Combining Texts

All the ideas for 'Defending the Axioms', 'What Numbers Are' and 'Essence, Necessity and Explanation'

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18 ideas

2. Reason / D. Definition / 4. Real Definition
15118 A successful Aristotelian 'definition' is what sciences produces after an investigation [Koslicki]
2. Reason / D. Definition / 6. Definition by Essence
15116 Essences cause necessary features, and definitions describe those necessary features [Koslicki]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 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
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17813 Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17812 Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 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
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
9. Objects / D. Essence of Objects / 1. Essences of Objects
15110 An essence and what merely follow from it are distinct [Koslicki]
9. Objects / D. Essence of Objects / 3. Individual Essences
15113 Individuals are perceived, but demonstration and definition require universals [Koslicki]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
15112 If an object exists, then its essential properties are necessary [Koslicki]
14. Science / A. Basis of Science / 2. Demonstration
15111 In demonstration, the explanatory order must mirror the causal order of the phenomena [Koslicki]
15115 In a demonstration the middle term explains, by being part of the definition [Koslicki]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
15117 Greek uses the same word for 'cause' and 'explanation' [Koslicki]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
15114 Discovering the Aristotelian essence of thunder will tell us why thunder occurs [Koslicki]