Combining Texts

All the ideas for 'Perpetual Peace', 'The Philosophy of Mathematics' and 'Abstraction Reconsidered'

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22 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
9193 ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
9194 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
9195 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
9186 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
9187 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
9191 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
9192 The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
10735 Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
10732 If concepts are just recognitional, then general judgements would be impossible [Geach]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
10731 For abstractionists, concepts are capacities to recognise recurrent features of the world [Geach]
18. Thought / E. Abstraction / 8. Abstractionism Critique
10733 The abstractionist cannot explain 'some' and 'not' [Geach]
10734 Only a judgement can distinguish 'striking' from 'being struck' [Geach]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
21075 The state of nature always involves the threat of war [Kant]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
20569 Kant made the social contract international and cosmopolitan [Kant, by Oksala]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
21079 The a priori general will of a people shows what is right [Kant]
24. Political Theory / B. Nature of a State / 3. Constitutions
21077 Each nation should, from self-interest, join an international security constitution [Kant]
21078 A constitution must always be improved when necessary [Kant]
25. Social Practice / B. Equalities / 3. Legal equality
21076 Equality is where you cannot impose a legal obligation you yourself wouldn't endure [Kant]
25. Social Practice / C. Rights / 1. Basis of Rights
20570 There is now a growing universal community, and violations of rights are felt everywhere [Kant]
20571 There are political and inter-national rights, but also universal cosmopolitan rights [Kant]
25. Social Practice / E. Policies / 1. War / c. Combatants
21073 Hiring soldiers is to use them as instruments, ignoring their personal rights [Kant]
25. Social Practice / E. Policies / 1. War / e. Peace
21074 Some trust in the enemy is needed during wartime, or peace would be impossible [Kant]