Combining Texts

All the ideas for 'The Lagoon: how Aristotle invented science', 'Maths as a Science of Patterns' and 'De formis'

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10 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy
21355 The Pre-Socratics are not simple naturalists, because they do not always 'leave the gods out' [Leroi]
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
6302 Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
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]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / c. Primary qualities
16719 The primary qualities are mixed to cause secondary qualities [Burley]