Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Sets, Aggregates and Numbers' and 'On Simple Theories of a Complex World'

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11 ideas

2. Reason / D. Definition / 2. Aims of Definition
10528 Definitions concern how we should speak, not how things are [Fine,K]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17818 How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau]
17822 Nothing is 'intrinsically' numbered [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
17817 Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10529 If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
10530 Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
17815 We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]
17821 You can ask all sorts of numerical questions about any one given set [Yourgrau]
14. Science / B. Scientific Theories / 1. Scientific Theory
21687 It seems obvious to prefer the simpler of two theories, on grounds of beauty and convenience [Quine]
21688 There are four suspicious reasons why we prefer simpler theories [Quine]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]