Combining Texts

Ideas for 'fragments/reports', 'Apriority and Existence' and 'Approaches to Intentionality'

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3 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
If 'the number of Democrats is on the rise', does that mean that 50 million is on the rise? [Yablo]
     Full Idea: If someone says 'the number of Democrats is on the rise', he or she wants to focus on Democrats, not numbers. If the number is 50 million, is 50 million really on the rise?
     From: Stephen Yablo (Apriority and Existence [2000], §14)
     A reaction: This is a very nice warning from Yablo, against easy platonism, or any sort of platonism at all. We routinely say that numbers are 'increasing', but the real meaning needs entangling. Here it refers to people joining a party.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
We must treat numbers as existing in order to express ourselves about the arrangement of planets [Yablo]
     Full Idea: It is only by making as if to countenance numbers that one can give expression in English to a fact having nothing to do with numbers, a fact about stars and planets and how they are numerically proportioned.
     From: Stephen Yablo (Apriority and Existence [2000], §13)
     A reaction: To avoid the phrase 'numerically proportioned', he might have alluded to the 'pattern' of the stars and planets. I'm not sure which -ism this is, but it seems to me a good approach. The application is likely to precede the theory.
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Platonic objects are really created as existential metaphors [Yablo]
     Full Idea: The means by which platonic objects are simulated is existential metaphor. Numbers are conjured up as metaphorical measures of cardinality.
     From: Stephen Yablo (Apriority and Existence [2000], §12)
     A reaction: 'Fictional' might be a better word than 'metaphorical', since the latter usually implies some sort of comparison.