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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Structure and Nature' and 'On Denoting'

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66 ideas

1. Philosophy / C. History of Philosophy / 5. Modern Philosophy / b. Modern philosophy beginnings
Russell started a whole movement in philosophy by providing an analysis of descriptions [Read on Russell]
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Russell's theories aim to preserve excluded middle (saying all sentences are T or F) [Sawyer on Russell]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
'Elizabeth = Queen of England' is really a predication, not an identity-statement [Russell, by Lycan]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
The idea of a variable is fundamental [Russell]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
Names don't have a sense, but are disguised definite descriptions [Russell, by Sawyer]
Russell says names are not denotations, but definite descriptions in disguise [Russell, by Kripke]
Russell says a name contributes a complex of properties, rather than an object [Russell, by Sawyer]
Are names descriptions, if the description is unknown, false, not special, or contains names? [McCullogh on Russell]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
Logically proper names introduce objects; definite descriptions introduce quantifications [Russell, by Bach]
The meaning of a logically proper name is its referent, but most names are not logically proper [Russell, by Soames]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
Russell rewrote singular term names as predicates [Russell, by Ayer]
"Nobody" is not a singular term, but a quantifier [Russell, by Lycan]
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
Russell implies that all sentences containing empty names are false [Sawyer on Russell]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Critics say definite descriptions can refer, and may not embody both uniqueness and existence claims [Grayling on Russell]
Definite descriptions fail to refer in three situations, so they aren't essentially referring [Russell, by Sainsbury]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
Russell's theory must be wrong if it says all statements about non-existents are false [Read on Russell]
The theory of descriptions eliminates the name of the entity whose existence was presupposed [Russell, by Quine]
Russell's theory explains non-existents, negative existentials, identity problems, and substitutivity [Russell, by Lycan]
Russell showed how to define 'the', and thereby reduce the ontology of logic [Russell, by Lackey]
The theory of definite descriptions reduces the definite article 'the' to the concepts of predicate logic [Russell, by Horwich]
Russell implies that 'the baby is crying' is only true if the baby is unique [Grayling on Russell]
Russell explained descriptions with quantifiers, where Frege treated them as names [Russell, by McCullogh]
Russell avoids non-existent objects by denying that definite descriptions are proper names [Russell, by Miller,A]
Denying definite description sentences are subject-predicate in form blocks two big problems [Russell, by Forbes,G]
Russell says apparent referring expressions are really assertions about properties [Russell, by Cooper,DE]
The theory of descriptions lacks conventions for the scope of quantifiers [Lackey on Russell]
Non-count descriptions don't threaten Russell's theory, which is only about singulars [Laycock on Russell]
Denoting is crucial in Russell's account of mathematics, for identifying classes [Russell, by Monk]
Russell's analysis means molecular sentences are ambiguous over the scope of the description [Kaplan on Russell]
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
Existence is entirely expressed by the existential quantifier [Russell, by McGinn]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
I apply structuralism to concrete and abstract objects indiscriminately [Quine]
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
7. Existence / D. Theories of Reality / 6. Physicalism
My ontology is quarks etc., classes of such things, classes of such classes etc. [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
Russell showed that descriptions may not have ontological commitment [Russell, by Linsky,B]
7. Existence / E. Categories / 3. Proposed Categories
The Theory of Description dropped classes and numbers, leaving propositions, individuals and universals [Russell, by Monk]
8. Modes of Existence / B. Properties / 12. Denial of Properties
Russell can't attribute existence to properties [McGinn on Russell]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
9. Objects / A. Existence of Objects / 4. Impossible objects
If the King of France is not bald, and not not-bald, this violates excluded middle [Linsky,B on Russell]
19. Language / B. Reference / 1. Reference theories
Russell argued with great plausibility that we rarely, if ever, refer with our words [Russell, by Cooper,DE]
19. Language / B. Reference / 2. Denoting
Referring is not denoting, and Russell ignores the referential use of definite descriptions [Donnellan on Russell]
Denoting phrases are meaningless, but guarantee meaning for propositions [Russell]
In 'Scott is the author of Waverley', denotation is identical, but meaning is different [Russell]
A definite description 'denotes' an entity if it fits the description uniquely [Russell, by Recanati]
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
By eliminating descriptions from primitive notation, Russell seems to reject 'sense' [Russell, by Kripke]
19. Language / B. Reference / 5. Speaker's Reference
Russell assumes that expressions refer, but actually speakers refer by using expressions [Cooper,DE on Russell]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Russell rejected sense/reference, because it made direct acquaintance with things impossible [Russell, by Recanati]
'Sense' is superfluous (rather than incoherent) [Russell, by Miller,A]
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
The theory of definite descriptions aims at finding correct truth conditions [Russell, by Lycan]
19. Language / D. Propositions / 3. Concrete Propositions
In graspable propositions the constituents are real entities of acquaintance [Russell]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
The ontological argument begins with an unproven claim that 'there exists an x..' [Russell]