Combining Texts

All the ideas for 'fragments/reports', 'On Second-Order Logic' and 'Varieties of Ontological Dependence'

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16 ideas

2. Reason / D. Definition / 4. Real Definition
Real definitions don't just single out a thing; they must also explain its essence [Koslicki]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
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
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
'∀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
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
Why should compactness be definitive of logic? [Boolos, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
It is more explanatory if you show how a number is constructed from basic entities and relations [Koslicki]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Many concepts can only be expressed by second-order logic [Boolos]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
The relata of grounding are propositions or facts, but for dependence it is objects and their features [Koslicki]
9. Objects / D. Essence of Objects / 2. Types of Essence
Modern views want essences just to individuate things across worlds and times [Koslicki]
9. Objects / D. Essence of Objects / 4. Essence as Definition
For Fine, essences are propositions true because of identity, so they are just real definitions [Koslicki]
We need a less propositional view of essence, and so must distinguish it clearly from real definitions [Koslicki]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
A good explanation captures the real-world dependence among the phenomena [Koslicki]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
We can abstract to a dependent entity by blocking out features of its bearer [Koslicki]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
A virtue is a combination of intelligence, strength and luck [Ion]