Combining Texts

All the ideas for 'Defending the Axioms', 'Lecture on Applicability of Mathematics' and 'Varieties of Ontological Dependence'

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16 ideas

2. Reason / D. Definition / 4. Real Definition
17311 Real definitions don't just single out a thing; they must also explain its essence [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 / 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 / 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 / 4. Axioms for Number / a. Axioms for numbers
17312 It is more explanatory if you show how a number is constructed from basic entities and relations [Koslicki]
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 / b. Indispensability of mathematics
8732 It is spooky the way mathematics anticipates physics [Weinberg]
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]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
17314 The relata of grounding are propositions or facts, but for dependence it is objects and their features [Koslicki]
9. Objects / D. Essence of Objects / 2. Types of Essence
17313 Modern views want essences just to individuate things across worlds and times [Koslicki]
9. Objects / D. Essence of Objects / 4. Essence as Definition
17309 For Fine, essences are propositions true because of identity, so they are just real definitions [Koslicki]
17315 We need a less propositional view of essence, and so must distinguish it clearly from real definitions [Koslicki]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
17317 A good explanation captures the real-world dependence among the phenomena [Koslicki]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
17316 We can abstract to a dependent entity by blocking out features of its bearer [Koslicki]