Combining Texts

All the ideas for 'Epistemological Disjunctivism', 'Languages of Art (2nd edn)' and 'Higher-Order Logic'

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29 ideas

2. Reason / E. Argument / 1. Argument
19504 My modus ponens might be your modus tollens [Pritchard,D]
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]
10. Modality / B. Possibility / 9. Counterfactuals
19503 An improbable lottery win can occur in a nearby possible world [Pritchard,D]
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
19505 Moore begs the question, or just offers another view, or uses 'know' wrongly [Pritchard,D, by PG]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
19499 We can have evidence for seeing a zebra, but no evidence for what is entailed by that [Pritchard,D]
19500 Favouring: an entailment will give better support for the first belief than reason to deny the second [Pritchard,D]
19502 Maybe knowledge just needs relevant discriminations among contrasting cases [Pritchard,D]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
19498 Epistemic internalism usually says justification must be accessible by reflection [Pritchard,D]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
19506 Externalism is better than internalism in dealing with radical scepticism [Pritchard,D]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / c. Disjunctivism
19496 Disjunctivism says perceptual justification must be both factual and known by the agent [Pritchard,D]
19497 Metaphysical disjunctivism says normal perceptions and hallucinations are different experiences [Pritchard,D]
13. Knowledge Criteria / C. External Justification / 10. Anti External Justification
19495 Epistemic externalism struggles to capture the idea of epistemic responsibility [Pritchard,D]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
19501 We assess error against background knowledge, but that is just what radical scepticism challenges [Pritchard,D]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
19507 Radical scepticism is merely raised, and is not a response to worrying evidence [Pritchard,D]
21. Aesthetics / B. Nature of Art / 1. Defining Art
20440 Art is a referential activity, hence indefinable, but it has a set of symptoms [Goodman]
21. Aesthetics / B. Nature of Art / 5. Art as Language
20439 Artistic symbols are judged by the fruitfulness of their classifications [Goodman, by Giovannelli]
21. Aesthetics / B. Nature of Art / 7. Ontology of Art
20438 A performance is only an instance of a work if there is not a single error [Goodman]
21. Aesthetics / C. Artistic Issues / 2. Copies of Art
20437 A copy only becomes an 'instance' of an artwork if there is a system of notation [Goodman]