The sophisticated kind theory

ABSTRACT

Generic sentences are commonsense statements of the form ‘Fs are G,’ like ‘Bears have fur’ or ‘Rattlesnakes are poisonous.’ Kind theories hold that rather than being general statements about individual objects, they are particular statements about kinds. This paper examines the standard objections against the kind theory and argues that they only apply to the most simplified version of the theory. The more sophisticated version, which has received little discussion in the literature in spite of having been formulated concurrently with the simple version, is immune to this standard battery of objections. After discussing four distinctive features of generic sentences, the paper then presents a modernized extension of the sophisticated kind theory which explains the presence of these features. Although the choice between a kind theory and the more standardly accepted adverbial quantificational theory is complex, these considerations suggest that the two approaches are at least deserving of equal consideration for the purposes of natural language semantics.

KEYWORDS:

• Semantics
• generics
• kinds
• quantification
• sortals
• presupposition

Acknowledgements

This project originated out of a conversation with Itamar Francez, who jumpstarted it with astute observations about some interesting linguistic data. Jason Bridges, Chris Kennedy, and Malte Willer deserve special thanks for their integral role in shaping the larger body of research of which this paper forms a part. The two anonymous peer reviewers at Inquiry made deep and interesting suggestions about how to reformulate the main argument of the paper, and these were happily taken up. I am grateful to John Collins for encouraging me to emphasize the data on co-predication. Julian Grove was incredibly helpful when it came to bug checking the final version of the analysis. Finally, the participants in the 2015 Genericity conference at Harvard University, including Alex Anthony, Kristina Gerhman, Michael Glanzberg, Sally Haslanger, Samia Hesni, James Kirkpatrick, Dimitra Lazaridou-Chatzigoga, Joseph Milburn, Paul Nichols, Bernhard Nickel, Jennifer Saul, Rachel Sterken, Preston Stovall, and Ravi Thakral, offered no shortage of useful feedback.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 ‘Fully compositional’ will mean a theory that maps the syntactic structure of a given sentence to its truth conditions, via nothing more than definitions of each individual word in the sentence, and a small number of very general composition rules that specify how the denotation of any syntactic constituent is to be derived from the denotations of its subconstituents. Paradigmatic formulations of this kind of theory can be found in Montague (1973), Gamut (1991), and Heim and Kratzer (1998).

2 They can also take the form ‘The F is G,’ ‘An F is G,’ or even ‘Your F is G.’ Sentences with these surface forms are very close in meaning to sentences of the form under discussion, but they differ in a number of subtle ways which place them beyond the scope of this paper. My focus, therefore, will be on sentences of the form ‘Fs are G.’ Here I take my cue from Carlson (1977a) and Carlson (1977b) which focuses on the bare plural generic as the paradigmatic case, in part because that is the only surface form in English that gives rise to a generic interpretation unambiguously. (‘The dog has four legs,’ for instance, also has an interpretation on which it’s about a specific dog that is under discussion.).

3 Though interested parties can consult Section 5, which starts in on answering some of these bigger questions.

4 I will use this ‘characterized by’ expression as a loose, intuitive catch-all term for the idea that certain kinds have inherent, characteristic features which may defeasibly fail to obtain in isolated cases.

5 Most kind theories (Carlson 1977a and Chierchia 1998), with the notable exception of Liebesman (2011), make the further assumption that kinds are ordered by a subkind relation.

6 A quantificational analysis of indefinite generics was first suggested in Heim (1982), and first proposed as a general theory for generics as such in Farkas and Sugioka (1983), since which time it has more or less held sway in the literature: semantic theories that have become the industry standard such as those of Krifka et al. (1995) and Asher and Pelletier (1997) all argue generic sentences to have quantificational purport.

7 For those unfamiliar with generalized quantifier notation (Barwise and Cooper, 1981), a formula in generalized quantifier logic can be read in the following way: for any quantifier Q, read ‘Qx (F(x))(G(x))’ as ‘Q-many Fs are G.’ So ‘Every x (F(x))(G(x))’ can be interpreted as ‘Every F is G,’ ‘Most x (F(x))(G(x))’ can be interpreted as ‘Most Fs are G,’ and so forth. Different quantifiers are defined in different ways, but all of these definitions understand them as relations between sets. So the statement ‘Every x (F(x))(G(x))’ is true just in case the set of Fs is a subset of the set of Gs, and the statement ‘Most x (F(x))(G(x))’ is true just in case the intersection of the set of Fs and the set of Gs is greater in cardinality than the intersection of the set of Fs and the set of non-Gs.

8 This operator is typically referred to in the literature as Gn. So as to avoid confusion with Gen, this paper will follow terminology of Fara (2001) and call it the predicate modifier (PM for short).

