Combining Texts

Ideas for 'The Boundary Stones of Thought', 'Interview with Baggini and Stangroom' and 'On What There Is'

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7 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers

18842

Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals

18834

Infinitesimals do not stand in a determinate order relation to zero [Rumfitt]

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics

18846

Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

1613	Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine]

6. Mathematics / C. Sources of Mathematics / 7. Formalism

1616	Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine]

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism

1615	Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine]

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism

1614	Conceptualism holds that there are universals but they are mind-made [Quine]