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All the ideas for 'A Résumé of Metaphysics', 'works' and 'Philosophy of Mathematics'

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13 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
3. Truth / A. Truth Problems / 2. Defining Truth
In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
There is no clear boundary between the logical and the non-logical [Tarski]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall]
Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W]
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 / 3. Axioms for Geometry
Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman]
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]
22. Metaethics / C. The Good / 3. Pleasure / a. Nature of pleasure
Intelligent pleasure is the perception of beauty, order and perfection [Leibniz]
28. God / A. Divine Nature / 3. Divine Perfections
Perfection is simply quantity of reality [Leibniz]
29. Religion / D. Religious Issues / 3. Problem of Evil / b. Human Evil
Evil serves a greater good, and pain is necessary for higher pleasure [Leibniz]