Combining Texts

All the ideas for 'Function and Concept', 'works' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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


33 ideas

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
First-level functions have objects as arguments; second-level functions take functions as arguments [Frege]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
Relations are functions with two arguments [Frege]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers are ratios of quantities, such as lengths or masses [Frege]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
My Basic Law V is a law of pure logic [Frege]
Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Frege takes the existence of horses to be part of their concept [Frege, by Sommers]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege]
9. Objects / A. Existence of Objects / 3. Objects in Thought
The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman]
An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale]
A concept is a function whose value is always a truth-value [Frege]
A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
Frege took the study of concepts to be part of logic [Frege, by Shapiro]
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman]
19. Language / B. Reference / 5. Speaker's Reference
I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Armies and businesses create moralities in which their activity can do no wrong [Marx, by Weil]
24. Political Theory / D. Ideologies / 6. Liberalism / d. Liberal freedom
Liberal freedom is the right to be separate, and ignores the union of man with man [Marx]
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
Liberals want the right to be separate, rather than for people to be united [Marx]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Early Marx anticipates communitarian objections to liberalism [Marx, by Oksala]
24. Political Theory / D. Ideologies / 9. Communism
By saying the material dialectic of history aspires to the best, Marx agreed with capitalism [Weil on Marx]
False consciousness results from concealment by the superstructure [Marx, by Singer]
Marx says force is everything, and that the weak will become strong, while remaining the weak [Weil on Marx]
Marx rejected equal rights because they never actually treat people as equals [Marx, by Kymlicka]
24. Political Theory / D. Ideologies / 11. Capitalism
The essence of capitalism is the subordination of people to things [Marx, by Weil]
Capitalism changes the world, by socialising the idea of a commodity [Marx, by Bowie]
Marx thought capitalism was partly liberating, and could make labour and ownership more humane [Marx, by Bowie]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
The Ontological Argument fallaciously treats existence as a first-level concept [Frege]