Combining Texts

All the ideas for 'talk', 'Believing the Axioms I' and 'The Disorder of Things'

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29 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
13011 New axioms are being sought, to determine the size of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13013 The Axiom of Extensionality seems to be analytic [Maddy]
13014 Extensional sets are clearer, simpler, unique and expressive [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13021 The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
13022 Infinite sets are essential for giving an account of the real numbers [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13023 The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13024 Efforts to prove the Axiom of Choice have failed [Maddy]
13025 Modern views say the Choice set exists, even if it can't be constructed [Maddy]
13026 A large array of theorems depend on the Axiom of Choice [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
13019 The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13018 Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
7. Existence / E. Categories / 1. Categories
17377 All descriptive language is classificatory [Dupré]
7. Existence / E. Categories / 2. Categorisation
17376 We should aim for a classification which tells us as much as possible about the object [Dupré]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
17390 Natural kinds don't need essentialism to be explanatory [Dupré]
9. Objects / D. Essence of Objects / 10. Essence as Species
17389 A species might have its essential genetic mechanism replaced by a new one [Dupré]
17388 It seems that species lack essential properties, so they can't be natural kinds [Dupré]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
1556 By nature people are close to one another, but culture drives them apart [Hippias]
14. Science / A. Basis of Science / 4. Prediction
17374 The possibility of prediction rests on determinism [Dupré]
18. Thought / C. Content / 5. Twin Earth
17378 Presumably molecular structure seems important because we never have the Twin Earth experience [Dupré]
26. Natural Theory / B. Natural Kinds / 1. Natural Kinds
17381 Phylogenetics involves history, and cladism rests species on splits in lineage [Dupré]
17385 Kinds don't do anything (including evolve) because they are abstract [Dupré]
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
17375 Natural kinds are decided entirely by the intentions of our classification [Dupré]
17379 Borders between species are much less clear in vegetables than among animals [Dupré]
17384 Even atoms of an element differ, in the energy levels of their electrons [Dupré]
17387 Ecologists favour classifying by niche, even though that can clash with genealogy [Dupré]
17382 Cooks, unlike scientists, distinguish garlic from onions [Dupré]
17380 Wales may count as fish [Dupré]
27. Natural Reality / G. Biology / 5. Species
17383 Species are the lowest-level classification in biology [Dupré]
17386 The theory of evolution is mainly about species [Dupré]