Ideas from 'On Denoting' by Bertrand Russell [1905], by Theme Structure

[found in 'Logic and Knowledge' by Russell,Bertrand (ed/tr Marsh,Robert Charles) [Routledge 1956,0-415-09074-1]].

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5. Theory of Logic / E. Structures of Logic / 1. Logical Form
'Elizabeth = Queen of England' is really a predication, not an identity-statement
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
The idea of a variable is fundamental
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 says names are not denotations, but definite descriptions in disguise
Russell says a name contributes a complex of properties, rather than an object
Are names descriptions, if the description is unknown, false, not special, or contains names?
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
The meaning of a logically proper name is its referent, but most names are not logically proper
Logically proper names introduce objects; definite descriptions introduce quantifications
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
"Nobody" is not a singular term, but a quantifier
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
Definite descriptions fail to refer in three situations, so they aren't essentially referring
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
The theory of descriptions eliminates the name of the entity whose existence was presupposed
Russell's theory explains non-existents, negative existentials, identity problems, and substitutivity
Russell implies that 'the baby is crying' is only true if the baby is unique
Russell explained descriptions with quantifiers, where Frege treated them as names
Russell avoids non-existent objects by denying that definite descriptions are proper names
Non-count descriptions don't threaten Russell's theory, which is only about singulars
Russell's theory must be wrong if it says all statements about non-existents are false
Denoting is crucial in Russell's account of mathematics, for identifying classes
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
Existence is entirely expressed by the existential quantifier
7. Existence / E. Categories / 3. Proposed Categories
The Theory of Description dropped classes and numbers, leaving propositions, individuals and universals
8. Modes of Existence / B. Properties / 12. Denial of Properties
Russell can't attribute existence to properties
19. Language / B. Assigning Meanings / 5. Fregean Semantics
Russell rejected sense/reference, because it made direct acquaintance with things impossible
'Sense' is superfluous (rather than incoherent)
19. Language / B. Assigning Meanings / 6. Truth-Conditions Semantics
The theory of definite descriptions aims at finding correct truth conditions
19. Language / C. Reference / 2. Denoting
Referring is not denoting, and Russell ignores the referential use of definite descriptions
Denoting phrases are meaningless, but guarantee meaning for propositions
In 'Scott is the author of Waverley', denotation is identical, but meaning is different
A definite description 'denotes' an entity if it fits the description uniquely
19. Language / C. Reference / 4. Descriptive Reference / a. Sense and reference
By eliminating descriptions from primitive notation, Russell seems to reject 'sense'
19. Language / C. Reference / 5. Speaker's Reference
Russell assumes that expressions refer, but actually speakers refer by using expressions
28. God / C. Proofs of Reason / 2. Ontological Proof critique
The ontological argument begins with an unproven claim that 'there exists an x..'