Combining Texts

All the ideas for 'fragments/reports', 'Structuralism and the Notion of Dependence' and 'Notes on Logic'

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12 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo]
Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo]
'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo]
'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
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
Structuralism is right about algebra, but wrong about sets [Linnebo]
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
There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo]
7. Existence / D. Theories of Reality / 8. Facts / d. Negative facts
Facts can be both positive and negative [Wittgenstein, by Potter]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo]
19. Language / B. Reference / 1. Reference theories
The Electra: she knows this man, but not that he is her brother [Eucleides, by Diog. Laertius]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
The chief good is unity, sometimes seen as prudence, or God, or intellect [Eucleides]