Ideas from 'The Question of Ontology' by Kit Fine [2009], by Theme Structure

[found in 'Metametaphysics' (ed/tr Chalmers/Manley/Wasserman) [OUP 2009,978-0-19-954600-8]].

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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers

12215

The existence of numbers is not a matter of identities, but of constituents of the world

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

12211

It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced'

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

12209

The indispensability argument shows that nature is non-numerical, not the denial of numbers

7. Existence / A. Nature of Existence / 1. Nature of Existence

12214

'Exists' is a predicate, not a quantifier; 'electrons exist' is like 'electrons spin'

7. Existence / A. Nature of Existence / 4. Abstract Existence

12212

Just as we introduced complex numbers, so we introduced sums and temporal parts

7. Existence / A. Nature of Existence / 6. Criterion for Existence

12216

Real objects are those which figure in the facts that constitute reality

12218

Being real and being fundamental are separate; Thales's water might be real and divisible

7. Existence / D. Theories of Reality / 1. Ontologies

12217

For ontology we need, not internal or external views, but a view from outside reality

7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers

12213

Ontological claims are often universal, and not a matter of existential quantification