Combining Philosophers

All the ideas for Roderick Firth, Francesco Orsi and B Russell/AN Whitehead

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

41 ideas

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 / 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]
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
18680 To avoid misunderstandings supervenience is often expressed negatively: no A-change without B-change [Orsi]
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]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
6493 We are not conscious of pure liquidity, but of the liquidity of water [Firth]
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]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
18684 Rather than requiring an action, a reason may 'entice' us, or be 'eligible', or 'justify' it [Orsi]
22. Metaethics / B. Value / 1. Nature of Value / a. Nature of value
18666 Value-maker concepts (such as courageous or elegant) simultaneously describe and evaluate [Orsi]
18667 The '-able' concepts (like enviable) say this thing deserves a particular response [Orsi]
18685 Final value is favoured for its own sake, and personal value for someone's sake [Orsi]
18679 Things are only valuable if something makes it valuable, and we can ask for the reason [Orsi]
18682 A complex value is not just the sum of the values of the parts [Orsi]
18683 Trichotomy Thesis: comparable values must be better, worse or the same [Orsi]
18686 The Fitting Attitude view says values are fitting or reasonable, and values are just byproducts [Orsi]
22. Metaethics / B. Value / 1. Nature of Value / c. Objective value
18672 Values from reasons has the 'wrong kind of reason' problem - admiration arising from fear [Orsi]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
18677 A thing may have final value, which is still derived from other values, or from relations [Orsi]
22. Metaethics / B. Value / 2. Values / a. Normativity
18668 Truths about value entail normative truths about actions or attitudes [Orsi]
18670 The Buck-Passing view of normative values says other properties are reasons for the value [Orsi]
18669 Values can be normative in the Fitting Attitude account, where 'good' means fitting favouring [Orsi]