Combining Texts

All the ideas for 'Philosophy and Scientific Image of Man', 'Introduction to Zermelo's 1930 paper' and 'Reference and Generality (3rd ed)'

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11 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / c. Philosophy as generalisation
Philosophy aims to understand how things (broadly understood) hang together (broadly understood) [Sellars]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
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
Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
7. Existence / C. Structure of Existence / 2. Reduction
Reduction requires that an object's properties consist of its constituents' properties and relations [Sellars]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
We should abandon absolute identity, confining it to within some category [Geach, by Hawthorne]
9. Objects / F. Identity among Objects / 3. Relative Identity
Denial of absolute identity has drastic implications for logic, semantics and set theory [Wasserman on Geach]
Identity is relative. One must not say things are 'the same', but 'the same A as' [Geach]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
Leibniz's Law is incomplete, since it includes a non-relativized identity predicate [Geach, by Wasserman]