Combining Texts

All the ideas for 'Defending the Axioms', 'Introduction to 'Hippias Minor'' and 'Necessity, Essence and Individuation'

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30 ideas

1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
15169 Metaphysics is clarifying how we speak and think (and possibly improving it) [Sidelle]
2. Reason / E. Argument / 7. Thought Experiments
15164 We seem to base necessities on thought experiments and imagination [Sidelle]
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 / 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 / 10. Constructivism / b. Intuitionism
9548 A mathematical object exists if there is no contradiction in its definition [Waterfield]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / d. Dispositions as occurrent
15180 There doesn't seem to be anything in the actual world that can determine modal facts [Sidelle]
9. Objects / D. Essence of Objects / 2. Types of Essence
15184 Causal reference presupposes essentialism if it refers to modally extended entities [Sidelle]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
15172 Clearly, essential predications express necessary properties [Sidelle]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
15181 Being a deepest explanatory feature is an actual, not a modal property [Sidelle]
9. Objects / D. Essence of Objects / 15. Against Essentialism
15173 That the essence of water is its microstructure is a convention, not a discovery [Sidelle]
9. Objects / F. Identity among Objects / 3. Relative Identity
15185 We aren't clear about 'same stuff as this', so a principle of individuation is needed to identify it [Sidelle]
10. Modality / A. Necessity / 4. De re / De dicto modality
15175 Evaluation of de dicto modalities does not depend on the identity of its objects [Sidelle]
10. Modality / C. Sources of Modality / 3. Necessity by Convention
15032 Necessary a posteriori is conventional for necessity and nonmodal for a posteriority [Sidelle, by Sider]
15179 To know empirical necessities, we need empirical facts, plus conventions about which are necessary [Sidelle]
10. Modality / D. Knowledge of Modality / 3. A Posteriori Necessary
15171 The necessary a posteriori is statements either of identity or of essence [Sidelle]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
15167 Empiricism explores necessities and concept-limits by imagining negations of truths [Sidelle]
15177 Contradictoriness limits what is possible and what is imaginable [Sidelle]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
15176 The individuals and kinds involved in modality are also a matter of convention [Sidelle]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
15174 A thing doesn't need transworld identity prior to rigid reference - that could be a convention of the reference [Sidelle]
15183 'Dthat' operates to make a singular term into a rigid term [Sidelle]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
15165 A priori knowledge is entirely of analytic truths [Sidelle]
18. Thought / C. Content / 5. Twin Earth
15168 That water is essentially H2O in some way concerns how we use 'water' [Sidelle]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
15166 Causal reference seems to get directly at the object, thus leaving its nature open [Sidelle]
19. Language / B. Reference / 5. Speaker's Reference
15182 Because some entities overlap, reference must have analytic individuation principles [Sidelle]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
15178 Can anything in science reveal the necessity of what it discovers? [Sidelle]