Combining Texts

All the ideas for 'Defending the Axioms', 'A world of truthmakers?' and 'Maxims and Reflections'

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15 ideas

3. Truth / B. Truthmakers / 6. Making Negative Truths
If it were true that nothing at all existed, would that have a truthmaker? [Lewis]
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]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Many people imagine that to experience is to understand [Goethe]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
Man never understands how anthropomorphic he is [Goethe]
16. Persons / C. Self-Awareness / 2. Knowing the Self
We gain self-knowledge through action, not thought - especially when doing our duty [Goethe]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
Beauty is a manifestation of secret natural laws [Goethe]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
The happiest people link the beginning and end of life [Goethe]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
The best form of government teaches us to govern ourselves [Goethe]
25. Social Practice / C. Rights / 1. Basis of Rights
To get duties from people without rights, you must pay them well [Goethe]