Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Reflections on Value' and 'Structuralism and the Notion of Dependence'

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21 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
23881 All thought about values is philosophical, and thought about anything else is not philosophy [Weil]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
23885 Philosophy aims to change the soul, not to accumulate knowledge [Weil]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
23886 Systems are not unique to each philosopher. The platonist tradition is old and continuous [Weil]
3. Truth / A. Truth Problems / 1. Truth
23884 Truth is a value of thought [Weil]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
14085 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo]
14084 Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo]
14086 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo]
14087 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
14089 Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
14083 Structuralism is right about algebra, but wrong about sets [Linnebo]
14090 In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
14091 There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
14088 An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo]
22. Metaethics / B. Value / 1. Nature of Value / e. Means and ends
23882 Ends, unlike means, cannot be defined, which is why people tend to pursue means [Weil]
22. Metaethics / B. Value / 2. Values / a. Normativity
23883 Minds essentially and always strive towards value [Weil]