Combining Philosophers

Ideas for H.Putnam/P.Oppenheim, George Boolos and Stephen Yablo

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10 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
8865 If 'the number of Democrats is on the rise', does that mean that 50 million is on the rise? [Yablo]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10491 Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
10483 Mathematics and science do not require very high orders of infinity [Boolos]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10833 Many concepts can only be expressed by second-order logic [Boolos]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10490 Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism
19002 A nominalist can assert statements about mathematical objects, as being partly true [Yablo]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
8863 We must treat numbers as existing in order to express ourselves about the arrangement of planets [Yablo]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
10580 Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
8862 Platonic objects are really created as existential metaphors [Yablo]
10579 Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]