Combining Texts

All the ideas for 'Philosophy of Mathematics', 'On Aristotle's 'Metaphysics'' and 'The Barcan Formula and Metaphysics'

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9 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The Barcan Formulas express how to combine modal operators with classical quantifiers [Simchen]
The Barcan Formulas are orthodox, but clash with the attractive Actualist view [Simchen]
BF implies that if W possibly had a child, then something is possibly W's child [Simchen]
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]
7. Existence / E. Categories / 4. Category Realism
Different genera are delimited by modes of predication, which rest on modes of being [Aquinas]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
Serious Actualism says there are no facts at all about something which doesn't exist [Simchen]