Combining Philosophers

Ideas for Carneades, Anaxarchus and Willard Quine

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

display all the ideas for this combination of philosophers

21 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
8994 If analytic geometry identifies figures with arithmetical relations, logicism can include geometry [Quine]
16949 Klein summarised geometry as grouped together by transformations [Quine]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17905 Any progression will do nicely for numbers; they can all then be used to measure multiplicity [Quine]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
8997 There are four different possible conventional accounts of geometry [Quine]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
8463 Maths can be reduced to logic and set theory [Quine]
8203 All the arithmetical entities can be reduced to classes of integers, and hence to sets [Quine]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10242 I apply structuralism to concrete and abstract objects indiscriminately [Quine]
6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism
21696 Nominalism rejects both attributes and classes (where extensionalism accepts the classes) [Quine]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17738 Quine blurs the difference between knowledge of arithmetic and of physics [Jenkins on Quine]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
9556 Nearly all of mathematics has to quantify over abstract objects [Quine]
18198 Mathematics is part of science; transfinite mathematics I take as mostly uninterpreted [Quine]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8993 If mathematics follows from definitions, then it is conventional, and part of logic [Quine]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
21557 Russell confused use and mention, and reduced classes to properties, not to language [Quine, by Lackey]
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]
1635 Mathematics reduces to set theory (which is a bit vague and unobvious), but not to logic proper [Quine]
9004 If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [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]
8466 For Quine, intuitionist ontology is inadequate for classical mathematics [Quine, by Orenstein]
8467 Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit' [Quine, by Orenstein]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
1614 Conceptualism holds that there are universals but they are mind-made [Quine]