Combining Texts

All the ideas for 'fragments/reports', 'The Philosophy of Mathematics' and 'Atomism'

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18 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
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]
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]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
The social contract sees society as constituted by and for individuals [Taylor,C]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Assigning a right based on a human capacity implies that the capacity should be developed [Taylor,C]
If freedom depends on society and culture, the greatest freedom is in shaping them [Taylor,C]
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
Our reliance on other people close to us does not imply any political obligations [Taylor,C]
25. Social Practice / C. Rights / 1. Basis of Rights
A right is not just a rule, but also asserts certain ideas of moral worth [Taylor,C]
For most people the primacy of rights mainly concerns freedom [Taylor,C]
25. Social Practice / C. Rights / 4. Property rights
Property is not essential for life, but it may be essential for independence [Taylor,C]
25. Social Practice / E. Policies / 3. Welfare provision
If the state is neutral, there won't be sufficient community to support a welfare state [Taylor,C, by Kymlicka]