Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Abstract Objects: a Case Study' and 'Counterpart theory and Quant. Modal Logic'

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17 ideas

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 / 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 / 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 / 1. Essences of Objects
11976 Aristotelian essentialism says essences are not relative to specification [Lewis]
10. Modality / A. Necessity / 7. Natural Necessity
11978 Causal necessities hold in all worlds compatible with the laws of nature [Lewis]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
11979 It doesn't take the whole of a possible Humphrey to win the election [Lewis]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
16994 Counterpart theory is bizarre, as no one cares what happens to a mere counterpart [Kripke on Lewis]
11974 Counterparts are not the original thing, but resemble it more than other things do [Lewis]
11975 If the closest resembler to you is in fact quite unlike you, then you have no counterpart [Lewis]
11977 Essential attributes are those shared with all the counterparts [Lewis]