether we apply 'cold' or 'hot' to an object is quite separate from its change of temperature [Armstrong]
8535 To the claim that every predicate has a property, start by eliminating failure of application of predicate [Armstrong]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
8537 Tropes fall into classes, because exact similarity is symmetrical and transitive [Armstrong]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
8538 Trope theory needs extra commitments, to symmetry and non-transitivity, unless resemblance is exact [Armstrong]
8. Modes of Existence / D. Universals / 2. Need for Universals
8539 Universals are required to give a satisfactory account of the laws of nature [Armstrong]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
8529 Deniers of properties and relations rely on either predicates or on classes [Armstrong]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
8532 Resemblances must be in certain 'respects', and they seem awfully like properties [Armstrong]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
8530 Change of temperature in objects is quite independent of the predicates 'hot' and 'cold' [Armstrong]
8536 We want to know what constituents of objects are grounds for the application of predicates [Armstrong]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
8531 In most sets there is no property common to all the members [Armstrong]
9. Objects / D. Essence of Objects / 15. Against Essentialism
15753 Essences might support Resemblance Nominalism, but they are too coarse and ill-defined [Armstrong]
19. Language / C. Assigning Meanings / 3. Predicates
8533 Predicates need ontological correlates to ensure that they apply [Armstrong]
4035 There must be some explanation of why certain predicates are applicable to certain objects [Armstrong]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
8540 The introduction of sparse properties avoids the regularity theory's problem with 'grue' [Armstrong]
8541 Regularities theories are poor on causal connections, counterfactuals and probability [Armstrong]