Abstract
Though it is often claimed that some general terms are rigid designators, it has turned out to be difficult to give a satisfying definition that (1) avoids making all general terms rigid (the overgeneralization problem), and (2) even if a non-rigid reading is available, makes that non-rigid reading matter (the trivialization problem). Several authors have attempted to develop examples that meet the trivialization challenge, with Martí and Martínez-Fernández providing what is, perhaps, the most convincing strategy. I show that the type of example Martí and Martínez-Fernández offer nevertheless fails to meet the trivialization challenge and, accordingly, that we should still have serious doubts about whether continuing the search for a non-trivial definition of general term rigidity would be fruitful.
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Notes
The attempts by LaPorte (2000; a similar case is made in LaPorte 2013, p. 102), Salmon (2003) and López de Sa (2006) are extensively discussed and rejected in Martí and Martínez-Fernández (2011, pp. 279–82), and I will not repeat the details of their criticism here. In short, the objection is that LaPorte, Salmon and López de Sa equivocate on (or do not distinguish between) terms used to talk about the abstract universals themselves and when they have a predicative role. I discuss this issue briefly at the beginning of Sect. 2.
Of course, (1) has even more readings than this, depending on whether the denotation of ‘Jack’s car’ can vary across worlds. For ease of exposition I disregard this complication.
They also offer the example ‘the color of the sky is different from the actual color of the sky’ (2011, p. 290). This example runs into the exact same problems so I will not discuss the details.
I use the word ‘extension’ here for clarity. Martí and Martínez-Fernández and others authors might strictly speaking prefer ‘lower-order intension’ or something similar. The terminology should not matter to the point but I think talking about ‘extensions’ makes the distinctions that are crucial for our purposes somewhat easier to see.
It is an interesting question whether similar ambiguities could be generated using other, special modal operators. I predict that if they can, then these ambiguities can be explained by distinguishing between a sentence operator reading and a predicate-modifier reading of the relevant modal operator, too. To be honest, however, I suspect that insofar as (4) has the readings Martí and Martínez-Fernández assume, it is in fact because when reading (4) as a natural language sentence we do not ordinarily interpret ‘actually’ as a modal operator but as a device for emphasis or contrast (see Yalcin 2015; Haraldsen 2015). In that case, ‘actually’ does not make any truth-conditional contribution at all. The two readings of (4) can then be accounted for by the “non-rigid” and “rigid” readings given above, which involve just standard scope ambiguities involving the definite article and the modal operator.
References
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Acknowledgements
I am grateful to Ka Ho Lam and two anonymous referees for helpful comments on earlier versions of this paper.
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The research behind this article was made possible in part through a grant from the SASPRO Mobility Programme of the Slovak Academy of Sciences [Grant Number 0086/01/03/-b].
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Haraldsen, F. Rigidity and triviality. Synthese 195, 1993–1999 (2018). https://doi.org/10.1007/s11229-016-1311-x
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DOI: https://doi.org/10.1007/s11229-016-1311-x