Combining Texts

All the ideas for 'Defending the Axioms', 'works' and 'The Value Problem'

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11 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom has a higher value than understanding, which has a higher value than knowledge [Greco]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
If value is practical, knowledge is no better than true opinion [Greco]
13. Knowledge Criteria / C. External Justification / 10. Anti External Justification
Externalist theories don't explain why knowledge has value [Greco]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
There are two sides to men - the pleasantly social, and the violent and creative [Diderot, by Berlin]