Abstract
Consider a cat on a mat. On the one hand, there seems to be just one cat, but on the other there seem to be many things with as good a claim as anything in the vicinity to being a cat. Hence, the problem of the many. In his ‘Many, but Almost One,’ David Lewis offered two solutions. According to the first, only one of the many is indeed a cat, although it is indeterminate exactly which one. According to the second, the many are all cats, but they are almost identical to each other, and hence they are almost one. For Lewis, the two solutions do not compete with each other but are mutually complementary, as each one can assist the other. This paper has two aims: to give some reasons against the first of these two solutions, but then to defend the second as a self-standing solution from Lewis’s considerations to the contrary.
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Notes
See inter alia (Fine 1975; Keefe 2000). Strictly speaking, sharpenings are of the language as a whole, and not of isolated expressions. How to characterize satisfactorily the notion of admissible that these connections (possibly among others) constitute, though central to a full defense of the view of vagueness as semantic indecision, is not crucial for our present concerns. Notice that ‘is admissible’ is, of course, itself vague: this is arguably part of what accounts, in this framework, for the phenomenon of “higher-order” vagueness. Complications involving this will be set aside here.
For further info about Tama, see http://news.bbc.co.uk/1/hi/sci/tech/652293.stm. As with the usual examples involving ‘is bald,’ ‘is rich,’ etc., this involves idealization regarding which feature is such that the predicates seem tolerant with respect to small changes in it, but not with respect to big ones: number of hairs, amount of money, and here replacement of natural organs by artificial prosthesis. If whole organs seem too big for this—when attending to particularly important ones such as brains, hearts and so on—replace the series by a longer one in which merely tiny bits thereof are replaced.
By contrast with other solutions by disqualification, the present one is “metaphysically austere” in the sense of not positing a further (“vague in itself”) entity, over and above the many candidates, with a better claim to be a cat. Lewis (1993) contains what are—for some, myself included—the main reasons against vagueness in rebus: it is hard to have a correct conception of what a vague entity would be, and the phenomena allegedly motivating the view are neatly accommodated by the alternative views. Regarding the problem of the many, it is not even clear that the view would actually provide a solution. To begin with, it is not clear why being, at least possibly, vague in rebus should be a feature of things like cats at all: hence, adding a vague object to the 1,001 candidates only makes it a paradox of the 1,002 cats. Furthermore, and perhaps even more importantly, it is not clear why there would not be 1,001 vague cat-candidates.
I.e. something that would indeed be a paradigmatic cat, if existing isolated from the other candidates (if being paradigmatic requires being determinately a cat): see the discussion in the next section, particularly footnote 8.
The formulation is slightly altered; the original one runs: “With respect to any kind of ordinary things, if something is a typical member of the kind, then, if there are entities that differ from that thing, in any respects relevant to being a member of the kind, quite minutely, then each of those entities is a member of that kind.” (Unger 1980, p. 447).
Thus the present consideration is crucially different from the apparently similar one offered by McKinnon (2002), when claiming the envisaged sharpenings are rendered inadmissible by violating the maxim of “Non-Arbitrary Differences” (here stated for coins):
- (nad) :
-
For any coin and non-coin, there is a principled difference between them which forms the basis for one’s being a coin and the other’s being a non-coin;
which, he says, “imposes the following penumbral connection on every permissible sharpening: if \(d\) is a coin, then so is \(e\) unless it differs from \(d\) in a principled way” (2002, p. 333)—a principled difference is a relevant difference in the features that are relevant for something being a coin, so that the coin-candidates do not differ in a principled way. (nad) crucially differs from (pmd) in not being restricted to paradigmatic cases. But without the restriction, there is every reason to reject the claim that (nad) is a penumbral truth. Rather, it is an intuitively appealing but ultimately rejectable soritical principle, which is inconsistent with there being (paradigmatic) coins and (paradigmatic) non-coins, which can be connected in a sorites series made up of individuals that do not differ from their adjacent ones in a principled way.
Such an explanation might try to exploit the thought voiced by Lewis himself: “When is something very cat-like, yet not a cat?—When it is just a little less than a whole cat, almost all of a cat with a little left out. Or when it is just a little more than a cat, a cat plus a little something extra. Or when it is both a little more and a little less.” (Lewis 1993, p. 171). For some (admittedly, non-conclusive) misgivings regarding this idea, see below footnote 12.
On standard ways of characterizing what it is for something to satisfy a determinacy-involving matrix, see (McGee 1998). More precisely: none of the ordinary cases of cats we can point to are such—as arguably nothing excludes that there be counterfactual determinate cats in worlds where for each tiny particle it is determinately the case whether it is part of them of not.
