There is a standard quantificational view of generic sentences according to which they have a tripartite logical form involving a phonologically null generic operator called ‘Gen’. Recently, a number of theorists have questioned the standard view and revived a competing proposal according to which generics involve the predication of properties to kinds. This paper offers a novel argument against the kind-predication approach on the basis of the invalidity of Generic Excluded Middle, a principle according to which any sentence of the form ⌜Either Fs are G or Fs are not G⌝ is true. I argue that the kind-predication approach erroneously predicts that GEM is valid, and that it can only avoid this conclusion by either collapsing into a form of the quantificational analysis or otherwise garnering unpalatable metaphysical commitments. I also show that, while the quantificational approach does not validate GEM as a matter of logical form, the principle may be validated on certain semantic analyses of the generic operator, and so, such theories should be rejected.
There is a standard view of characterising sentences (or
(1)
a.
Ravens are black.
b.
A duck lays eggs.
c.
The tiger has stripes.
d.
This kind of animal has a mane. [Uttered while pointing at a lion.]
It is well-known that such sentences manage to express generic generalisations about groups of particular events, facts, or individuals without the presence of an overt or articulated quantifier or operator appearing to be responsible for expressing this content. For example, (1a) expresses a generalisation about ravens similar, say, to that which is expressed by
Nevertheless, proponents of the standard quantificational view argue that, despite appearances, generics are essentially quantificational. That is, despite the lack of any overt or pronounced elements that are responsible for their general content, generics have a tripartite logical form involving a quantifier, a restrictor clause, and a matrix clause, akin to explicitly quantificational sentences like
However, a number of theorists have recently argued against the standard approach and revived a competing proposal (
(2)
a.
Dodos are extinct.
b.
Potatoes were cultivated in South America.
These theorists argue that, not only does the kind-predication view provide a unified semantic analysis for characterising sentences and genuinely kind-predicational sentences like those in (2), it better explains complex copredications, like
Determining whether the kind-predication approach or the quantificational approach is correct is a delicate task. In this paper, I will attempt to adjudicate between these theories by considering the following principle concerning generics:
Investigating whether GEM is valid is a useful tool for evaluating theories of generics more generally, since it provides a simple, yet overlooked, test for whether a theory of generics is empirically adequate. For if GEM is invalid, it follows that any semantic analysis that validates GEM is empirically inadequate. Conversely, if GEM is valid, any semantic analysis that invalidates GEM is empirically inadequate.
In this paper, I will argue that GEM is invalid and I will present a novel argument against the kind-predication approach on the grounds that it erroneously predicts that GEM is valid. Ultimately, I think that the kind-predication approach can avoid validating GEM, but only by either endorsing quantificational structure or committing itself to unpalatable metaphysical consequences. Conversely, I will also argue in favour of the standard quantificational approach to generics on the grounds that it has the resources to predict the invalidity of GEM, although this is by no means guaranteed. In particular, I show that certain semantic analyses of the generic operator
The paper is structured as follows. Section 2 outlines the logical forms that the kind-predication and quantificational approaches posit for generic sentences. Section 3 introduces Generic Excluded Middle and argues that it is invalid. It then draws out some consequences of the invalidity of GEM for the two approaches. Section 4 argues that, to capture the invalidity of GEM, the kind-predication approach must either collapse into a form of the quantificational approach or else garner unpalatable metaphysical commitments. Section 5 considers what additional assumptions are needed for quantificational accounts of generics to validate GEM by considering a number of specific semantic analyses. Section 6 concludes.
Let us begin by carefully distinguishing the logical forms that the quantificational approach and the kind-predication approach postulate for generics. According to the quantificational approach, the logical form of generic sentences is a tripartite quantificational structure consisting of a phonologically null quantifier called ‘Gen’. The generic operator
(3)
where
While we have not yet provided a semantic interpretation for the above notation, nor tied it directly to the syntax, this schema provides us with a useful means to represent various readings of characterising sentences. Indeed, a compelling piece of linguistic evidence in support of the quantificational analysis comes from Carlson’s observation that some sentences appear to have more than one generic interpretation (
(4)
Typhoons arise in this part of the Pacific.
a.
