Combining Texts

All the ideas for 'Defending the Axioms', 'Artistic Value and Opportunistic Moralism' and 'Disputed questions about truth'

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13 ideas

3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Truth is the conformity of being to intellect [Aquinas]
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]
7. Existence / A. Nature of Existence / 3. Being / f. Primary being
Being is basic to thought, and all other concepts are additions to being [Aquinas]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
A work can be morally and artistically excellent, despite rejecting moral truth [John,E]
The works we value most are in sympathy with our own moral views [John,E]
We should understand what is morally important in a story, without having to endorse it [John,E]
We value morality in art because that is what we care about - but it is a contingent fact [John,E]