Combining Texts

All the ideas for 'The Metaontology of Abstraction', 'Defending the Axioms' and 'Proof that every set can be well-ordered'

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18 ideas

2. Reason / F. Fallacies / 1. Fallacy
12223 It is a fallacy to explain the obscure with the even more obscure [Hale/Wright]
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 / F. Referring in Logic / 1. Naming / d. Singular terms
12230 Singular terms refer if they make certain atomic statements true [Hale/Wright]
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 / e. Countable infinity
15897 Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine]
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
12225 Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
12224 Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
12226 The identity of Pegasus with Pegasus may be true, despite the non-existence [Hale/Wright]
8. Modes of Existence / B. Properties / 3. Types of Properties
12229 Maybe we have abundant properties for semantics, and sparse properties for ontology [Hale/Wright]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
18443 A successful predicate guarantees the existence of a property - the way of being it expresses [Hale/Wright]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
12227 Abstractionism needs existential commitment and uniform truth-conditions [Hale/Wright]
12228 Equivalence abstraction refers to objects otherwise beyond our grasp [Hale/Wright]
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
12231 Reference needs truth as well as sense [Hale/Wright]