Combining Texts

All the ideas for 'Natural Goodness', 'Higher-Order Logic' and 'Model Theory for Modal Logic I'

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27 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
22496 Wisdom only implies the knowledge achievable in any normal lifetime [Foot]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
9560 S5 provides the correct logic for necessity in the broadly logical sense [Fine,K]
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]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
23694 All criterions of practical rationality derive from goodness of will [Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
23686 Moral reason is not just neutral, because morality is part of the standard of rationality [Foot, by Hacker-Wright]
23693 Practical rationality must weigh both what is morally and what is non-morally required [Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
23687 Moral virtues arise from human nature, as part of what makes us good human beings [Foot, by Hacker-Wright]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
22492 Virtues are as necessary to humans as stings are to bees [Foot]
22493 Sterility is a human defect, but the choice to be childless is not [Foot]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
22491 Moral evaluations are not separate from facts, but concern particular facts about functioning [Foot]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
22497 Deep happiness usually comes from the basic things in life [Foot]
22498 Happiness is enjoying the pursuit and attainment of right ends [Foot]
23. Ethics / A. Egoism / 1. Ethical Egoism
23695 Good actions can never be justified by the good they brings to their agent [Foot]
23. Ethics / B. Contract Ethics / 5. Free Rider
22499 We all know that just pretending to be someone's friend is not the good life [Foot]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
22495 Someone is a good person because of their rational will, not their body or memory [Foot]
23. Ethics / F. Existentialism / 7. Existential Action
22502 Refraining from murder is not made good by authenticity or self-fulfilment [Foot]