Combining Texts

All the ideas for 'Infinity: Quest to Think the Unthinkable', 'Counterparts and Identity' and 'The Raft and the Pyramid'

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31 ideas

2. Reason / A. Nature of Reason / 6. Coherence
8797 The negation of all my beliefs about my current headache would be fully coherent [Sosa]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
18823 To say there could have been people who don't exist, but deny those possible things, rejects Barcan [Stalnaker, by Rumfitt]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10859 A set is 'well-ordered' if every subset has a first element [Clegg]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10857 Set theory made a closer study of infinity possible [Clegg]
10864 Any set can always generate a larger set - its powerset, of subsets [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
10872 Extensionality: Two sets are equal if and only if they have the same elements [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
10875 Pairing: For any two sets there exists a set to which they both belong [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
10876 Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
10878 Infinity: There exists a set of the empty set and the successor of each element [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
10877 Powers: All the subsets of a given set form their own new powerset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10879 Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
10871 Axiom of Existence: there exists at least one set [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10874 Specification: a condition applied to a set will always produce a new set [Clegg]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10880 Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
10861 Beyond infinity cardinals and ordinals can come apart [Clegg]
10860 An ordinal number is defined by the set that comes before it [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10854 Transcendental numbers can't be fitted to finite equations [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / k. Imaginary numbers
10858 By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
10853 Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10866 Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10869 The Continuum Hypothesis is independent of the axioms of set theory [Clegg]
10862 The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
16409 Unlike Lewis, I defend an actualist version of counterpart theory [Stalnaker]
16411 If possible worlds really differ, I can't be in more than one at a time [Stalnaker]
16412 If counterparts exist strictly in one world only, this seems to be extreme invariant essentialism [Stalnaker]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
8794 There are very few really obvious truths, and not much can be proved from them [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / e. Pro-foundations
8796 A single belief can trail two regresses, one terminating and one not [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
8799 If mental states are not propositional, they are logically dumb, and cannot be foundations [Sosa]
8795 Mental states cannot be foundational if they are not immune to error [Sosa]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
8798 Vision causes and justifies beliefs; but to some extent the cause is the justification [Sosa]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
16410 Extensional semantics has individuals and sets; modal semantics has intensions, functions of world to extension [Stalnaker]