Combining Texts

All the ideas for 'fragments/reports', 'On the Question of Absolute Undecidability' and 'On Body and Force, Against the Cartesians'

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13 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]
14. Science / D. Explanation / 2. Types of Explanation / h. Explanations by function
To explain a house we must describe its use, as well as its parts [Leibniz]
15. Nature of Minds / C. Capacities of Minds / 10. Conatus/Striving
Active force is not just potential for action, since it involves a real effort or striving [Leibniz]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
God's laws would be meaningless without internal powers for following them [Leibniz]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
All qualities of bodies reduce to forces [Leibniz]
Power is passive force, which is mass, and active force, which is entelechy or form [Leibniz]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]