Combining Texts

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

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16 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 / A. Nature of Existence / 3. Being / d. Non-being
Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius]
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]
19. Language / F. Communication / 1. Rhetoric
Destroy seriousness with laughter, and laughter with seriousness [Gorgias]
Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato]
25. Social Practice / E. Policies / 1. War / a. Just wars
The only just cause for a war is a wrong received [Vitoria]
Leaders can only attack foreigners who have done wrong (as with their own subjects) [Vitoria]
25. Social Practice / E. Policies / 1. War / c. Combatants
Princes should not justify a war to their subjects, and doing so would undermine the state [Vitoria]
25. Social Practice / E. Policies / 1. War / d. Non-combatants
Sacking a city is lawful if it motivates the attacking troops [Vitoria]