Combining Texts

All the ideas for 'Laches', 'The Philosophy of Mathematics' and 'Morality, Action, and Outcome'

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15 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Don't assume that wisdom is the automatic consequence of old age [Plato]
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]
20. Action / C. Motives for Action / 5. Action Dilemmas / b. Double Effect
We see a moral distinction between doing and allowing to happen [Foot]
We see a moral distinction between our aims and their foreseen consequences [Foot]
Acts and omissions only matter if they concern doing something versus allowing it [Foot]
23. Ethics / B. Contract Ethics / 1. Contractarianism
A good moral system benefits its participants, and so demands reciprocity [Foot]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Virtues can have aims, but good states of affairs are not among them [Foot]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
Some virtues imply rules, and others concern attachment [Foot]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]