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Full Idea
One strategy is whenever we are presented with a sentence that might appear to entail the existence of numbers, all that we have to do is paraphrase it using a quantified logic, plus identity.
Gist of Idea
Maybe number statements can be paraphrased into quantifications plus identities
Source
Jonathan Tallant (Metaphysics: an introduction [2011], 03.5)
Book Ref
Tallant,Jonathan: 'Metaphysics - an introduction' [Continuum 2011], p.49
A Reaction
This nominalist strategy seems fine for manageable numbers, but gets in trouble with numbers too big to count (e.g. grains of sand in the world) , or genuine infinities.
| 21699 | Russell offered a paraphrase of definite description, to avoid the commitment to objects [Quine] |
| 14227 | We could refer to tables as 'xs that are arranged tablewise' [Inwagen] |
| 8262 | How can a theory of meaning show the ontological commitments of two paraphrases of one idea? [Lowe] |
| 10314 | An expression is a genuine singular term if it resists elimination by paraphrase [Hale] |
| 18491 | The idea of 'making' can be mere conceptual explanation (like 'because') [Künne] |
| 10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
| 18861 | Maybe number statements can be paraphrased into quantifications plus identities [Tallant] |