Combining Texts

All the ideas for 'Maths as a Science of Patterns', 'Against the Logicians (two books)' and 'fragments/reports'

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18 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
22764 Ordinary speech is not exact about what is true; we say we are digging a well before the well exists [Sext.Empiricus]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
12268 Contradiction is impossible [Antisthenes (I), by Aristotle]
2. Reason / D. Definition / 13. Against Definition
602 Some fools think you cannot define anything, but only say what it is like [Antisthenes (I), by Aristotle]
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]
9. Objects / D. Essence of Objects / 9. Essence and Properties
22762 Some properties are inseparable from a thing, such as the length, breadth and depth of a body [Sext.Empiricus]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
22759 Fools, infants and madmen may speak truly, but do not know [Sext.Empiricus]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
22760 Madmen are reliable reporters of what appears to them [Sext.Empiricus]
18. Thought / D. Concepts / 2. Origin of Concepts / b. Empirical concepts
22763 We can only dream of a winged man if we have experienced men and some winged thing [Sext.Empiricus]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
1664 I would rather go mad than experience pleasure [Antisthenes (I)]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
21385 Antisthenes said virtue is teachable and permanent, is life's goal, and is like universal wealth [Antisthenes (I), by Long]
28. God / C. Attitudes to God / 2. Pantheism
2631 Antisthenes says there is only one god, which is nature [Antisthenes (I), by Cicero]