Combining Texts

Ideas for 'Frege philosophy of mathematics', 'Rationality' and 'works'

expand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

11 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
8717 Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
9896 A prime number is one which is measured by a unit alone [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
18255 Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
9895 A number is a multitude composed of units [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
9852 We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9829 The identity of a number may be fixed by something outside structure - by counting [Dummett]
9828 Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
9876 Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
10113 The grounding of mathematics is 'in the beginning was the sign' [Hilbert]
10115 Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
10116 Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman]