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Full Idea
Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass.
Gist of Idea
Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier
Source
Stephen Yablo (Abstract Objects: a Case Study [2002], 08)
Book Ref
-: 'Nous' [-], p.231
A Reaction
See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning.
| 10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
| 10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
| 10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |