Combining Texts

All the ideas for 'Ethics: Inventing Right and Wrong', 'Infinity: Quest to Think the Unthinkable' and 'Identity, Ostension, and Hypostasis'

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33 ideas

1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
11103 We aren't stuck with our native conceptual scheme; we can gradually change it [Quine]
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]
7. Existence / B. Change in Existence / 2. Processes
11092 A river is a process, with stages; if we consider it as one thing, we are considering a process [Quine]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
11093 We don't say 'red' is abstract, unlike a river, just because it has discontinuous shape [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
11101 General terms don't commit us ontologically, but singular terms with substitution do [Quine]
7. Existence / E. Categories / 5. Category Anti-Realism
11096 Discourse generally departmentalizes itself to some degree [Quine]
8. Modes of Existence / E. Nominalism / 4. Concept Nominalism
11099 Understanding 'is square' is knowing when to apply it, not knowing some object [Quine]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
11094 'Red' is a single concrete object in space-time; 'red' and 'drop' are parts of a red drop [Quine]
11097 Red is the largest red thing in the universe [Quine]
9. Objects / F. Identity among Objects / 1. Concept of Identity
17595 To unite a sequence of ostensions to make one object, a prior concept of identity is needed [Quine]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
11095 We should just identify any items which are indiscernible within a given discourse [Quine]
18. Thought / D. Concepts / 5. Concepts and Language / b. Concepts are linguistic
11104 Concepts are language [Quine]
18. Thought / E. Abstraction / 1. Abstract Thought
11102 Apply '-ness' or 'class of' to abstract general terms, to get second-level abstract singular terms [Quine]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / f. Ethical non-cognitivism
4761 The 'error theory' of morals says there is no moral knowledge, because there are no moral facts [Mackie, by Engel]