Combining Texts

All the ideas for 'What is so bad about Contradictions?', 'Structuralism and the Notion of Dependence' and 'Preface to Great Instauration (Renewal)'

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13 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Philosophy is like a statue which is worshipped but never advances [Bacon]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen]
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]
12. Knowledge Sources / B. Perception / 1. Perception
The senses deceive, but also show their own errors [Bacon]
14. Science / A. Basis of Science / 3. Experiment
Nature is revealed when we put it under pressure rather than observe it [Bacon]