Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Michael Hallett and Peter John Olivi

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9 ideas

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 / 5. The Infinite / g. Continuum Hypothesis

17836

The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]

8. Modes of Existence / A. Relations / 1. Nature of Relations

16659

Relations do not add anything to reality, though they are real aspects of the world [Olivi]

9. Objects / C. Structure of Objects / 4. Quantity of an Object

16672

Quantity is the quantified parts of a thing, plus location and coordination [Olivi]

16673

Quantity just adds union and location to the extension of parts [Olivi]

14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction

20653

Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]

27. Natural Reality / G. Biology / 5. Species

16663

Things are limited by the species to certain modes of being [Olivi]