Combining Texts

All the ideas for 'The Metaontology of Abstraction', 'Zettel' and 'Believing the Axioms I'

expand these ideas     |    start again     |     specify just one area for these texts

24 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
2626 A philosopher is outside any community of ideas [Wittgenstein]
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 / 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]
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 / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
6569 'This sentence is false' sends us in a looping search for its proposition [Wittgenstein, by Fogelin]
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]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
3790 Causes of beliefs are irrelevant to their contents [Wittgenstein]
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]