Typhoons in general have a common origin in this part of the Pacific
b.
There arise typhoons in this part of the Pacific
The ambiguity in (4) is evidence for the quantificational approach because quantified sentences often exhibit the same type of ambiguity. Moreover, the quantificational approach can accommodate the two readings of (4) by partitioning the surface material into the restrictor and matrix clauses in different ways. In (4a), the bare plural
What does the quantificational approach say about the semantics of
Contrastingly, according to the kind-predication approach, the logical form of generic sentences is a simple dyadic subject–predicate structure, roughly equivalent to the logical form of atomic sentences that predicate properties of individuals. On this view, bare plurals refer to kinds and the sentence predicates a property of that kind. Consequently, characterising sentences of the schema (5a) receive the logical form (5b) as in:
(5)
a.
Fs are G
b.
G(F-kind)
Proponents of the kind-predication approach draw a strong analogy between sentences involving genuine reference to kinds like in (6a) and generic sentences like in (7a), arguing that they have essentially the same logical form:
(6)
a.
Dinosaurs are extinct.
b.
extinct(dinosaur-kind)
(7)
a.
Tigers have stripes.
b.
striped(tiger-kind)
The kind-predication view is motivated by a number of considerations. First, proponents of the kind-predication approach claim that the lack of any phonological or orthographical realisation of
What does the kind-predication approach say about the nature of kinds and how they can be predicated properties usually reserved for first-order individuals? What is the nature of tiger-kind and how can it have the property of being striped when such properties seem to be satisfied only by first-order individuals like tigers? Proponents of the kind-predication approach sometimes claim that kinds are whatever are the referents of bare plural nouns and that providing an account of kind-predication is in the remit of metaphysics, not semantics (
Having laid out the quantificational and kind-predication approaches to generics, let us now turn to Generic Excluded Middle, repeated below for convenience.
Before we examine whether GEM is valid, let us unpack its content. For discursive lucidity, let us distinguish between the
Unfortunately, despite any intuitive appeal that GEM might enjoy, the principle is subject to systematic counterexamples as witnessed by the following sentences:
(8)
a.
Books are paperbacks or books are not paperbacks.
b.
Fair coins land heads or fair coins do not land heads.
c.
Lions are male or lions are not male.
A counterexample to GEM is a disjunction constituted by a characterising sentence and its opposite, neither of which are true. Observe, then, that sentence (8a) is a counterexample to GEM: on their generic readings, the sentences ‘Books are paperbacks’ and ‘Books aren’t paperbacks’ aren’t true, even though it is true that books are either paperbacks or not paperbacks. Similar remarks apply for the other examples. On their generic readings, the sentences ‘Fair coins land heads’, ‘Fair coins don’t land heads’, ‘Lions are male’, and ‘Lions are not male’ aren’t true, even though it is true that fair coins land either heads or tails and that lions are either male or not male. With sufficient ingenuity, such counterexamples multiply without limit. Therefore, GEM is invalid.
I shall now offer an argument against the kind-predication approach to generics, an argument that also supports the quantificational approach. Let us first consider whether the kind-predication approach predicts the invalidity of GEM. To answer this question, GEM should be reformulated to highlight the bipartite logical structure that the kind-predication approach assigns to generics:
where ‘
(9)
a.
b.
c.
This should not be surprising, since the kind-predication approach treats bare plurals as individual-denoting terms and sentences headed by individual-denoting terms generally treat sentential and predicate negation equivalently, as evidenced in (10):
(10)
a.
It is not the case that John is happy.
b.
John is not happy.
c.
