Combining Texts

All the ideas for 'Dissoi Logoi - on Double Arguments', 'Letters' and 'Infinity: Quest to Think the Unthinkable'

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33 ideas

3. Truth / H. Deflationary Truth / 2. Deflationary Truth
1564 True and false statements can use exactly the same words [Anon (Diss)]
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
10860 An ordinal number is defined by the set that comes before it [Clegg]
10861 Beyond infinity cardinals and ordinals can come apart [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]
13. Knowledge Criteria / E. Relativism / 4. Cultural relativism
1561 Anything can be acceptable in some circumstances and unacceptable in others [Anon (Diss)]
1559 Thracians think tattooing adds to a girl's beauty, but elsewhere it is a punishment [Anon (Diss)]
1560 Lydians prostitute their daughters to raise a dowery, but no Greek would marry such a girl [Anon (Diss)]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
1567 How could someone who knows everything fail to act correctly? [Anon (Diss)]
21. Aesthetics / C. Artistic Issues / 1. Artistic Intentions
23903 When we admire a work, we see ourselves as its creator [Weil]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
1563 Every apparent crime can be right in certain circumstances [Anon (Diss), by PG]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
1562 It is right to lie to someone, to get them to take medicine they are reluctant to take [Anon (Diss)]
24. Political Theory / D. Ideologies / 5. Democracy / b. Consultation
1566 The first priority in elections is to vote for people who support democracy [Anon (Diss)]
25. Social Practice / B. Equalities / 1. Grounds of equality
23901 Relationships depend on equality, so unequal treatment kills them [Weil]
25. Social Practice / E. Policies / 5. Education / c. Teaching
1565 We learn language, and we don't know who teaches us it [Anon (Diss)]
29. Religion / B. Monotheistic Religion / 5. Bible
23904 The cruelty of the Old Testament put me off Christianity [Weil]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
23902 I attach little importance to immortality, which is an undecidable fact, and irrelevant to us [Weil]