Combining Texts

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

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17 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
Reasoning needs arbitrary faith in preliminary hypotheses (Mode 14) [Agrippa, by Diog. Laertius]
All discussion is full of uncertainty and contradiction (Mode 11) [Agrippa, by Diog. Laertius]
Proofs often presuppose the thing to be proved (Mode 15) [Agrippa, by Diog. Laertius]
All reasoning endlessly leads to further reasoning (Mode 12) [Agrippa, by Diog. Laertius]
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]
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]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
Agrippa's Trilemma: justification is infinite, or ends arbitrarily, or is circular [Agrippa, by Williams,M]
13. Knowledge Criteria / E. Relativism / 1. Relativism
Everything is perceived in relation to another thing (Mode 13) [Agrippa, by Diog. Laertius]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Pherecydes said the first principle and element is earth [Pherecydes, by Sext.Empiricus]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero]