Combining Texts

All the ideas for 'fragments/reports', 'Higher-Order Logic' and 'On What Grounds What'

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26 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
13734 Modern Quinean metaphysics is about what exists, but Aristotelian metaphysics asks about grounding [Schaffer,J]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
13751 If you tore the metaphysics out of philosophy, the whole enterprise would collapse [Schaffer,J]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
13743 We should not multiply basic entities, but we can have as many derivative entities as we like [Schaffer,J]
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
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [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]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
13741 If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers' [Schaffer,J]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
13748 Grounding is unanalysable and primitive, and is the basic structuring concept in metaphysics [Schaffer,J]
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
13747 Supervenience is just modal correlation [Schaffer,J]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
13744 The cosmos is the only fundamental entity, from which all else exists by abstraction [Schaffer,J]
7. Existence / E. Categories / 4. Category Realism
13739 Maybe categories are just the different ways that things depend on basic substances [Schaffer,J]
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 / 8. Parts of Objects / c. Wholes from parts
13742 There exist heaps with no integral unity, so we should accept arbitrary composites in the same way [Schaffer,J]
13752 The notion of 'grounding' can explain integrated wholes in a way that mere aggregates can't [Schaffer,J]
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
13749 Belief in impossible worlds may require dialetheism [Schaffer,J]
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
13740 'Moorean certainties' are more credible than any sceptical argument [Schaffer,J]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]