Combining Philosophers
Ideas for Eucleides, H.L.A. Hart 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
16949
|
Klein summarised geometry as grouped together by transformations [Quine]
|
8994
|
If analytic geometry identifies figures with arithmetical relations, logicism can include geometry [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]
|
9004
|
If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine]
|
1635
|
Mathematics reduces to set theory (which is a bit vague and unobvious), but not to logic proper [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]
|
8467
|
Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit' [Quine, by Orenstein]
|
8466
|
For Quine, intuitionist ontology is inadequate for classical mathematics [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]
|