Combining Texts

All the ideas for 'First Things First', 'Infinity: Quest to Think the Unthinkable' and 'talk'

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44 ideas

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]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
15105 F(x) walked into a bar. The barman said.. [Sommers,W]
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 / A. Nature of Existence / 3. Being / d. Non-being
12408 Sartre to Waitress: Coffee with no cream, please... [Sommers,W]
7. Existence / D. Theories of Reality / 4. Anti-realism
12397 Said Plato: 'The things that we feel... [Sommers,W]
11. Knowledge Aims / B. Certain Knowledge / 5. Cogito Critique
12407 Barman to Descartes: Would you like another drink?... [Sommers,W]
12399 There was a young student called Fred... [Sommers,W]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
20963 A philosopher and his wife are out for a drive... [Sommers,W]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / c. Empirical idealism
12404 Dear Sir, Your astonishment's odd.... [Sommers,W]
12403 There once was a man who said: 'God... [Sommers,W]
12402 ..But if he's a student of Berkeley... [Sommers,W]
12409 The philosopher Berkeley once said.. [Sommers,W]
12. Knowledge Sources / B. Perception / 1. Perception
14694 "My dog's got synaesthesia." How does he smell? ..... [Sommers,W]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / b. Evidentialism
19520 Evidentialism is not axiomatic; the evidence itself inclines us towards evidentialism [Conee]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
19521 If pure guesses were reliable, reliabilists would have to endorse them [Conee]
19522 More than actual reliability is needed, since I may mistakenly doubt what is reliable [Conee]
19523 Reliabilism is poor on reflective judgements about hypothetical cases [Conee]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
12401 A toper who spies in the distance... [Sommers,W]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
12410 There once was a man who said 'Damn!... [Sommers,W]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
9392 How do behaviourists greet each other? [Sommers,W]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
12405 'If you're aristocratic,' said Nietzsche... [Sommers,W]
24. Political Theory / D. Ideologies / 2. Anarchism
9391 Why do anarchists drink herbal tea? [Sommers,W]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
12400 Cries the maid: 'You must marry me Hume!'... [Sommers,W]
16527 Causation - we all thought we knew it/ Till Hume came along and saw through it/…. [Sommers,W]
27. Natural Reality / D. Time / 1. Nature of Time / c. Idealist time
17592 The barman called 'Time!', and Augustine said..... [Sommers,W]
27. Natural Reality / D. Time / 2. Passage of Time / c. Tenses and time
15208 The past, present and future walked into a bar.... [Sommers,W]