Combining Texts

All the ideas for 'Defending the Axioms', 'Empty Names' and 'The Confessions'

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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 / F. Referring in Logic / 1. Naming / a. Names
Semantic theory should specify when an act of naming is successful [Sawyer]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
Millians say a name just means its object [Sawyer]
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
Sentences with empty names can be understood, be co-referential, and even be true [Sawyer]
Frege's compositional account of truth-vaues makes 'Pegasus doesn't exist' neither true nor false [Sawyer]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
Definites descriptions don't solve the empty names problem, because the properties may not exist [Sawyer]
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]
24. Political Theory / D. Ideologies / 9. Communism
The nature of people is decided by the government and politics of their society [Rousseau]