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Single Idea 19002

[filed under theme 6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism ]

Full Idea

If I am a nominalist non-Platonist, I think it is false that 'there are primes over 10', but I want to be able to say it like everyone else. I argue that this because the statement has a part that I do believe, a part that remains interestingly true.

Gist of Idea

A nominalist can assert statements about mathematical objects, as being partly true

Source

Stephen Yablo (Aboutness [2014], 05.8)

Book Ref

Yablo,Stephen: 'Aboutness' [Princeton 2014], p.90

A Reaction

This is obviously a key motivation for Yablo's book, as it reinforces his fictional view of abstract objects, but aims to capture the phenomena, by investigating what such sentences are 'about'. Admirable.

The 14 ideas from 'Aboutness'

18993 If sentences point to different evidence, they must have different subject-matter [Yablo]
18992 Sentence-meaning is the truth-conditions - plus factors responsible for them [Yablo]
18994 The content of an assertion can be quite different from compositional content [Yablo]
18996 A statement S is 'partly true' if it has some wholly true parts [Yablo]
18997 Truth-conditions as subject-matter has problems of relevance, short cut, and reversal [Yablo]
18999 y is only a proper part of x if there is a z which 'makes up the difference' between them [Yablo]
18998 Parthood lacks the restriction of kind which most relations have [Yablo]
19001 'Pegasus doesn't exist' is false without Pegasus, yet the absence of Pegasus is its truthmaker [Yablo]
19002 A nominalist can assert statements about mathematical objects, as being partly true [Yablo]
19003 Most people say nonblack nonravens do confirm 'all ravens are black', but only a tiny bit [Yablo]
19004 Gettier says you don't know if you are confused about how it is true [Yablo]
19005 Not-A is too strong to just erase an improper assertion, because it actually reverses A [Yablo]
19006 An 'enthymeme' is an argument with an indispensable unstated assumption [Yablo]
19007 A theory need not be true to be good; it should just be true about its physical aspects [Yablo]