Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Abstract Objects: a Case Study' and 'Varieties of Ontological Dependence'

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18 ideas

2. Reason / D. Definition / 4. Real Definition
17311 Real definitions don't just single out a thing; they must also explain its essence [Koslicki]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
17312 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 / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
10580 Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
10579 Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
17314 The relata of grounding are propositions or facts, but for dependence it is objects and their features [Koslicki]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
10577 Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo]
10578 We are thought to know concreta a posteriori, and many abstracta a priori [Yablo]
9. Objects / D. Essence of Objects / 2. Types of Essence
17313 Modern views want essences just to individuate things across worlds and times [Koslicki]
9. Objects / D. Essence of Objects / 4. Essence as Definition
17309 For Fine, essences are propositions true because of identity, so they are just real definitions [Koslicki]
17315 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
17317 A good explanation captures the real-world dependence among the phenomena [Koslicki]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
17316 We can abstract to a dependent entity by blocking out features of its bearer [Koslicki]