Combining Texts

All the ideas for 'Infinity: Quest to Think the Unthinkable', 'Metaphysics: an introduction' and 'Capitalism and Community'

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33 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
18859 Metaphysics is a quest for truthmakers [Tallant]
2. Reason / D. Definition / 12. Paraphrase
18861 Maybe number statements can be paraphrased into quantifications plus identities [Tallant]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
18866 Maybe only 'positive' truths need truth-makers [Tallant]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
18860 A truthmaker is the minimal portion of reality that will do the job [Tallant]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
18863 What is the truthmaker for a possible new power? [Tallant]
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]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
18864 The wisdom of Plato and of Socrates are not the same property [Tallant]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
18865 Substance must have two properties: individuation, and property-bearing [Tallant]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
18862 Are propositions all the thoughts and sentences that are possible? [Tallant]
24. Political Theory / D. Ideologies / 11. Capitalism
22252 Capitalism may actually be the best way to foster community [Conway,D]
22253 Capitalism is just the market, with optional limited government, and perhaps democracy [Conway,D]
22256 Capitalism prefers representative democracy, which avoids community decision-making [Conway,D]
22255 Capitalism breaks up extended families, and must then provide welfare for the lonely people [Conway,D]
22257 Capitalism is anti-community, by only valuing individuals, and breaking up families [Conway,D]