Combining Texts

All the ideas for 'Higher-Order Logic', 'Criterion of Validity in Reasoning' and 'Does Conceivability Entail Possibility?'

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18 ideas

2. Reason / A. Nature of Reason / 4. Aims of Reason
14779 I reason in order to avoid disappointment and surprise [Peirce]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
14777 That a judgement is true and that we judge it true are quite different things [Peirce]
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 / 3. Value of Logic
14780 Only study logic if you think your own reasoning is deficient [Peirce]
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]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
14778 Facts are hard unmoved things, unaffected by what people may think of them [Peirce]
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 / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
16473 Modal Rationalism: conceivability gives a priori access to modal truths [Chalmers, by Stalnaker]
19258 Evaluate primary possibility from some world, and secondary possibility from this world [Chalmers, by Vaidya]