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Ideas for 'Metaphysics', 'Causality and Explanation' and 'Science without Numbers'

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27 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
560 Mathematical precision is only possible in immaterial things [Aristotle]
9076 Mathematics studies the domain of perceptible entities, but its subject-matter is not perceptible [Aristotle]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
10958 Perhaps numbers are substances? [Aristotle]
13273 Pluralities divide into discontinous countables; magnitudes divide into continuous things [Aristotle]
8958 In Field's version of science, space-time points replace real numbers [Field,H, by Szabó]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
12074 The one in number just is the particular [Aristotle]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
17844 The unit is stipulated to be indivisible [Aristotle]
17845 If only rectilinear figures existed, then unity would be the triangle [Aristotle]
17859 Units came about when the unequals were equalised [Aristotle]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17861 Two men do not make one thing, as well as themselves [Aristotle]
646 When we count, are we adding, or naming numbers? [Aristotle]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
18221 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
17843 The idea of 'one' is the foundation of number [Aristotle]
17850 Each many is just ones, and is measured by the one [Aristotle]
17851 Number is plurality measured by unity [Aristotle]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
9793 Mathematics studies abstracted relations, commensurability and proportion [Aristotle]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
8757 The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H]
13738 It is a simple truth that the objects of mathematics have being, of some sort [Aristotle]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
12339 Aristotle removes ontology from mathematics, and replaces the true with the beautiful [Aristotle, by Badiou]
6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism
18212 Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
10261 The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro]
18218 Hilbert explains geometry, by non-numerical facts about space [Field,H]
9623 Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
18215 It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
18216 Abstractions can form useful counterparts to concrete statements [Field,H]
18214 Mathematics is only empirical as regards which theory is useful [Field,H]
18210 Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H]