Combining Texts

All the ideas for 'The Intrinsic Quality of Experience', 'The Symposium' and 'works'

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62 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
14179 The finest branch of wisdom is justice and moderation in ordering states and families [Plato]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
15901 Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
13444 Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD]
18098 Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
15505 If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10701 Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter]
10865 The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
13016 The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / b. Combinatorial sets
14199 Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10082 There are infinite sets that are not enumerable [Cantor, by Smith,P]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox
13483 Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / e. Mirimanoff's paradox
8710 The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
15910 Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
15905 Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
9983 Cantor took the ordinal numbers to be primary [Cantor, by Tait]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
17798 Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
9971 Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait]
9892 Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
14136 A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
15906 Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine]
11015 Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
15903 A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine]
18251 Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
15902 Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine]
15908 It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
13464 Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
10112 The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
8733 The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro]
17889 CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner]
13447 Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD]
10883 Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten]
13528 Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS]
9555 Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
18174 Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy]
15893 Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
18173 Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
10232 Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
18176 Pure mathematics is pure set theory [Cantor]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
8631 Cantor says that maths originates only by abstraction from objects [Cantor, by Frege]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
1607 Diotima said the Forms are the objects of desire in philosophical discourse [Plato, by Roochnik]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
174 True opinion without reason is midway between wisdom and ignorance [Plato]
15. Nature of Minds / B. Features of Minds / 5. Qualia / b. Qualia and intentionality
8130 Qualities of experience are just representational aspects of experience ('Representationalism') [Harman, by Burge]
16. Persons / E. Rejecting the Self / 1. Self as Indeterminate
180 We call a person the same throughout life, but all their attributes change [Plato]
181 Only the gods stay unchanged; we replace our losses with similar acquisitions [Plato]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
8715 Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend]
18. Thought / E. Abstraction / 2. Abstracta by Selection
13454 Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
4026 Beauty is harmony with what is divine, and ugliness is lack of such harmony [Plato]
172 Love of ugliness is impossible [Plato]
173 Beauty and goodness are the same [Plato]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
183 Stage two is the realisation that beauty of soul is of more value than beauty of body [Plato]
184 Progress goes from physical beauty, to moral beauty, to the beauty of knowledge, and reaches absolute beauty [Plato]
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
171 Music is a knowledge of love in the realm of harmony and rhythm [Plato]
22. Metaethics / B. Value / 2. Values / g. Love
176 Love follows beauty, wisdom is exceptionally beautiful, so love follows wisdom [Plato]
14177 Love assists men in achieving merit and happiness [Plato]
179 Love is desire for perpetual possession of the good [Plato]
22. Metaethics / C. The Good / 1. Goodness / d. Good as virtue
177 If a person is good they will automatically become happy [Plato]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
14178 Happiness is secure enjoyment of what is good and beautiful [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
170 The only slavery which is not dishonourable is slavery to excellence [Plato]
182 The first step on the right path is the contemplation of physical beauty when young [Plato]
27. Natural Reality / C. Space / 3. Points in Space
10863 Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg]
28. God / A. Divine Nature / 2. Divine Nature
13465 Only God is absolutely infinite [Cantor, by Hart,WD]
28. God / A. Divine Nature / 3. Divine Perfections
175 Gods are not lovers of wisdom, because they are already wise [Plato]