Combining Texts

All the ideas for 'works', 'Authority and the Individual' and 'Believing the Axioms I'

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31 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
13011 New axioms are being sought, to determine the size of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13014 Extensional sets are clearer, simpler, unique and expressive [Maddy]
13013 The Axiom of Extensionality seems to be analytic [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13021 The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
13022 Infinite sets are essential for giving an account of the real numbers [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13023 The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13024 Efforts to prove the Axiom of Choice have failed [Maddy]
13025 Modern views say the Choice set exists, even if it can't be constructed [Maddy]
13026 A large array of theorems depend on the Axiom of Choice [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
13019 The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13018 Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
7334 Anti-realism needs an intuitionist logic with no law of excluded middle [Dummett, by Miller,A]
7. Existence / D. Theories of Reality / 4. Anti-realism
3303 For anti-realists there are no natural distinctions between objects [Dummett, by Benardete,JA]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
23154 We divide mankind into friend and foe, and cooperate with one and compete with the other [Russell]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
23153 Gradually loyalty to a creed increased, which could even outweigh nationality [Russell]
23152 Increasingly war expands communities, and unifies them through fear [Russell]
23155 In early societies the leaders needed cohesion, but the rest just had to obey [Russell]
24. Political Theory / A. Basis of a State / 2. Population / b. State population
23156 The economic and political advantages of great size seem to have no upper limit [Russell]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
23157 Government has a negative purpose, to prevent trouble, and a positive aim of realising our desires [Russell]
24. Political Theory / C. Ruling a State / 2. Leaders / b. Monarchy
23151 A monarch is known to everyone in the group, and can thus unite large groups [Russell]
24. Political Theory / C. Ruling a State / 4. Changing the State / b. Devolution
23167 Power should be with smaller bodies, as long as it doesn't restrict central powers [Russell]
24. Political Theory / D. Ideologies / 2. Anarchism
23168 A state is essential, to control greedy or predatory impulses [Russell]
23163 In an anarchy universities, research, books, and even seaside holidays, would be impossible [Russell]
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
23166 In democracy we are more aware of being governed than of our tiny share in government [Russell]
24. Political Theory / D. Ideologies / 8. Socialism
23162 Managers are just as remote from workers under nationalisation as under capitalism [Russell]
23165 Socialists say economic justice needs some state control of industries, and of foreign trade [Russell]
23160 Being a slave of society is hardly better than being a slave of a despot [Russell]
25. Social Practice / A. Freedoms / 1. Slavery
23158 Slavery began the divorce between the work and the purposes of the worker [Russell]
25. Social Practice / B. Equalities / 1. Grounds of equality
23161 Slaves can be just as equal as free people [Russell]
25. Social Practice / B. Equalities / 4. Economic equality
23159 Scarce goods may be denied entirely, to avoid their unequal distribution [Russell]
25. Social Practice / D. Justice / 1. Basis of justice
23164 Modern justice is seen as equality, apart from modest extra rewards for exceptional desert [Russell]