Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Minds, Brains and Science' and 'Seven Quodlibets'

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15 ideas

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]
8. Modes of Existence / A. Relations / 1. Nature of Relations
Relations are expressed either as absolute facts, or by a relational concept [William of Ockham]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
Cut wood doesn't make a new substance, but seems to make separate subjects [William of Ockham]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
Hot water naturally cools down, which is due to the substantial form of the water [William of Ockham]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
If an animal approached from a distance, we might abstract 'animal' from one instance [William of Ockham]
17. Mind and Body / C. Functionalism / 7. Chinese Room
Maybe understanding doesn't need consciousness, despite what Searle seems to think [Searle, by Chalmers]
A program won't contain understanding if it is small enough to imagine [Dennett on Searle]
If bigger and bigger brain parts can't understand, how can a whole brain? [Dennett on Searle]
17. Mind and Body / D. Property Dualism / 6. Mysterianism
There are no secure foundations to prove the separate existence of mind, in reason or experience [William of Ockham]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
To love God means to love whatever God wills to be loved [William of Ockham]