Combining Texts

All the ideas for 'fragments/reports', 'On Second-Order Logic' and 'Number Determiners, Numbers, Arithmetic'

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19 ideas

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 / F. Referring in Logic / 1. Naming / d. Singular terms
10001 An adjective contributes semantically to a noun phrase [Hofweber]
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]
10007 Quantifiers for domains and for inference come apart if there are no entities [Hofweber]
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
10002 '2 + 2 = 4' can be read as either singular or plural [Hofweber]
9998 What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber]
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 / 1. Mathematical Platonism / a. For mathematical platonism
10003 Why is arithmetic hard to learn, but then becomes easy? [Hofweber]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
10008 Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
10005 Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
10000 We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
10006 First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber]
15. Nature of Minds / C. Capacities of Minds / 4. Objectification
10004 Our minds are at their best when reasoning about objects [Hofweber]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]