An immediate upshot of the observation that the kind-predication approach does not distinguish between negated generics and their unnegated opposites is that, for the kind-predication approach, K–GEM is a special instance of the Law of Excluded Middle:
In other words, the kind-predication approach and LEM jointly entail K–GEM. According to the kind-predication approach, bare plural DPs like
On the other hand, the quantificational approach does not entail GEM, at least not as a matter of logical form. To see this, we must first again reformulated GEM to highlight the relevant tripartite structure that the quantificational approach assigns as the logical form of generics:
An immediate consequence of this reformulation is that, unlike the kind-predication approach, the quantificational approach and LEM do not jointly entail GEM. After all, the quantificational approach postulates enough structure to distinguish between the logical forms of negated generics and their unnegated opposite counterparts:
(11)
a.
b.
(12)
a.
b.
Given that the quantificational approach can logically distinguish between these sentences, it does not follow that sentences of the form (11a) entail sentences of the form (12a), at least not as a matter of logical form. That is, for everything that we have said so far, neither
To summarise the discussion, the fact that the kind-predication approach entails GEM is significant evidence that the approach is incorrect. For given LEM, if the kind-predication approach is correct, then the disjunction ‘Books are paperbacks or books are not paperbacks’ is true. But neither disjunct is true; neither ‘Books are paperbacks’ nor ‘Books are not paperbacks’ is true. Consequently, the original disjunction is not true, and so the kind-predication approach is incorrect. Furthermore, the fact that the quantificational approach does not immediately entail GEM is a significant advantage to its predictive power, since it avoids the unpalatable predication that sentences like those in (8) are true. Nevertheless, there may be specific semantic analyses of
The question remains whether the kind-predication theorist has enough linguistic or metaphysical resources at her disposal to account for the invalidity of GEM. The following section will consider this question, arguing that either the kind-predication theorist must either embrace quantificational structure or else commit herself to some unpalatable metaphysical consequences.
In the previous section, I argued the simple kind-predication approach cannot account for the invalidity of GEM. However, the kind-predication theorist may respond to this argument either by (i) rejecting the Law of Excluded Middle, the principle upon which my argument relied, or by (ii) adopting additional covert material in the logical form of generics that allows them to distinguish between negated generics and their unnegated opposites. In this section, I shall consider and reject these responses.
It may be tempting to resist the above argument by rejecting LEM. After all, if LEM is invalid, then not every individual must either satisfy a property
There are at least two independently motivated strategies for rejecting LEM to which defenders of the kind-predication approach might appeal. First, one might argue that a generic is neither true nor false if the denotation of its subject term is undefined.
Is there any independent reason to think that bare plurals in characterising sentences are sometimes undefined? Some theorists have pointed out that not just any nominal constituent can form a kind-referring definite DP (
(13)
a.
The Coke bottle has a narrow neck.
b.
#The green bottle has a narrow neck.
If this point extends to bare plural DPs, then bare plural DPs that fail to refer to well-established kinds are undefined and sentences in which they are contained are neither true nor false. On this response, our truth-value judgements about counterexamples to GEM are mistaken. While we mistakenly judge the sentence ‘Fair coins land heads or fair coins do not land heads’ to be false, it is actually truth-valueless, since
However, this strategy is inadequate for at least three reasons. First, the strategy will not work for all of the counterexamples to GEM. Some bare plural DPs in the counterexamples are not obvious candidates for reference failure, since it is highly plausible that they denote well-established kinds (if they denote kinds at all). For example, book-kind and lion-kind have as good a chance as any to satisfy “well-establishedness” in the intended sense. And we can truly assert generics involve the bare plurals
Second, the strategy incorrectly predicts truth-value judgements about the counterexamples to GEM. The counterexamples to GEM and their individual disjuncts are typically judged as False, not the ‘squeamish’ “I-don’t-know” or ‘Neither’ commonly reported by LEM-deniers.
Third, and more generally, the strategy inaccurately predicts that bare plural DPs must refer to well-established kinds for the characterising sentences in which they are contained to be felicitous. But, while characterising sentences containing definite DPs that supposedly refer to non-well-established kinds are infelicitous, their bare plural counterparts sound fine (
(14)
a.
#The green bottle has a narrow neck.
b.
Green bottles have narrow necks.
