Combining Texts

All the ideas for 'Reportatio', 'The Philosophy of Mathematics' and 'Draft Statement of Human Obligations'

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20 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]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
Every human yearns for an unattainable transcendent good [Weil]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Where human needs are satisfied we find happiness, friendship and beauty [Weil]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
We cannot equally respect what is unequal, so equal respect needs a shared ground [Weil]
23. Ethics / F. Existentialism / 4. Boredom
Life needs risks to avoid sickly boredom [Weil]
24. Political Theory / B. Nature of a State / 4. Citizenship
We all need to partipate in public tasks, and take some initiative [Weil]
24. Political Theory / D. Ideologies / 3. Conservatism
We need both equality (to attend to human needs) and hierarchy (as a scale of responsibilities) [Weil]
25. Social Practice / A. Freedoms / 3. Free speech
Deliberate public lying should be punished [Weil]
25. Social Practice / A. Freedoms / 6. Political freedom
We have liberty in the space between nature and accepted authority [Weil]
25. Social Practice / C. Rights / 4. Property rights
People need personal and collective property, and a social class lacking property is shameful [Weil]
25. Social Practice / D. Justice / 3. Punishment / d. Reform of offenders
Crime should be punished, to bring the perpetrator freely back to morality [Weil]
28. God / A. Divine Nature / 3. Divine Perfections
God is not wise, but more-than-wise; God is not good, but more-than-good [William of Ockham]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
Attention to a transcendent reality motivates a duty to foster the good of humanity [Weil]
28. God / C. Attitudes to God / 4. God Reflects Humanity
We could never form a concept of God's wisdom if we couldn't abstract it from creatures [William of Ockham]