Combining Texts

All the ideas for 'Science and Method', 'A Powers Theory of Modality' and 'Principia Mathematica'

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40 ideas

3. Truth / B. Truthmakers / 11. Truthmaking and Correspondence
12463 Unlike correspondence, truthmaking can be one truth to many truthmakers, or vice versa [Jacobs]
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]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
10245 One geometry cannot be more true than another [Poincaré]
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 / 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]
8. Modes of Existence / A. Relations / 3. Structural Relations
14375 If structures result from intrinsic natures of properties, the 'relations' between them can drop out [Jacobs]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
14378 Science aims at identifying the structure and nature of the powers that exist [Jacobs]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
12467 Powers come from concrete particulars, not from the laws of nature [Jacobs]
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]
10. Modality / A. Necessity / 10. Impossibility
14377 Possibilities are manifestations of some power, and impossibilies rest on no powers [Jacobs]
10. Modality / B. Possibility / 1. Possibility
14376 States of affairs are only possible if some substance could initiate a causal chain to get there [Jacobs]
10. Modality / B. Possibility / 9. Counterfactuals
14379 Counterfactuals invite us to consider the powers picked out by the antecedent [Jacobs]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
14372 Possible worlds are just not suitable truthmakers for modality [Jacobs]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
12466 All modality is in the properties and relations of the actual world [Jacobs]
10. Modality / C. Sources of Modality / 6. Necessity from Essence
14371 We can base counterfactuals on powers, not possible worlds, and hence define necessity [Jacobs]
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
12465 Concrete worlds, unlike fictions, at least offer evidence of how the actual world could be [Jacobs]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
12464 If some book described a possibe life for you, that isn't what makes such a life possible [Jacobs]
12469 Possible worlds semantics gives little insight into modality [Jacobs]
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]
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]