Combining Texts

All the ideas for 'Defending the Axioms', 'On Certainty' and 'Lectures on the Philosophy of Right'

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13 ideas

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 / B. Internal Justification / 4. Foundationalism / a. Foundationalism
Foundations need not precede other beliefs [Wittgenstein]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
Total doubt can't even get started [Wittgenstein, by Williams,M]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
If you are not certain of any fact, you cannot be certain of the meaning of your words either [Wittgenstein]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
We are only free, with rights, if we claim our freedom, and there are no natural rights [Hegel, by Houlgate]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
Representatives by region ignores whether they care about the national interest [Hegel, by Pinkard]
25. Social Practice / C. Rights / 1. Basis of Rights
The absolute right is the right to have rights [Hegel]