Combining Texts

All the ideas for 'fragments/reports', 'Philosophy of Mathematics' and 'Explanation and Reference'

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12 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
Using proper names properly doesn't involve necessary and sufficient conditions [Putnam]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
9. Objects / D. Essence of Objects / 5. Essence as Kind
Putnam bases essences on 'same kind', but same kinds may not share properties [Mackie,P on Putnam]
14. Science / B. Scientific Theories / 2. Aim of Science
Science aims at truth, not at 'simplicity' [Putnam]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
I now think reference by the tests of experts is a special case of being causally connected [Putnam]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
26. Natural Theory / B. Natural Kinds / 5. Reference to Natural Kinds
Natural kind stereotypes are 'strong' (obvious, like tiger) or 'weak' (obscure, like molybdenum) [Putnam]
Express natural kinds as a posteriori predicate connections, not as singular terms [Putnam, by Mackie,P]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]