Combining Texts

All the ideas for 'The Logic of Boundaryless Concepts', 'Elusive Knowledge' and 'Philosophy of Arithmetic'

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14 ideas

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic guides thinking, but it isn't a substitute for it [Rumfitt]
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]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
The timid student has knowledge without belief, lacking confidence in their correct answer [Lewis]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
To say S knows P, but cannot eliminate not-P, sounds like a contradiction [Lewis]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
Justification is neither sufficient nor necessary for knowledge [Lewis]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
Knowing is context-sensitive because the domain of quantification varies [Lewis, by Cohen,S]
We have knowledge if alternatives are eliminated, but appropriate alternatives depend on context [Lewis, by Cohen,S]
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]