Combining Texts

All the ideas for 'Defending the Axioms', 'Deflating Existential Consequence' and 'On Sufficient Reason'

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21 ideas

2. Reason / B. Laws of Thought / 1. Laws of Thought
19404 Necessities rest on contradiction, and contingencies on sufficient reason [Leibniz]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
12442 'Mickey Mouse is a fictional mouse' is true without a truthmaker [Azzouni]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
12439 Truth is dispensable, by replacing truth claims with the sentence itself [Azzouni]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
12437 Truth lets us assent to sentences we can't explicitly exhibit [Azzouni]
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 / e. Empty names
12446 Names function the same way, even if there is no object [Azzouni]
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 / 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]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
12447 That all existents have causal powers is unknowable; the claim is simply an epistemic one [Azzouni]
7. Existence / D. Theories of Reality / 7. Fictionalism
12445 If fictional objects really don't exist, then they aren't abstract objects [Azzouni]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
12449 Modern metaphysics often derives ontology from the logical forms of sentences [Azzouni]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
12440 If objectual quantifiers ontologically commit, so does the metalanguage for its semantics [Azzouni]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
12438 In the vernacular there is no unequivocal ontological commitment [Azzouni]
12441 We only get ontology from semantics if we have already smuggled it in [Azzouni]
9. Objects / A. Existence of Objects / 4. Impossible objects
12448 Things that don't exist don't have any properties [Azzouni]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
19403 Each of the infinite possible worlds has its own laws, and the individuals contain those laws [Leibniz]
27. Natural Reality / F. Chemistry / 3. Periodic Table
12450 The periodic table not only defines the elements, but also excludes other possible elements [Azzouni]