Combining Texts

All the ideas for 'Phenomenalism', 'The Theory of Transfinite Numbers' and 'Sets, Aggregates and Numbers'

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9 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
9616 A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]
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 / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
15896 Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
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 / 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]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
2614 Modern phenomenalism holds that objects are logical constructions out of sense-data [Ayer]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
2615 The concept of sense-data allows us to discuss appearances without worrying about reality [Ayer]