Combining Texts

All the ideas for 'Laches', 'Maths as a Science of Patterns' and 'Russell'

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12 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
291 Don't assume that wisdom is the automatic consequence of old age [Plato]
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
6408 Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
6414 Two propositions might seem self-evident, but contradict one another [Grayling]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
293 Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]