Combining Philosophers

All the ideas for John Buridan, Leopold Kronecker and Michael Hallett

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12 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
1403 A rational donkey would starve to death between two totally identical piles of hay [Buridan, by PG]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17833 The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
17834 Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
17837 Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
12427 All of mathematics is properties of the whole numbers [Kronecker]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
10091 God made the integers, all the rest is the work of man [Kronecker]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17836 The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16678 Without magnitude a thing would retain its parts, but they would have no location [Buridan]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
16793 A thing is (less properly) the same over time if each part is succeeded by another [Buridan]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / b. Primary/secondary
16726 Why can't we deduce secondary qualities from primary ones, if they cause them? [Buridan]
14. Science / A. Basis of Science / 2. Demonstration
16577 Induction is not demonstration, because not all of the instances can be observed [Buridan]
14. Science / C. Induction / 2. Aims of Induction
16576 Science is based on induction, for general truths about fire, rhubarb and magnets [Buridan]