Abstract
Whereas neo-Fregeans, such as Hale and Wright, as well as other abstractionists, e.g., Linnebo, employ abstraction principles in their views of reference and objecthood—the idea being that abstraction principles ensure that a relevant term objectually refers—some recent developments, e.g., Schiffer’s and Thomasson’s, aim at avoiding them. The aim of this paper is to question the extent to which this is feasible. In the case of Thomasson, this question has to do with the notion of co-application conditions—that is, with “rules that (supposing the term to have been successfully applied) specify under what conditions the term would be applied again to one and the same entity” (Thomasson, 2007, 40). I argue that Thomasson’s characterisation of co-application conditions requires them to be stated via an abstraction principle. If this is correct, then it is not clear why Thomasson’s view has an advantage over its predecessors, which also reveals some further difficulties for the views under consideration.
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Notes
Throughout the paper I focus on the difference that Thomasson herself, as I explain later, calls “the most crucial”. However, this is not to say that there are no differences at all between Thomasson’s view and that of the neo-Fregeans. Here I forego any discussion of such further differences, but see, e.g., Eklund (2017).
Hale and Wright in particular advocate the idea that an abstraction principle may be seen as an implicit definition—that is, such a definition that fixes the meaning of an expression by imposing a constraint on the use of longer expressions containing it. For this formulation cf. Hale and Wright (2000, 286). A good survey of the neo-Fregean take on how abstraction principles fix reference may be found in Hale and Crispin (2009).
For more on how abstraction principles fix reference, as well as a discussion of the challenges that this idea faces, see Ebert (2016).
Of course, objecthood so understood requires that it is possible to identify expressions as functioning as singular terms independently of the assumption that those expressions purport to refer to objects; presumably, via some syntactic criteria. In what follows, I forego any discussion of such criteria and simply assume that they can be made out. For proponents, see, e.g., Dummett (1973, 54–80), Hale (1995, 1996) and Wright (1983, 10–12 and 53–64).
Whether they also, like abstraction principles, involve an equivalence relation is a further question. While it’s plausible that they do in the case of directions, it isn’t necessarily so in that of fictional characters, to give two examples that I mention below. There is, however, more to be said about that question and I get back to it in sections 4 and 5.
While abstracta are standardly the main focus of abstractionists, this isn’t exhaustive. Thomasson acknowledges that regarding Hale (142, fn. 14). See also Linnebo (2018) for a broad use of abstraction that includes all sorts of concreta.
Formally, the one-level criterion of identity says of two objects of some sort S that they are identical just in case they stand in some relation R: \(Sx \wedge Sy \rightarrow (x = y \leftrightarrow R(x,y))\). A standard example is the set-theoretic law of extensionality, which says that two sets are identical just in case they have precisely the same elements: \(Set(x) \wedge Set(y) \rightarrow (x = y \leftrightarrow \forall u (u \in x \leftrightarrow u \in y))\). Since the one-level criterion specifies a condition for two objects to be identical via a relation on those objects themselves, it clearly cannot play any role in singling out objects of one sort in terms of another sort. See Linnebo (2018, 35–38) for a further explanation of one- and two-level criteria of identity.
By such terms Thomasson understands “terms we tend to learn early in our cognitive or linguistic development” (2015, 104). Clearly, only concrete terms fall into this description. The examples that Thomasson gives include: ‘dog’, ‘cup’, ‘teddy’ (106).
As being non-spatial is one of abstracta’s most standard characteristics. For a discussion see, e.g., Wringe (2008).
Note that this also applies to fictional names, to which I return later—at least on Thomasson’s conception of fictional characters, by which they are abstract. For, while there are many views on what fictional characters may be, if there are any, they are usually taken to be either non-existent (or non-actual) concrete objects or existent abstract objects. Thomasson’s view (1999) represents the latter; in particular, she takes fictional characters to be abstract artifacts.
The idea goes back to Frege who famously wrote: “If we are to use the symbol a to signify an object, we must have a criterion for deciding in all cases whether b is the same as a, even if it is not always in our power to apply this criterion” (Frege, 1884, §62). I realise that in this paper I don’t present a separate argument for this idea and that this idea is explicitly rejected by both Schiffer (2003, 63, n. 14) and Thomasson (2015, 139–141). My aim is to show the seeming inconsistency that this rejection involves.
In, for example, Linnebo (2018).
Schiffer’s criticism of Thomasson’s transitions can be found in his 2019.
Thomasson refers here to Zalta (2014) who discusses this issue at length.
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Acknowledgements
Thanks to all who gave comments on the paper, at various stages of my work on it, especially to Matti Eklund, Thomas Hodgson and James Levine. Thanks also to two anonymous reviewers.
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Gnatek, Z. Co-application, Identity, and Abstraction: A Note on Amie Thomasson’s Easy Ontology. Erkenn (2024). https://doi.org/10.1007/s10670-023-00768-2
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DOI: https://doi.org/10.1007/s10670-023-00768-2