9 There are, however, a few small challenges one can raise against the adverbial quantificational theory, independently of anything that will be discussed here, which the author intends to explore in future work.

10 It should be mentioned that this advantage is still hypothetical, because existing attempts to situate indefinite generics with respect to what we know about the indefinite article get their truth conditions wrong, and analyses that come closer to getting their truth conditions right fail to situate indefinite generics with respect to what we know about the indefinite article or bare plural generics. But the extant work in this area (Heim 1982; Greenberg 2003; Krifka 2013) is at least promising and suggestive.

11 See Carlson (1977a), chap. 5.

12 Section 5 will give a model-theoretic semantics for PM that has these two desirable features, among others. Without going into the details here, the rough idea is that kinds denote processes that produce things, and that the predicate modifier lifts an object-level property F to the property of being a process which makes things that are F.

13 Leslie (2015) provides a battery of further semantic arguments against a simple kind theory.

14 See Nickel (2010a).

15 It is not easy to have clear intuitions about these cases, which probably means that more experiments need to be done on these data. Before coming to share Nickel’s intuitions, it is first necessary to think one’s way into the scenario for a while.

16 Nickel attributes the account below to Krifka et al. (1995), but that article only discusses generic statements like (8-a), not generic comparatives like (8-b):

(8)	(a) Fs get bigger as you head north. (b) Fs are bigger than Gs.

17 This bit of notation, derived from the framework laid forth in Church (1940), is the standard means in natural language semantics for indicating different logical types. Read e as a logical type set aside for particular objects, t as a logical type set aside for truth values, and any expression 〈α, β〉 in angle brackets as a logical type set aside for functions from entities of type $\alpha$ to entities of type $\text{β}$. To give some examples, a function of type $〈e,t〉$ is a one-place predicate, a function of type $〈e,〈e,t〉〉$ is a two-place predicate, a function of type $〈t,〈t,t〉〉$ is a two-place boolean operator, a function of type 〈〈e, t〉, 〈〈e, t〉, t〉 is an expression like the definite article, and a function of type is a generalized quantifier. And for any condition $\varphi$, read $\lambda x_{\alpha }$. $\varphi \left(x\right)$ as the function that maps any object of type $\alpha$ to the true just in case condition $\varphi$ holds of it, and to the false otherwise.

18 Currying (Schönfinkel 1924) is the process of translating a dyadic relation into an equivalent sequence of functions, each of which takes one argument.

19 That will come in Section 5, where we will see that PM in fact does not have scope effects with linear relations.

20 See Cohen (2001), p. 193.

21 This example originates from Schubert and Pelletier (1987), p. 407. Interestingly, they don’t seem to think it poses a problem for the kind theory.

22 That is, either by type-raising (Hendriks 1988) or quantifier raising (May 1977).

23 This approach derives from Hendriks (1988).

24 In natural language semantics, it is customary to use the circumfix symbol $\left[\right[\cdot \left]\right]$ for the object language interpretation function that maps expressions of English to denotations in the logical metalanguage. Following Roelofsen (2008), we will also use $\Vert \cdot \Vert$ for the metalanguage interpretation function that maps expressions in the logical metalanguage to their truth/reference definitions. Both of these interpretation functions operate relative to a model and a variable assignment function.

25 E.g. If you understand the sentence ‘Squirrels are black’ and the words from and Poland, then you should have everything you need to understand the sentence ‘Squirrels from Poland are black.’.

26 For example, their meaning is computed with respect to a contextually supplied modal base and ordering source (Kratzer et al. 1981), and they seem to be able to undergo modal subordination (Roberts 1989).

27 Note that only one of two possible interpretations of sentence (19) gives rise to this interpretation – the ‘Africa or Asia, but I don’t know which’ interpretation does not.

28 Including but not limited to Asher and Bonevac (2005), Alonso-Ovalle (2006), Fox (2007), Barker (2010).

29 Section 5 will lay out a definition for PM that involves an existential quantifier. That it is typically modals with existential force which give rise to free choice effects suggests that this definition might at least provide a promising start to tackling the problem.

30 For some classic discussion of contextual domain restriction, see Stalnaker (1970), p. 276 and Lewis (1979), Example 3. More modern treatments can be found in von Fintel (1994) and Stanley and Szabó (2000).

31 I will adopt the convention of using the symbol # to mark a sentence off as a contradictory, infelicitous, or otherwise semantically ill-formed. The symbols ? and ?? indicate lesser degrees of semantic anomaly.

32 For a related example, see Asher and Pelletier (1997), p. 1165–1166.

33 Condoravdi’s original example was the following:

(24)	A ghost has been haunting campus. Students are afraid.

That particular example will not do as a counterexample, because afraid is a stage-level predicate, and so it is difficult to hear the second sentence of (24) as a generic. But closely-related examples such as the one I present suggest themselves.

