Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Abstraction Reconsidered' and 'Essential vs Accidental Properties'

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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 / 4. Mathematical Empiricism / c. Against mathematical empiricism
10735 Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
10938 The extremes of essentialism are that all properties are essential, or only very trivial ones [Rami]
9. Objects / D. Essence of Objects / 3. Individual Essences
10940 An 'individual essence' is possessed uniquely by a particular object [Rami]
9. Objects / D. Essence of Objects / 5. Essence as Kind
10939 'Sortal essentialism' says being a particular kind is what is essential [Rami]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
10934 Unlosable properties are not the same as essential properties [Rami]
10. Modality / A. Necessity / 3. Types of Necessity
10933 Physical possibility is part of metaphysical possibility which is part of logical possibility [Rami]
10. Modality / B. Possibility / 2. Epistemic possibility
10932 If it is possible 'for all I know' then it is 'epistemically possible' [Rami]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
10732 If concepts are just recognitional, then general judgements would be impossible [Geach]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
10731 For abstractionists, concepts are capacities to recognise recurrent features of the world [Geach]
18. Thought / E. Abstraction / 8. Abstractionism Critique
10733 The abstractionist cannot explain 'some' and 'not' [Geach]
10734 Only a judgement can distinguish 'striking' from 'being struck' [Geach]