Combining Texts

All the ideas for 'Symposium', 'On the Question of Absolute Undecidability' and 'Essays on Active Powers 1: Active power'

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17 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 / C. Powers and Dispositions / 2. Powers as Basic
Powers are quite distinct and simple, and so cannot be defined [Reid]
Thinkers say that matter has intrinsic powers, but is also passive and acted upon [Reid]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
It is obvious that there could not be a power without a subject which possesses it [Reid]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / e. Cause of consciousness
Consciousness is the power of mind to know itself, and minds are grounded in powers [Reid]
16. Persons / F. Free Will / 4. For Free Will
Our own nature attributes free determinations to our own will [Reid]
20. Action / B. Preliminaries of Action / 2. Willed Action / c. Agent causation
Reid said that agent causation is a unique type of causation [Reid, by Stout,R]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
Day and night are constantly conjoined, but they don't cause one another [Reid, by Crane]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
Regular events don't imply a cause, without an innate conviction of universal causation [Reid]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Scientists don't know the cause of magnetism, and only discover its regulations [Reid]
Laws are rules for effects, but these need a cause; rules of navigation don't navigate [Reid]