Combining Texts

All the ideas for 'Internalism Exposed', 'On the Cosmos (lost)' and 'Philosophy of Arithmetic'

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19 ideas

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 / 1. Unifying an Object / a. Intrinsic unification
No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
We can't only believe things if we are currently conscious of their justification - there are too many [Goldman]
Internalism must cover Forgotten Evidence, which is no longer retrievable from memory [Goldman]
Internal justification needs both mental stability and time to compute coherence [Goldman]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
Coherent justification seems to require retrieving all our beliefs simultaneously [Goldman]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Reliability involves truth, and truth is external [Goldman]
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]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
Everything must involve numbers, or it couldn't be thought about or known [Philolaus]
Harmony must pre-exist the cosmos, to bring the dissimilar sources together [Philolaus]
There is no falsehood in harmony and number, only in irrational things [Philolaus]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
Existing things, and hence the Cosmos, are a mixture of the Limited and the Unlimited [Philolaus]
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
Self-created numbers make the universe stable [Philolaus]
27. Natural Reality / E. Cosmology / 1. Cosmology
Philolaus was the first person to say the earth moves in a circle [Philolaus, by Diog. Laertius]