Combining Texts

All the ideas for 'Morality, Action, and Outcome', 'Higher-Order Logic' and 'Mathematical Explanation'

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21 ideas

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]
9. Objects / D. Essence of Objects / 3. Individual Essences
13230 Particular essence is often captured by generality [Steiner,M]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
13229 Maybe an instance of a generalisation is more explanatory than the particular case [Steiner,M]
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
13231 Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M]
20. Action / C. Motives for Action / 5. Action Dilemmas / b. Double Effect
22465 We see a moral distinction between doing and allowing to happen [Foot]
22466 We see a moral distinction between our aims and their foreseen consequences [Foot]
22467 Acts and omissions only matter if they concern doing something versus allowing it [Foot]
23. Ethics / B. Contract Ethics / 1. Contractarianism
22470 A good moral system benefits its participants, and so demands reciprocity [Foot]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
22468 Virtues can have aims, but good states of affairs are not among them [Foot]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
22469 Some virtues imply rules, and others concern attachment [Foot]