Combining Texts

All the ideas for 'fragments/reports', 'What Numbers Are' and 'There Are No Abstract Objects'

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7 ideas

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17813

Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17812

Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]

8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta

14596

Call 'nominalism' the denial of numbers, properties, relations and sets [Dorr]

8. Modes of Existence / E. Nominalism / 5. Class Nominalism

14597

Natural Class Nominalism says there are primitive classes of things resembling in one respect [Dorr]

10. Modality / A. Necessity / 11. Denial of Necessity

14598

Abstracta imply non-logical brute necessities, so only nominalists can deny such things [Dorr]

26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature

1748	Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]

27. Natural Reality / G. Biology / 3. Evolution

5989	Archelaus said life began in a primeval slime [Archelaus, by Schofield]