Since bare plural DPs do not pattern with their definite DPs counterparts, there is little reason to think they only refer to well-established kinds. Moreover, many generics, whose DPs are gerrymandered and do not refer to anything well-established, are judged true. For example, the sentence ‘Australian Tour de France winners are Australian’ seems true, even though it is doubtful that Australian Tour de France winners is a well-established kind (cf.
Let us now turn to the second strategy for rejecting LEM. This strategy holds that the peculiarities of property inheritance allows for property gaps that, in turn, give rise to truth-value gaps. To see how this strategy works, recall that the kind-predication approach takes a kind to have an individual-level property just in case the kind inherits that property from its members. The idea, then, behind the second strategy is that kinds can fail to inherit certain properties (e.g., the property of being a G) from their members, while also failing to inherit the corresponding negative property (e.g., the property of not being a G). For example, one could argue that, even though fair coins are the kind of thing that can land heads, they do not instantiate this property to the extent that (or in a way in which) fair-coin-kind would inherit this property from its members. Similarly, even though fair coins are the kind of thing that might not land heads, they do not instantiate this property to the extent that (or in a way in which) fair-coin-kind would inherit the property of not landing heads from its members. If this is right, it seems plausible to say that it’s not true that fair-coin-kind lands heads and it’s not true that fair-coin-kind doesn’t land heads. Then, neither (8b) nor the sentence ‘Either fair-coin-kind lands heads or fair-coin-kind doesn’t land heads’ is true.
The problem with this strategy is it hinges on a rather opaque notion of property inheritance. To properly evaluate this approach, one would hope for a developed account of how kinds inherit properties from their members, one that also explains how property inheritance gives rise to the right kinds of property gaps. Unfortunately, proponents of the kind-predication view are generally sceptical that any useful general principles governing the property inheritance relation can be provided. For example, Liebesman writes:
Attempting to give a systematic account of the way in which material objects inherit properties from their parts is something of a fool’s errand. The quantity and salience of the parts that is required for inheritance varies greatly. […] The relationship between kinds and their members is similarly unsystematic. Generics ascribe properties to kinds and, given the multiplicity of properties and the multiplicity of ways kinds inherit properties from their members, no fully general account of inheritance will be forthcoming. (
The lack of any concrete theory of property inheritance makes it difficult to properly evaluate this proposal, especially since there are numerous ways that proponents of the kind-predication approach can develop their account of inheritance. Nevertheless, I want to raise two general concerns about this strategy.
First, it’s important just to appreciate how radical these kinds of property gaps are. According to this strategy, while fair-coin-kind doesn’t instantiate the property of landing heads, failing to instantiate that property is not enough for it not to be the case that fair-coin-kind lands heads. Furthermore, while fair-coin-kind doesn’t instantiate the property of
(15)
It is not the case that fair-coin-kind instantiates the property of landing heads, and it’s not the case that fair-coin-kind instantiates the property of not landing heads, but it is the case that fair-coin-kind either lands heads or doesn’t land heads.
Offhand, at least, such sentences sound highly contradictory. Proponents of the kind-predication approach must explain away the contradictory-soundness of such sentences, but it’s not clear how they would do so.
The second problem arises because the property inheritance approach is committed to the idea that certain generics and their opposites express propositions neither of which are true or false, or, at the very least, that certain generics and their opposites express partial propositions, which can be understood as partial functions from worlds to truth-values.
(16)
a.
b.
where, ‘
Next, let us specify the positive and negative extensions of the opposites of these generics analogously, as in (17).
(17)
a.
b.
Again, it should be clear from these equivalences that, given that the kind-predication approach identifies the negation of a generic with its opposite, the positive and negative extensions of the negation of a generic will be equivalent to the positive and negative extensions of its opposite, which, in turn, will be equivalent to the negative and positive extensions of the unnegated generic, respectively, as in (18):
(18)
a.
b.
