Combining Texts

All the ideas for 'Infinity: Quest to Think the Unthinkable', 'Epistemology: contemporary introduction' and 'Reductive Theories of Modality'

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47 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
9218 Maybe what distinguishes philosophy from science is its pursuit of necessary truths [Sider]
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 / A. Necessity / 7. Natural Necessity
2730 Because 'gold is malleable' is necessary does not mean that it is analytic [Audi,R]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
2715 Beliefs are based on perception, memory, introspection or reason [Audi,R]
11. Knowledge Aims / A. Knowledge / 4. Belief / e. Belief holism
2735 Could you have a single belief on its own? [Audi,R]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
2736 We can make certain of what we know, so knowing does not entail certainty [Audi,R]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
2722 Sense-data theory is indirect realism, but phenomenalism is direct irrealism [Audi,R]
2721 If you gradually remove a book's sensory properties, what is left at the end? [Audi,R]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
2727 Red and green being exclusive colours seems to be rationally graspable but not analytic [Audi,R]
2728 The concepts needed for a priori thought may come from experience [Audi,R]
12. Knowledge Sources / B. Perception / 3. Representation
2716 To see something as a field, I obviously need the concept of a field [Audi,R]
2717 How could I see a field and believe nothing regarding it? [Audi,R]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
2720 Sense-data (and the rival 'adverbial' theory) are to explain illusions and hallucinations [Audi,R]
2719 Sense data imply representative realism, possibly only representing primary qualities [Audi,R]
12. Knowledge Sources / B. Perception / 5. Interpretation
2718 Perception is first simple, then objectual (with concepts) and then propositional [Audi,R]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
2741 The principles of justification have to be a priori [Audi,R]
2729 Virtually all rationalists assert that we can have knowledge of synthetic a priori truths [Audi,R]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
2725 To remember something is to know it [Audi,R]
2724 I might remember someone I can't recall or image, by recognising them on meeting [Audi,R]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
2731 Justification is either unanchored (infinite or circular), or anchored (in knowledge or non-knowledge) [Audi,R]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
2739 Internalism about justification implies that there is a right to believe something [Audi,R]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
2732 Maths may be consistent with observations, but not coherent [Audi,R]
2733 It is very hard to show how much coherence is needed for justification [Audi,R]
2734 A consistent madman could have a very coherent belief system [Audi,R]
13. Knowledge Criteria / C. External Justification / 1. External Justification
2738 Consistent accurate prediction looks like knowledge without justified belief [Audi,R]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
2740 A reliability theory of knowledge seems to involve truth as correspondence [Audi,R]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
2737 'Reliable' is a very imprecise term, and may even mean 'justified' [Audi,R]
16. Persons / C. Self-Awareness / 4. Errors in Introspection
2726 We can be ignorant about ourselves, for example, our desires and motives [Audi,R]