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All the ideas for 'fragments/reports', 'Philosophy of Mathematics' and 'On Denoting'

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80 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]
2. Reason / D. Definition / 2. Aims of Definition
Definitions should be replaceable by primitives, and should not be creative [Brown,JR]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Naïve set theory assumed that there is a set for every condition [Brown,JR]
Nowadays conditions are only defined on existing sets [Brown,JR]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The 'iterative' view says sets start with the empty set and build up [Brown,JR]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
A flock of birds is not a set, because a set cannot go anywhere [Brown,JR]
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]
If a proposition is false, then its negation is true [Brown,JR]
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
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]
Russell's theory must be wrong if it says all statements about non-existents are false [Read on Russell]
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 / K. Features of Logics / 1. Axiomatisation
Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematics is the only place where we are sure we are right [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / n. Pi
π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
Mathematics represents the world through structurally similar models. [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
There is no limit to how many ways something can be proved in mathematics [Brown,JR]
Computers played an essential role in proving the four-colour theorem of maps [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Set theory may represent all of mathematics, without actually being mathematics [Brown,JR]
When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
To see a structure in something, we must already have the idea of the structure [Brown,JR]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
The irrationality of root-2 was achieved by intellect, not experience [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
There is an infinity of mathematical objects, so they can't be physical [Brown,JR]
Numbers are not abstracted from particulars, because each number is a particular [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Empiricists base numbers on objects, Platonists base them on properties [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Does some mathematics depend entirely on notation? [Brown,JR]
For nomalists there are no numbers, only numerals [Brown,JR]
The most brilliant formalist was Hilbert [Brown,JR]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
There are no constructions for many highly desirable results in mathematics [Brown,JR]
Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
David's 'Napoleon' is about something concrete and something abstract [Brown,JR]
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]
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]
18. Thought / E. Abstraction / 1. Abstract Thought
'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR]
The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR]
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]
A definite description 'denotes' an entity if it fits the description uniquely [Russell, by Recanati]
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]
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]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR]
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]