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All the ideas for 'Laches', 'Plural Quantification' and 'Philosophy of Mathematics'

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16 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Don't assume that wisdom is the automatic consequence of old age [Plato]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
2. Reason / D. Definition / 12. Paraphrase
'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
A pure logic is wholly general, purely formal, and directly known [Linnebo]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Second-order quantification and plural quantification are different [Linnebo]
Traditionally we eliminate plurals by quantifying over sets [Linnebo]
Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo]
Plural plurals are unnatural and need a first-level ontology [Linnebo]
Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
Ordinary speakers posit objects without concern for ontology [Linnebo]
19. Language / C. Assigning Meanings / 3. Predicates
Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]