Thus, this strategy effectively abandons the idea that generic sentences and their negation determine an extension and an anti-extension that are mutually exclusive and jointly exhaustive with respect to the universe of discourse in the occasion of use. Furthermore, this abandonment percolates down to how the semantics treats the extension and anti-extension of predicate terms. These are treated in a non-standard way, so that the property denoted by the anti-extension of a predicate term is not simply the complement of its extension.
The problem with this suggestion is that it is difficult to maintain this kind of semantics alongside other commitments held by the kind-predication approach, while also providing a systematic treatment of negation that respects our intuitive truth-value judgements about certain classes of generics. Consider, for example, Liebesman’s quantificational glosses for the truth-conditions for ‘Mosquitoes carry WNV’ in (19) and its translation into the above notation in (20) (cf.
(19)
Mosquitoes carry WNV
(20)
Observe that the opposite, ‘Mosquitoes don’t carry WNV’, is intuitively false, but when we try to state its semantic content using the above notation and by applying the quantificational gloss from (19) in the natural way, we get the following equivalences:
(21)
These truth-conditions are clearly inadequate: the sentence ‘Mosquitoes don’t carry WNV’ is intuitively false, even though the vast majority of mosquitoes aren’t WNV-carriers, but the above semantics predicts that it is true, since some mosquitoes don’t carry WNV.
Alternatively, proponents of the kind-predication approach might make the
(22)
But, while this is empirically adequate, adopting this approach across the board threatens to collapse the distinction between positive and negative extensions that allow the kind-predication proponent to reject LEM in the first place. Furthermore, it requires negation to interact in generic sentences in an entirely unsystematic manner, taking different truth-conditional scope in different circumstances. The non-systematicity in the behaviour of negation would be a serious blow to the plausibility of this strategy.
These brief remarks do not count decisively against the property inheritance approach. But I hope they serve to highlight some reasons to be cautious about adopting this approach.
The other option is that the kind-predication theorist might appeal to additional covert structure in the logical form of generic sentences already encoded in the syntax of generics (
Let us see how this works in practice. Following Chierchia (
(23)
a.
b.
where
(24)
a.
b.
(25)
a.
b.
Furthermore, with this additional descriptive power, the sophisticated kind-predication theorist can agree that LEM is valid without admitting that GEM is valid for exactly the same reasons why the quantificational theorist can.
While I have no general in-principle objections to these sophisticated versions of the kind-predication approach, I should like to observe that these strategies essentially concede that the logical form of generic sentences is quantificational.
In Section 3, I argued that the quantificational approach does not entail GEM as a matter of logical form, but specific semantic analyses of
To see how the quantificational approach to generics can invalidate GEM, we must consider how specific semantic analyses of
Normality-based accounts typically deploy (restricted) universal quantification over normal individuals or normal worlds. For example, according to Yael Greenberg’s (
(26)
where ‘
Contrastingly, probability-based versions of the orthodoxy typically deploy universal or majority-based quantification over all suitable smoothed out admissible temporal segments of possible worlds that extrapolate from the current history so far. For example, Cohen (
(27)
Let
Let
where
To see how these theories work, consider the truth-conditions that that they assign to (1a), repeated below as (28) with a LF as in (28a):
(28)
(= (1a)) Ravens are black.
a.
Gen x[raven(x)][black(x)]
(29)
(28a) is true iff
(30)
(28a) is true iff
Both of these analyses are empirically adequate with respect to (28). On Greenberg’s theory, (28a) is true iff, in all appropriately accessible worlds, every contextually relevant and normal raven is black in those worlds. And on Cohen’s theory, (28a) is true iff the probability of an arbitrary raven’s being black is greater than 0.5.
But how do these accounts fare with our counterexamples to GEM? Consider, again, the sentences in (8), repeated below as (31).
(31)
a.
(=(8a)) Books are paperbacks or books are not paperbacks.
b.
(=(8b)) Fair coins land heads or fair coins do not land heads.
c.
(=(8c)) Lions are male or lions are not male.
