Combining Philosophers
Ideas for B Hale / C Wright, Immanuel Kant and Anaxagoras
expand these ideas
|
start again
|
choose
another area for these philosophers
display all the ideas for this combination of philosophers
8 ideas
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
3343
|
Euclid's could be the only viable geometry, if rejection of the parallel line postulate doesn't lead to a contradiction [Benardete,JA on Kant]
|
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
8737
|
Kant suggested that arithmetic has no axioms [Kant, by Shapiro]
|
5557
|
Axioms ought to be synthetic a priori propositions [Kant]
|
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 / 5. Definitions of Number / d. Hume's Principle
8784
|
Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright]
|
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
8787
|
The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright]
|
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10629
|
If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
|
10628
|
The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
|