Combining Philosophers

Ideas for Eurytus, E.J. Lowe and Michal Walicki

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15 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
4240 It might be argued that mathematics does not, or should not, aim at truth [Lowe]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17758 Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki]
17755 Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki]
17756 The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki]
17760 Two infinite ordinals can represent a single infinite cardinal [Walicki]
17757 Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
17762 In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17754 Inductive proof depends on the choice of the ordering [Walicki]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
8297 Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
8266 Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe]
8302 Fs and Gs are identical in number if they one-to-one correlate with one another [Lowe]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
8298 Sets are instances of numbers (rather than 'collections'); numbers explain sets, not vice versa [Lowe]
8311 If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2 [Lowe]
4241 If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects [Lowe]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
8310 Does the existence of numbers matter, in the way space, time and persons do? [Lowe]