Greenberg’s account clearly and correctly predicts that (8a) is false. For, according to her theory, the first disjunct ‘Books are paperbacks’ is true just in case, roughly speaking, in all appropriately accessible worlds, every contextually relevant and normal book is paperbacked in those worlds. Similarly, the second disjunct, ‘Books are not paperbacks’, is true just in case in all appropriately accessible worlds, every contextually relevant and normal book is not paperbacked in those worlds. But since only some of those books are paperbacks in those worlds, and the others are hardbacks, neither disjunct is true, and so the disjunction is false overall. These remarks generalise to (8b) and (8c); Greenberg’s theory predicts they are false for analogous reasons. And, abstracting away from the specifics of Greenberg’s theory, we can observe that any theory involving universal quantification over (perhaps suitably restricted) normal individuals or worlds can, in principle, avoid validating GEM, since there is no guarantee that either a universal generalisation nor its opposite is true.
Matters are more complicated on Cohen’s account. It is clear that Cohen’s semantics predicts that (8b) is false. For both disjuncts are false on Cohen’s semantics: the first disjunct ‘Fair coins land heads’ is false, since
But things are trickier for (8a) and (8c). As I have stated Cohen’s semantics in (7), it predicts that these disjunctions are true, since the vast majority of books are paperbacks and most lions are female. This is clearly the wrong result. But, in part to account for these kinds of sentences, Cohen proposes that a generic
(32)
1.
2.
In words, a reference class
Cohen then hardwires the requirement that generics are homogeneous directly into his truth-conditions, as we can see in the following, simplified revision of (27):
(33)
Let
Let
What exactly counts as a “salient” partition? Cohen (
(34)
Books are paperbacks.
Assuming that the concept
Similar remarks apply to (8c). While the majority of lions are female, if we partition the domain of lions according to sex, there will be a subclass of lions that are not male – the female lions – and there will be a subclass of lions that are not not male – the male lions. The existence of these subclasses means that the homogeneity requirement is not satisfied for both ‘Lions are male’ and ‘Lions are female’, and so both of these sentence are false. Thus, Cohen’s account predicts that (8c) is false. Thus, Cohen’s account avoids validating GEM.
In the previous subsection, we observed a distinction between those theories of generics that invalidate GEM as a straightforward consequence of their semantics, such as Greenberg’s, and those theories of generics that require additional assumptions to invalidate GEM, such as Cohen’s semantics and his homogeneity constraint. In this subsection, I want to demonstrate how specific semantic and metaphysical assumptions about the nature of
Von Fintel (
(35)
where
Given Homogeneity, it directly follows that
(36)
Given (36), LEM, and the substitution of material equivalences, GEM immediately follows. Given LEM,
However, there is reason to doubt that the
(37)
A:
Has Elmo stopped smoking?
B:
Hey, wait a minute! I had no idea Elmo used to smoke.
C:
#Hey, wait a minute! I had no idea that Elmo stopped smoking.
B’s complaint to the presuppositional component of A’s utterance is felicitous, but C’s complaint to the asserted, non-presuppositional component is infelicitous. Consequently, the claim that Elmo used to smoke is a presupposition, whereas the claim that Elmo stopped smoking is not.
If characterising sentences trigger presuppositions that either all or no individual in a certain domain satisfied the predicate, then we would expect that C’s complaint to A’s utterance would be felicitous. But this is clearly not the case.
(38)
A:
Are cats black?
B:
Hey, wait a minute! I had no idea that cats could be black.
C:
#Hey, wait a minute! I had no idea that either all or no normally coloured cats had to be black.
While B’s complaint to a clearly presuppositional component of A’s utterance is felicitous, C’s complaint is not. Consequently, characterising sentences fail the HWM test.
Second, generic sentences fail projection tests for presuppositions. It is well-known that presuppositions project from questions, as evidenced by the fact that the question in (37) commits the speaker to the belief that Elmo used to smoke. If characterising sentences trigger homogeneity presuppositions, the question in (38) would commit A to the belief that either all or no normally coloured cats are black. But this is not the case. The question of whether cats are black is compatible with normally coloured cats being coloured in a variety of ways — normally coloured cats may be brown, ginger, white, black, or any mixture of the four.
