Combining Texts

All the ideas for 'The Sign of Four', 'The Scientific Image' and 'Structuralism and the Notion of Dependence'

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15 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]
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]
10. Modality / A. Necessity / 11. Denial of Necessity
Empiricists deny what is unobservable, and reject objective modality [Fraassen]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
To 'accept' a theory is not to believe it, but to believe it empirically adequate [Fraassen, by Bird]
14. Science / B. Scientific Theories / 2. Aim of Science
To accept a scientific theory, we only need to believe that it is empirically adequate [Fraassen]
14. Science / C. Induction / 1. Induction
If you eliminate the impossible, the truth will remain, even if it is weird [Conan Doyle]
14. Science / D. Explanation / 3. Best Explanation / c. Against best explanation
Why should the true explanation be one of the few we have actually thought of? [Fraassen, by Bird]
14. Science / D. Explanation / 4. Explanation Doubts / a. Explanation as pragmatic
An explanation is just descriptive information answering a particular question [Fraassen, by Salmon]