Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Nonexistent Objects' and 'Reply to Fifth Objections'

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12 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]
9. Objects / A. Existence of Objects / 4. Impossible objects
18948 There is an object for every set of properties (some of which exist, and others don't) [Parsons,T, by Sawyer]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
3626 Knowing the attributes is enough to reveal a substance [Descartes]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge
3630 Our thinking about external things doesn't disprove the existence of innate ideas [Descartes]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
3631 A blind man may still contain the idea of colour [Descartes]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
3640 Possible existence is a perfection in the idea of a triangle [Descartes]
3639 Necessary existence is a property which is uniquely part of God's essence [Descartes]