Combining Texts

All the ideas for 'The Dappled World', 'Sets, Aggregates and Numbers' and 'fragments/reports'

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8 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau]
Nothing is 'intrinsically' numbered [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]
You can ask all sorts of numerical questions about any one given set [Yourgrau]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle]
14. Science / B. Scientific Theories / 1. Scientific Theory
Theories can never represent accurately, because their components are abstract [Cartwright,N, by Portides]