Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Minds, Brains and Science' and 'The Condemnation of 1277'

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14 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]
10. Modality / B. Possibility / 1. Possibility
In future, only logical limits can be placed on divine omnipotence [Anon (Par), by Boulter]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
It is heresy to require self-evident foundational principles in order to be certain [Anon (Par)]
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]
25. Social Practice / E. Policies / 5. Education / d. Study of history
It is heresy to teach that history repeats every 36,000 years [Anon (Par)]
28. God / A. Divine Nature / 3. Divine Perfections
It is heresy to teach that natural impossibilities cannot even be achieved by God [Anon (Par)]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
It is heresy to teach that we can know God by his essence in this mortal life [Anon (Par)]