Combining Texts

All the ideas for 'Propositional Objects', 'Philosophy of Arithmetic' and 'On Platonism in Mathematics'

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14 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Very few things in set theory remain valid in intuitionist mathematics [Bernays]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Multiplicity in general is just one and one and one, etc. [Husserl]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Restricted Platonism is just an ideal projection of a domain of thought [Bernays]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Mathematical abstraction just goes in a different direction from logic [Bernays]
11. Knowledge Aims / A. Knowledge / 4. Belief / e. Belief holism
How do you distinguish three beliefs from four beliefs or two beliefs? [Quine]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Husserl identifies a positive mental act of unification, and a negative mental act for differences [Husserl, by Frege]
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
We clarify concepts (e.g. numbers) by determining their psychological origin [Husserl, by Velarde-Mayol]
18. Thought / E. Abstraction / 8. Abstractionism Critique
Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl]
Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
A 'proposition' is said to be the timeless cognitive part of the meaning of a sentence [Quine]
19. Language / D. Propositions / 6. Propositions Critique
The problem with propositions is their individuation. When do two sentences express one proposition? [Quine]
27. Natural Reality / C. Space / 3. Points in Space
The concept of a 'point' makes no sense without the idea of absolute position [Quine]