Combining Texts

Ideas for 'Abstract Objects: a Case Study', 'Theory of Science (Wissenschaftslehre, 4 vols)' and 'Intro to 'The Reason's Proper Study''

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

display all the ideas for this combination of texts

8 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
9618 Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10624 The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10628 The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
10629 If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
9830 Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
10580 Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
10622 The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
10579 Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]