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All the ideas for 'Two Problems of Epistemology', 'The Art of the Infinite' and 'On Concept and Object'

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16 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
A thought can be split in many ways, so that different parts appear as subject or predicate [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale]
9. Objects / A. Existence of Objects / 3. Objects in Thought
Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett]
14. Science / A. Basis of Science / 6. Falsification
Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
Frege equated the concepts under which an object falls with its properties [Frege, by Dummett]
18. Thought / D. Concepts / 5. Concepts and Language / b. Concepts are linguistic
As I understand it, a concept is the meaning of a grammatical predicate [Frege]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
For all the multiplicity of languages, mankind has a common stock of thoughts [Frege]