Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'The Concept of Logical Consequence' and 'Essays on Active Powers 4: Liberty of Agents'

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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 / B. Logical Consequence / 1. Logical Consequence
Validity is where either the situation or the interpretation blocks true premises and false conclusion [Etchemendy, by Read]
Etchemendy says fix the situation and vary the interpretation, or fix interpretations with varying situations [Etchemendy, by Read]
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]
16. Persons / F. Free Will / 2. Sources of Free Will
The first motion or effect cannot be produced necessarily, so the First Cause must be a free agent [Reid]
16. Persons / F. Free Will / 3. Constraints on the will
A willed action needs reasonable understanding of what is to be done [Reid]
16. Persons / F. Free Will / 4. For Free Will
We are morally free, because we experience it, we are accountable, and we pursue projects [Reid]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
A motive is merely an idea, like advice, and not a force for action [Reid]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
We all know that mere priority or constant conjunction do not have to imply causation [Reid]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
The principle of the law of nature is that matter is passive, and is acted upon [Reid]