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Full Idea
A mathematical entity exists if and only if it is possible that there be instantiations of that structure. This transforms the question of truthmakers for the existence of mathematical entities into a question of truthmakers for certain possibilities.
Gist of Idea
In mathematics, truthmakers are possible instantiations of structures
Source
David M. Armstrong (Truth and Truthmakers [2004], 09.3)
Book Ref
Armstrong,D.M.: 'Truth and Truthmakers' [CUP 2004], p.117
A Reaction
This modal approach to structuralism [for which he endorses Hellman 1989] opens up a modal approach to other truthmakers, which places dispositions at the centre of physical truthmaking. No sets of Meinongian objects?
Related Idea
Idea 12225 Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright]
| 18384 | One truthmaker will do for a contingent truth and for its contradictory [Armstrong] |
| 18386 | What is the truthmaker for 'it is possible that there could have been nothing'? [Armstrong] |
| 18387 | The truthmakers for possible unicorns are the elements in their combination [Armstrong] |
| 18394 | In mathematics, truthmakers are possible instantiations of structures [Armstrong] |
| 17283 | If the truth-making relation is modal, then modal truths will be grounded in anything [Fine,K] |
| 10749 | Necessary truths seem to all have the same truth-maker [Oliver] |
| 15140 | The converse Barcan formula will not allow contingent truths to have truthmakers [Williamson] |
| 15141 | Truthmaker is incompatible with modal semantics of varying domains [Williamson] |
| 18343 | Maybe a truth-maker also works for the entailments of the given truth [Rami] |
| 18826 | 'True at a possibility' means necessarily true if what is said had obtained [Rumfitt] |