Making the Lightness of Being Bearable: Arithmetical Platonism, Fictional Realism and Cognitive Command
- Making the Lightness of Being Bearable: Arithmetical Platonism, Fictional Realism and Cognitive Command
I Introduction
In this paper I wish to defend a minimalist version of arithmetical Platonism — which I shall refer to as ‘minimal Platonism’ — from an objection which alleges that an advocate of this view is committed to an unduly capacious ontology.1 The objection, which I shall call the ‘Lightness of Being’ objection, runs as follows. The minimal Platonist is committed to the claim that arithmetical objects, such as numbers, exist provided that two conditions are met. The first is that terms for numerals are singular terms — where something’s being a singular [End Page 453] term is judged on the basis of purely syntactic criteria.2 The second is that some sentences in which these singular terms feature are non-trivially true.3 However, the names of fictional characters are also singular terms (when judged by the metaphysically lightweight criteria used by advocates of minimal Platonism). Furthermore some sentences which feature in fictional discourse — sentences such as
(B) ‘Holmes lives in Baker Street’
and
(H) ‘Hamlet acts as though he is mad’
may plausibly be judged to be true. So, by parity of reasoning, fictional characters must exist. But this is a reductio ad absurdum: it offends against the ‘robust sense of reality’ which a level-headed Platonist ought to cultivate.
Divers and Miller (1995, 132–6) — to whom the objection is due — have already argued that a number of initially attractive responses to this problem do not stand up to scrutiny. These include reading sentences such as B and H as elliptical versions of
(B*) ‘In the stories by Conan Doyle, Holmes lives in Baker Street’
and
(H*) ‘In Shakespeare’s play, Hamlet acts as though he is mad’4,
denying that sentences about fiction have assertoric content (so that they are not in the market for truth or falsity)5; denying that such sentences have a truth-value; adopting an error-theoretic account of fictional discourse; and arguing that sentences about fiction, though having genuine assertoric content, are not typically the objects of assertion, so that their [End Page 454] general acceptance cannot be construed as a mark of their truth.6 I shall not reproduce their arguments, which I take to be decisive, here.
Instead, I shall argue that, despite initial thoughts to the contrary, the minimal Platonist should embrace the capacious ontology which the objector takes her to be committed to. My defense of this perhaps initially alarming claim will rest on two points. The first is that the minimal Platonist should have no objection to claiming that fictional characters such as Hamlet and Superman are abstract objects. The second is that the minimal Platonist is still in a position to argue that there is a realism-relevant difference between fictional discourse and discourse about arithmetic — and hence a difference in metaphysical status between fictional characters and numbers. The difference is that fictional discourse lacks a feature that Wright (1992 chs. 3 ff) calls ‘Cognitive Command’ whereas it is plausible that discourse about arithmetic possesses it.7
Before going any further, however, I need to say something about the dialectical situation. Divers and Miller’s objection is only an interesting one if there are no conclusive reasons for objecting to the existence of abstract objects as such. If there were, the objection would be otiose. For the purpose of this paper I shall assume that there are not, and that [End Page 455] the dispute between minimal Platonists and nominalists is one that is open.8
This will affect how I present some of the material that follows. For example, I shall not consider strategies for objecting to the existence of fictional characters that take the following schematic form. ‘Fictional characters, if they exist, are abstract objects. But there are no abstract objects. So, fictional characters do not exist.’ Anyone who is in a position to assert the second of these premisses already has sufficient reason to dismiss minimal Platonism — so they do not need the Lightness of Being objection. I do not think anyone is in this position. But that is not the topic of this paper.
