Combining Texts

All the ideas for 'Defending the Axioms', 'Scientific Thought' and 'The Architecture of Theories'

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15 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]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
A thing is simply a long event, linked by qualities, and spatio-temporal unity [Broad]
If short-lived happenings like car crashes are 'events', why not long-lived events like Dover Cliffs? [Broad]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
Physical and psychical laws of mind are either independent, or derived in one or other direction [Peirce]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
The world is full of variety, but laws seem to produce uniformity [Peirce]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
The present and past exist, but the future does not [Broad, by Dummett]
We could say present and past exist, but not future, so that each event adds to the total history [Broad]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
We imagine the present as a spotlight, moving across events from past to future [Broad]
27. Natural Reality / G. Biology / 3. Evolution
Darwinian evolution is chance, with the destruction of bad results [Peirce]