Combining Texts

All the ideas for 'Reply to Fourth Objections', 'The Philosophy of Mathematics' and 'Of the original contract'

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15 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]
17. Mind and Body / E. Mind as Physical / 6. Conceptual Dualism
The concept of mind excludes body, and vice versa [Descartes]
20. Action / C. Motives for Action / 5. Action Dilemmas / a. Dilemmas
Moral questions can only be decided by common opinion [Hume]
24. Political Theory / A. Basis of a State / 3. Natural Values / b. Natural equality
People must have agreed to authority, because they are naturally equal, prior to education [Hume]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
The idea that society rests on consent or promises undermines obedience [Hume]
We no more give 'tacit assent' to the state than a passenger carried on board a ship while asleep [Hume]
The people would be amazed to learn that government arises from their consent [Hume]
25. Social Practice / A. Freedoms / 7. Freedom to leave
Poor people lack the knowledge or wealth to move to a different state [Hume]
25. Social Practice / C. Rights / 4. Property rights
We all know that the history of property is founded on injustices [Hume]