Combining Texts

All the ideas for 'Defending the Axioms', 'A Combinatorial Theory of Possibility' and 'Letters to Johann Bernoulli'

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13 ideas

3. Truth / B. Truthmakers / 6. Making Negative Truths
Negative existentials have 'totality facts' as truthmakers [Armstrong, by 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]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
A piece of flint contains something resembling perceptions and appetites [Leibniz]
Entelechies are analogous to souls, as other minds are analogous to our own minds [Leibniz]
10. Modality / B. Possibility / 1. Possibility
All possibilities are recombinations of properties in the actual world [Armstrong, by Lewis]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / c. Possible but inconceivable
What we cannot imagine may still exist [Leibniz]
22. Metaethics / B. Value / 2. Values / e. Death
Death is just the contraction of an animal [Leibniz]