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All the ideas for 'Commentary on 'De Anima'', 'Defeasibility Theory' and 'Philosophy of Mathematics'

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16 ideas

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]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
Indefeasibility does not imply infallibility [Grundmann]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
Can a defeater itself be defeated? [Grundmann]
Simple reliabilism can't cope with defeaters of reliably produced beliefs [Grundmann]
You can 'rebut' previous beliefs, 'undercut' the power of evidence, or 'reason-defeat' the truth [Grundmann]
Defeasibility theory needs to exclude defeaters which are true but misleading [Grundmann]
Knowledge requires that there are no facts which would defeat its justification [Grundmann]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
'Moderate' foundationalism has basic justification which is defeasible [Grundmann]
22. Metaethics / B. Value / 2. Values / e. Death
The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus]