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Single Idea 10579

[filed under theme 6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics ]

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.

The 33 ideas from Stephen Yablo

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]
18998 Parthood lacks the restriction of kind which most relations have [Yablo]
18999 y is only a proper part of x if there is a z which 'makes up the difference' between them [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]
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]
8858 Philosophers keep finding unexpected objects, like models, worlds, functions, numbers, events, sets, properties [Yablo]
8859 The main modal logics disagree over three key formulae [Yablo]
8862 Platonic objects are really created as existential metaphors [Yablo]
8861 Hardly a word in the language is devoid of metaphorical potential [Yablo]
8864 We quantify over events, worlds, etc. in order to make logical possibilities clearer [Yablo]
8863 We must treat numbers as existing in order to express ourselves about the arrangement of planets [Yablo]
8865 If 'the number of Democrats is on the rise', does that mean that 50 million is on the rise? [Yablo]
10805 A sentence should be recarved to reveal its content or implication relations [Yablo]
19493 Governing possible worlds theory is the fiction that if something is possible, it happens in a world [Yablo]
19494 Fictionalism allows that simulated beliefs may be tracking real facts [Yablo]
14381 A statue is essentially the statue, but its lump is not essentially a statue, so statue isn't lump [Yablo, by Rocca]
19489 For me, fictions are internally true, without a significant internal or external truth-value [Yablo]
19490 Make-believe can help us to reason about facts and scientific procedures [Yablo]
19491 'The clouds are angry' can only mean '...if one were attributing emotions to clouds' [Yablo]
9138 An infinite series of sentences asserting falsehood produces the paradox without self-reference [Yablo, by Sorensen]