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All the ideas for '04: Gospel of St John', 'Abstract Entities' and 'Philosophy of Mathematics'

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14 ideas

2. Reason / A. Nature of Reason / 2. Logos
In the beginning was the Word, and the Word was with God, and the word was God [John]
3. Truth / A. Truth Problems / 2. Defining Truth
Jesus said he bore witness to the truth. Pilate asked, What is truth? [John]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
In classical semantics singular terms refer, and quantifiers range over domains [Linnebo]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The axioms of group theory are not assertions, but a definition of a structure [Linnebo]
To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo]
7. Existence / A. Nature of Existence / 4. Abstract Existence
Some abstract things have a beginning and end, so may exist in time (though not space) [Swoyer]
7. Existence / D. Theories of Reality / 1. Ontologies
Ontologists seek existence and identity conditions, and modal and epistemic status for a thing [Swoyer]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Can properties exemplify other properties? [Swoyer]
9. Objects / A. Existence of Objects / 5. Simples
Quantum field theory suggests that there are, fundamentally, no individual things [Swoyer]