Combining Texts

All the ideas for 'reports', 'Maths as a Science of Patterns' and 'Internalism Exposed'

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14 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
6299 Axioms are often affirmed simply because they produce results which have been accepted [Resnik]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
6304 Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
6300 Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
6303 Sets are positions in patterns [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
6295 There are too many mathematical objects for them all to be mental or physical [Resnik]
6296 Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
6301 Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
6302 Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
10. Modality / A. Necessity / 8. Transcendental Necessity
3016 Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
6871 We can't only believe things if we are currently conscious of their justification - there are too many [Goldman]
6872 Internalism must cover Forgotten Evidence, which is no longer retrievable from memory [Goldman]
6874 Internal justification needs both mental stability and time to compute coherence [Goldman]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
6873 Coherent justification seems to require retrieving all our beliefs simultaneously [Goldman]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
6875 Reliability involves truth, and truth is external [Goldman]