Notice that it would not suffice to merely point that, although nothing is such that it is determinately a cat, it can still be true that determinately there are cats in the vicinity of Tibbles. For this by itself seems to fail to capture any difference with (intuitively) borderline cases in the middle of the sorties series. See (Williams 2006).
For Armstrong, however, things may be partially identical in virtue of sharing a “non-mereological constituent,” like two different states of affairs involving the same universal but different (perhaps indeed distinct) particulars. In the present paper, as in Lewis’s, two things are (at least) partially identical iff there is something that is part of both. Partial identity is therefore simply identity of some parts.
Lewis’s second, almost-identity solution is thus an “over-population” solution, in (Weatherson 2004)’s taxonomy, as it rejects the premise that there is at most one cat on the mat. According to Weatherson, however, this is a misattribution, and he quotes Lewis stating that the second solution is of a “kind which concedes that the many are cats, but seeks to deny that the cats are really many” (Lewis 1993, p. 175). But, as we have just seen, Lewis is quite explicit in claiming that, strictly speaking, there are many cats. As to the quote provided by Weatherson, occurring before the discussion of the second solution has started properly, it can be seen as a way of making, non-strictly, the point about non-strict counting to be considered shortly.
As an aside, let me mention that properly elaborated this response may also provide a way of resisting the suggestion that expressions of the sort of ‘is a rock,’ ‘is a cat,’ ‘is a conscious being’ and the like signify maximal properties, in Ted Sider’s (2001, 2003) sense—and its consequence that, contrary to appearances, the properties of being a rock, a cat, or a conscious being turn out to extrinsic, in unexpected ways. (A property F is maximal, in this sense, iff (roughly) large parts of an F are not themselves Fs.) The main consideration Sider provides in favor of the contention seems to involve in effect the counting intuition:
Otherwise in the vicinity of every house there would be a multitude of houses; in the vicinity of every cat there would be a multitude of cats. (Sider 2003, p. 139)
Sider is of course very familiar with mechanisms that could alternatively explain away intuitions about counting—he himself appeals to the independently motivated mechanism of domain restriction in defending universalism from the charge that in most conversations people would not count “weird” mereological sums as things over and above their more natural constituents. This is why, I take it, he aims to offer a further, independent motivation:
Forget about counting; consult your linguistic intuitions about whether House-minus is a house directly. Mine say that it is not. (2001, p. 359)
But this further consideration seems to me to be rather weak: for what it is worth, mine say that it is.
As one referee notices, assuming the proposal about definite description in the previous section, ‘Tibbles is the cat on the mat’ will turn out to be similarly indeterminate (in the relaxed reading), given the “many” solution to the problem of the many. By contrast, the so-called “supervaluationist” solution to the problem of the many can allow that it be true, provided there are penumbral connections appropriately linking ‘Tibbles’ to ‘the cat on the mat.’
References
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Acknowledgments
Earlier versions were presented in seminars at Arché, LOGOS, Institute Jean Nicod, and PERSP Metaphysics, and in conferences in Murcia, Ovronnaz, and Rio de Janeiro. Thanks to the audiences in these occasions, and Elizabeth Barnes, Jiri Benovsky, Eline Busck, Óscar Cabaco, Marta Campdelacreu, Ramiro Caso, Pablo Cobreros, Fabrice Correia, Aurélien Darbellay, Esa Díaz-León, Richard Dietz, José A Díez, Paul Egré, Kit Fine, Manuel García-Carpintero, José Gil-Férez, Mario Gómez-Torrente, Patrick Greenough, Katherine Hawley, Mark Heller, John Horden, Andrea Iacona, Frank Jackson, Carrie Jenkins, Andrew Jorgensen, Philipp Keller, Teresa Marques, Sebastiano Moruzzi, Joan Pagès, Manuel Pérez Otero, Bryan Pickel, Murali Ramachandran, Marco Rufino, Pablo Rychter, Mark Sainsbury, Roy Sorensen, Stephan Torre, Giuliano Torrengo, Raphael van Riel, Achille Varzi, Robbie Williams, Tim Williamson, Crispin Wright, Elia Zardini, Ezequiel Zerbudis, and anonymous referees. Research has been partially funded by 2009SGR-1077 (Generalitat de Catalunya), FFI2008-06153, FFI2012-35026, and CSD2009-0056 (Gobierno de España), and ITN FP7-238128 (European Community).
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López de Sa, D. Lewis vs Lewis on the problem of the many. Synthese 191, 1105–1117 (2014). https://doi.org/10.1007/s11229-013-0314-0
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DOI: https://doi.org/10.1007/s11229-013-0314-0