Combining Texts

All the ideas for 'Must We Believe in Set Theory?', 'Perpetual Peace' and 'Reply to Richards'

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21 ideas

1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
22140 The greatest philosophers are methodical; it is what makes them great [Grice]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10482 The logic of ZF is classical first-order predicate logic with identity [Boolos]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10492 A few axioms of set theory 'force themselves on us', but most of them don't [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
10485 Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10484 The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10491 Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
10483 Mathematics and science do not require very high orders of infinity [Boolos]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10490 Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
8. Modes of Existence / D. Universals / 1. Universals
10488 It is lunacy to think we only see ink-marks, and not word-types [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10487 I am a fan of abstract objects, and confident of their existence [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10489 We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
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]