Combining Texts

All the ideas for 'Topics', 'Principia Mathematica' and 'Introduction to 'Evidentialism''

expand these ideas     |    start again     |     specify just one area for these texts

62 ideas

1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
12274 Begin examination with basics, and subdivide till you can go no further [Aristotle]
2. Reason / C. Styles of Reason / 1. Dialectic
12260 Dialectic starts from generally accepted opinions [Aristotle]
2. Reason / D. Definition / 1. Definitions
12291 There can't be one definition of two things, or two definitions of the same thing [Aristotle]
12292 Definitions are easily destroyed, since they can contain very many assertions [Aristotle]
2. Reason / D. Definition / 5. Genus and Differentia
12272 We describe the essence of a particular thing by means of its differentiae [Aristotle]
12279 The differentia indicate the qualities, but not the essence [Aristotle]
12283 In definitions the first term to be assigned ought to be the genus [Aristotle]
12289 The genera and the differentiae are part of the essence [Aristotle]
12261 Differentia are generic, and belong with genus [Aristotle]
12263 'Genus' is part of the essence shared among several things [Aristotle]
2. Reason / D. Definition / 6. Definition by Essence
12285 The definition is peculiar to one thing, not common to many [Aristotle]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
9542 The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21720 Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
10044 Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro]
18208 We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead]
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
8204 Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead]
9359 Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
21707 Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
10036 In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel]
5. Theory of Logic / L. Paradox / 2. Aporiai
11261 Puzzles arise when reasoning seems equal on both sides [Aristotle]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
18248 A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
12273 Unit is the starting point of number [Aristotle]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / a. Defining numbers
18152 Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
10025 Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes]
8683 Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend]
10037 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10093 The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman]
8691 The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
10305 In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
8684 Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
8746 To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro]
7. Existence / E. Categories / 3. Proposed Categories
12267 There are ten categories: essence, quantity, quality, relation, place, time, position, state, activity, passivity [Aristotle]
8. Modes of Existence / B. Properties / 1. Nature of Properties
12282 An individual property has to exist (in past, present or future) [Aristotle]
8. Modes of Existence / B. Properties / 3. Types of Properties
12264 An 'accident' is something which may possibly either belong or not belong to a thing [Aristotle]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
12280 Genus gives the essence better than the differentiae do [Aristotle]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
13269 In the case of a house the parts can exist without the whole, so parts are not the whole [Aristotle]
9. Objects / D. Essence of Objects / 3. Individual Essences
12284 Everything that is has one single essence [Aristotle]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
12262 An 'idion' belongs uniquely to a thing, but is not part of its essence [Aristotle]
9. Objects / E. Objects over Time / 11. End of an Object
12290 Destruction is dissolution of essence [Aristotle]
9. Objects / E. Objects over Time / 12. Origin as Essential
12286 If two things are the same, they must have the same source and origin [Aristotle]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
12033 An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM]
9. Objects / F. Identity among Objects / 9. Sameness
12266 'Same' is mainly for names or definitions, but also for propria, and for accidents [Aristotle]
12287 Two identical things have the same accidents, they are the same; if the accidents differ, they're different [Aristotle]
12288 Numerical sameness and generic sameness are not the same [Aristotle]
10. Modality / A. Necessity / 6. Logical Necessity
12259 Reasoning is when some results follow necessarily from certain claims [Aristotle]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
10040 Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / b. Evidentialism
19518 Evidentialism says justifications supervene on the available evidence [Conee/Feldman]
14. Science / C. Induction / 1. Induction
12271 Induction is the progress from particulars to universals [Aristotle]
14. Science / C. Induction / 3. Limits of Induction
12293 We say 'so in cases of this kind', but how do you decide what is 'of this kind'? [Aristotle]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
21725 The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B]
23474 A judgement is a complex entity, of mind and various objects [Russell/Whitehead]
23455 The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead]
23480 The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead]
18275 Only the act of judging completes the meaning of a statement [Russell/Whitehead]
19. Language / D. Propositions / 3. Concrete Propositions
23453 Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
19519 Rational decisions are either taken to be based on evidence, or to be explained causally [Conee/Feldman]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
12277 Friendship is preferable to money, since its excess is preferable [Aristotle]
12276 Justice and self-control are better than courage, because they are always useful [Aristotle]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
12275 We value friendship just for its own sake [Aristotle]
24. Political Theory / A. Basis of a State / 1. A People / a. Human distinctiveness
12281 Man is intrinsically a civilized animal [Aristotle]
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
12265 All water is the same, because of a certain similarity [Aristotle]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
12278 'Being' and 'oneness' are predicated of everything which exists [Aristotle]