Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Mathematics without Numbers' and 'The Good State'

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16 ideas

2. Reason / D. Definition / 2. Aims of Definition
Definitions concern how we should speak, not how things are [Fine,K]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
Experience, sympathy and history are sensible grounds for laying claim to rights [Grayling]
24. Political Theory / C. Ruling a State / 1. Social Power
Politics is driven by power cliques [Grayling]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
It is essential for democracy that voting is free and well informed [Grayling]
Democracies should require a supermajority for major questions [Grayling]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
A cap on time of service would restrict party control and career ambitions [Grayling]
24. Political Theory / D. Ideologies / 5. Democracy / e. Democratic minorities
Majority decisions are only acceptable if the minority interests are not vital [Grayling]
25. Social Practice / B. Equalities / 1. Grounds of equality
Liberty and equality cannot be reconciled [Grayling]
25. Social Practice / D. Justice / 1. Basis of justice
The very concept of democracy entails a need for justice [Grayling]
25. Social Practice / D. Justice / 2. The Law / a. Legal system
There should be separate legislative, executive and judicial institutions [Grayling]