Combining Texts

All the ideas for 'Universal Prescriptivism', 'On Second-Order Logic' and 'Apriority and Existence'

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24 ideas

4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
8859 The main modal logics disagree over three key formulae [Yablo]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
8865 If 'the number of Democrats is on the rise', does that mean that 50 million is on the rise? [Yablo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10833 Many concepts can only be expressed by second-order logic [Boolos]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
8863 We must treat numbers as existing in order to express ourselves about the arrangement of planets [Yablo]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
8862 Platonic objects are really created as existential metaphors [Yablo]
7. Existence / D. Theories of Reality / 7. Fictionalism
8864 We quantify over events, worlds, etc. in order to make logical possibilities clearer [Yablo]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
8858 Philosophers keep finding unexpected objects, like models, worlds, functions, numbers, events, sets, properties [Yablo]
19. Language / F. Communication / 6. Interpreting Language / d. Metaphor
8861 Hardly a word in the language is devoid of metaphorical potential [Yablo]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
2705 How can intuitionists distinguish universal convictions from local cultural ones? [Hare]
2712 You can't use intuitions to decide which intuitions you should cultivate [Hare]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
2706 Emotivists mistakenly think all disagreements are about facts, and so there are no moral reasons [Hare]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism
2708 An 'ought' statement implies universal application [Hare]
2704 If morality is just a natural or intuitive description, that leads to relativism [Hare]
2703 Descriptivism say ethical meaning is just truth-conditions; prescriptivism adds an evaluation [Hare]
2707 If there can be contradictory prescriptions, then reasoning must be involved [Hare]
2709 Prescriptivism sees 'ought' statements as imperatives which are universalisable [Hare]
2711 Prescriptivism implies a commitment, but descriptivism doesn't [Hare]
23. Ethics / D. Deontological Ethics / 3. Universalisability
2710 Moral judgements must invoke some sort of principle [Hare]