Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Explanations in reply to Mr Bradley' and 'Reply to Fifth Objections'

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12 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophers should be more inductive, and test results by their conclusions, not their self-evidence [Russell]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
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
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
Arithmetical undecidability is always settled at the next stage up [Koellner]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
Knowing the attributes is enough to reveal a substance [Descartes]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge
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
A blind man may still contain the idea of colour [Descartes]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
Possible existence is a perfection in the idea of a triangle [Descartes]
Necessary existence is a property which is uniquely part of God's essence [Descartes]