Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Mind and Body' and 'Infinity: Quest to Think the Unthinkable'

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36 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]
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 / C. Structure of Existence / 2. Reduction
4986 A weaker kind of reductionism than direct translation is the use of 'bridge laws' [Kirk,R]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / c. Parts of consciousness
5001 Maybe we should see intentionality and consciousness as a single problem, not two [Kirk,R]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / a. Nature of intentionality
4993 If a bird captures a worm, we could say its behaviour is 'about' the worm [Kirk,R]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
5000 Behaviourism says intentionality is an external relation; language of thought says it's internal [Kirk,R]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
4982 Dualism implies some brain events with no physical cause, and others with no physical effect [Kirk,R]
17. Mind and Body / B. Behaviourism / 1. Behaviourism
4991 Behaviourism seems a good theory for intentional states, but bad for phenomenal ones [Kirk,R]
4994 Behaviourism offers a good alternative to simplistic unitary accounts of mental relationships [Kirk,R]
17. Mind and Body / B. Behaviourism / 2. Potential Behaviour
4992 In 'holistic' behaviourism we say a mental state is a complex of many dispositions [Kirk,R]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
4990 The inverted spectrum idea is often regarded as an objection to behaviourism [Kirk,R]
17. Mind and Body / E. Mind as Physical / 3. Eliminativism
4984 All meaningful psychological statements can be translated into physics [Kirk,R]
17. Mind and Body / E. Mind as Physical / 4. Connectionism
4998 Instead of representation by sentences, it can be by a distribution of connectionist strengths [Kirk,R]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
4985 If mental states are multiply realisable, they could not be translated into physical terms [Kirk,R]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
4997 It seems unlikely that most concepts are innate, if a theory must be understood to grasp them [Kirk,R]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
4999 For behaviourists language is just a special kind of behaviour [Kirk,R]
19. Language / B. Reference / 1. Reference theories
4995 Behaviourists doubt whether reference is a single type of relation [Kirk,R]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]