Combining Philosophers
Ideas for David Fair, E.J. Lowe and Oliver,A/Smiley,T
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10 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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4240
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It might be argued that mathematics does not, or should not, aim at truth [Lowe]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
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14246
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If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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8297
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Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
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8266
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Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe]
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8302
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Fs and Gs are identical in number if they one-to-one correlate with one another [Lowe]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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14247
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Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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8298
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Sets are instances of numbers (rather than 'collections'); numbers explain sets, not vice versa [Lowe]
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8311
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If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2 [Lowe]
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4241
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If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects [Lowe]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
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8310
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Does the existence of numbers matter, in the way space, time and persons do? [Lowe]
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