34 To the author’s knowledge, there are no cases in which this has been observed in determiner or adverbial quantifiers, but there is some evidence of a deictic/anaphoric-deictic only contrast in modal auxiliary verbs. For instance, Klecha (2011) argues that gonna can domain restrict either deictically or anaphorically, whereas will can only domain restrict anaphorically.

35 See Carlson (1982), p. 153.

36 In principle, indexical predicates shouldn’t be the only kind that sound awkward in subject position of a generic sentence. But the way they pin their extensions to the particular circumstances in which they are uttered makes them especially useful as illustrative examples.

37 For a good contemporary overview, see Lowe (2009).

38 Certain accounts of sortal predicates collapse these two conditions, but we may follow Geach (1980) in assuming that competence in (32-a) is a necessary but not sufficient condition for competence in (32-b).

39 A few further conditions must be met in order for this test to tell us anything. Most importantly, ‘What is that?’ must be uttered with what one might argue to be its most basic, literal meaning, in which the person asking the question lacks any means of substantively identifying the object. Sometimes, we also ask ‘What is that?’ in contexts where we have already identified the object, but we want to know further facts about it that would explain its significance. In those contexts, the question means something more like: ‘Why are you treating this object in that way?’ And there it can make perfect sense to use an indexically modified predicate. For example:

(36)	(Ashley is looking longingly at a comb.) Whitney: What is that thing? Ashley: It’s a comb that used to belong to my mother.

In this case, the very context that a nonstandard construal of ‘What is that?’ available is the context that makes comb that belonged to my mother into a sortal predicate. In a moment, we will look at similar examples of context sensitivity sortals.

40 Surely that must be what Aquinas had in mind when he wrote that nominal (or substantival) predicates ‘carry their subject with them,’ whereas adjectival predicates ‘add the thing signified to the substantive.’ See Aquinas (1947).

41 This is leaving to one side contexts in which the salient domain restriction is to e.g. dobermans in a particular room, all of whom have natural ears. The point is that the assignment of truth values in (46) arises in contexts where the corresponding generic would go the other way.

42 This is just a way of saying that and is a function mapping any pair of entities or functions of the same type to a third entity or function of that type. So functions of type $〈t,〈t,t〉〉$ or $〈〈e,t〉,〈〈〈e,t〉,〈e,t〉〉〉$ are of type $〈\alpha ,〈\alpha ,\alpha 〉〉$ but e.g. functions of type $〈e,〈e,t〉〉$, $〈〈e,t〉,〈〈e,t〉,t〉〉$, or $〈〈e,t〉,e〉$ are not. .

43 For the full explanation of this metaphysical picture, see Teichman (2015), chap. 3. The full semantic analysis is spread out between chapters 3 and 4.

44 Note that this talk of being a process which makes a certain sort of object is just an informal, inuitive gloss on one component of the model-theoretic analysis that is to be given momentarily. It is a philosophical interpretation of the analysis, not the analysis itself. Rather than analyzing genericity in terms of the habitual property of ‘making things that are G,’ it analyzes genericity in terms of kinds and the ideal outcomes we associate with them, which are encoded as a kind of modality.

45 Formally, it has the structure of a bouletic modality, though of course there is no actual volition in this example.

46 This definition requires that some rather than all members of the kind K have property f to allow for the possibility of production processes that make more than one variety of thing. For instance, the process of Ferrari production at Maranello might have the property of making things that are red, and also have the property of making things that are blue. This further wrinkle in the analysis is not required to cover the data described in this paper, but it is necessary for covering some of the standard examples that are also discussed in the literature, such as sexual dimorphism-related pairs like ‘Cattle have horns’ and ‘Cattle have udders.’ To capture the data discussed in this paper, it would be just as well to replace the final existential quantifier with a universal quantifier and the final conjunction with a material implication.

47 It would go beyond the scope of this paper to consider examples which involve introducing new kinds into discourse, but it will be useful to have a framework that allows for this. For example, chap. 4 of Teichman (2015) argues that a pragmatic accommodation procedure which can introduce new kinds into a discourse offers one possible avenue for explaining the Condoravdi cases.

48 The static analysis will predict sentences like (53) to be false, and it will predict that generic sentences do not contextually domain restrict. Those who are happy to stop at capturing those data points can stick with the static version of the analysis and skip the following subsection.

49 See in particular the appendix to the second edition. For other presentations of incremental typed logic, see van Eijck (1999) and van Eijck and Unger (2010), chap. 12. This is a close cousin of the theories presented in Groenendijk and Stokhof (1990), Muskens (1996) and van Eijck (1977).

50 Fully specifying an anaphora resolution algorithm lies outside the scope of this paper, but the author’s preferred approach to the problem can be found in Martin and Pollard (2012).

51 For more details, see Teichman (2015), chap. 4.