Combining Texts

All the ideas for 'works', 'Equality' and 'Higher-Order Logic'

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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 / D. Assumptions for Logic / 3. Contradiction
10121 Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal]
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]
23. Ethics / D. Deontological Ethics / 3. Universalisability
3282 The general form of moral reasoning is putting yourself in other people's shoes [Nagel]
24. Political Theory / A. Basis of a State / 4. Original Position / c. Difference principle
3278 An egalitarian system must give priority to those with the worst prospects in life [Nagel]
25. Social Practice / B. Equalities / 1. Grounds of equality
3275 Equality was once opposed to aristocracy, but now it opposes public utility and individual rights [Nagel]
3281 The ideal of acceptability to each individual underlies the appeal to equality [Nagel]
3277 In judging disputes, should we use one standard, or those of each individual? [Nagel]
25. Social Practice / B. Equalities / 2. Political equality
3274 Equality can either be defended as good for society, or as good for individual rights [Nagel]
3273 Equality nowadays is seen as political, social, legal and economic [Nagel]
25. Social Practice / C. Rights / 1. Basis of Rights
3276 A morality of rights is very minimal, leaving a lot of human life without restrictions or duties [Nagel]