Combining Texts

All the ideas for 'Content Preservation', 'Chemistry' and 'Defending the Axioms'

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19 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]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
Supervenience is simply modally robust property co-variance [Hendry]
13. Knowledge Criteria / C. External Justification / 1. External Justification
Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Nuclear charge (plus laws) explains electron structure and spectrum, but not vice versa [Hendry]
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
Maybe two kinds are the same if there is no change of entropy on isothermal mixing [Hendry]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Maybe the nature of water is macroscopic, and not in the microstructure [Hendry]
The nature of an element must survive chemical change, so it is the nucleus, not the electrons [Hendry]
Maybe water is the smallest part of it that still counts as water (which is H2O molecules) [Hendry]
27. Natural Reality / F. Chemistry / 1. Chemistry
Compounds can differ with the same collection of atoms, so structure matters too [Hendry]
Water continuously changes, with new groupings of molecules [Hendry]
27. Natural Reality / F. Chemistry / 2. Modern Elements
Elements survive chemical change, and are tracked to explain direction and properties [Hendry]
Defining elements by atomic number allowed atoms of an element to have different masses [Hendry]
27. Natural Reality / F. Chemistry / 3. Periodic Table
Generally it is nuclear charge (not nuclear mass) which determines behaviour [Hendry]