Combining Texts

All the ideas for 'fragments/reports', 'The Empirical Stance' and 'Higher-Order Logic'

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19 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
12772 Philosophy is a value- and attitude-driven enterprise [Fraassen]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
12771 Is it likely that a successful, coherent, explanatory ontological hypothesis is true? [Fraassen]
1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
12773 Analytic philosophy has an exceptional arsenal of critical tools [Fraassen]
2. Reason / A. Nature of Reason / 6. Coherence
12770 We may end up with a huge theory of carefully constructed falsehoods [Fraassen]
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]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
1556 By nature people are close to one another, but culture drives them apart [Hippias]
14. Science / D. Explanation / 3. Best Explanation / c. Against best explanation
12769 Inference to best explanation contains all sorts of hidden values [Fraassen]
14. Science / D. Explanation / 4. Explanation Doubts / a. Explanation as pragmatic
12768 We accept many scientific theories without endorsing them as true [Fraassen]