Furthermore, it is well-known that presuppositions project from the antecedent of a conditional. For example, (39) presupposes that Elmo used to smoke:
(39)
If Elmo stopped smoking, then he’s probably feeling jittery.
If characterising sentences triggered homogeneity presuppositions, then (40) should entail that either all or no normally coloured cats are black. But this is clearly not the case:
(40)
If cats are black, then we better be careful crossing paths with cats.
Since passing the HWM and projection tests are plausible necessary conditions for the existence of presuppositions, this is strong evidence that the
To conclude this section, I want to focus on Bernhard Nickel’s (
According to Nickel’s theory, the generic operator
(41)
To see how Nickel’s theory works, consider the truth-conditions it gives for (1a) (= ‘Ravens are black’):
(42)
The sentence ‘Ravens are black’ is true at a context
On the assumption that the context makes salient normal ways of being coloured, the truth-conditions for (1a) is empirically adequate.
However, a complication for Nickel’s theory arises with negated generics like (43) (cf.
(43)
Ravens are not white.
Intuitively, (43) denies that normal ravens are white. But this is not predicted by Nickel’s semantics. The negation in (43) can either be interpreted as taking wide-scoping over the whole sentence or as taking narrow-scope over the verb phrase. Applying Nickel’s semantics to these interpretations yields the truth-conditions in (44) and (45), respectively:
(44)
It’s not the case that there is a way of being a normally coloured raven such that every raven that is normal in this way is white.
a.
All ways of being a normally coloured raven are such that, for each of these ways, there is some raven that isn’t white.
(45)
There is a way of being a normally coloured raven such that every raven that is normal in this way is not white.
By pushing the negation in (44) through the quantifiers, we see that it is equivalent to (44a), which does not capture the intuitive meaning of (4), as it is compatible with normally-coloured white ravens. And (45) isn’t right either, since it only rules out that the possibility that white is the
In order to capture the intuitive reading of negated generics like (43), Nickel requires that his semantics validates the following homogeneity principle:
(46)
All ways
Then this is true:
All ways of being an
Given Nickel’s homogeneity principle, (44a) entails (47):
(47)
All ways of being a normally coloured raven are such that, for each of these ways, all ravens that are normal in that way are non-white.
This is exactly what is needed to capture the intuitive meaning of (43).
However, the problem with Nickel’s homogeneity principle is that, together with his semantics and LEM, it entails that Generic Excluded Middle. To see this, consider an arbitrary instance of LEM:
(48)
I will now show that, regardless of which disjunct is true, GEM follows. This is straightforward when the first disjunct is true. For suppose
To show that the second disjunct also entails GEM, suppose
(49)
All ways of being a
By applying Nickel’s homogeneity principle to (49), it follows that:
(50)
All ways of being a
That is, there is no way
(51)
Now, since every
(52)
Applying Nickel’s semantics, it follows that (52) is true only if:
(53)
There is a way of being a
But, from (50), we have it that
(54)
And, finally, by disjunction-introduction,
The main lesson of this paper concerns the semantics of generics: any adequate theory of generics must predict that GEM is invalid. This observation is particularly important when deciding between kind-predication and quantificational approaches to the semantics of characterising sentences. If the arguments in this paper are correct, the kind-predication approach entails GEM and so it is false. On the other hand, the quantificational approach fares much better. No general argument that the quantificational approach entails GEM is forthcoming and some prominent semantic analyses for
See, for example, Krifka et al. (
This paper focuses mainly on bare plural generics of the form
For historical proponents of the kind-predication view, see Lawler (
See, e.g., Krifka et al. (
For further discussion on generics and copredications, see Collins (
An anonymous reviewer raises a concern about whether some of the sentences in (8) really are counterexamples to GEM or whether they conflate falsity and unassertability. It is worth emphasising that the claim that the target sentences are false is not an idiosyncratic judgement, and that there is wide support in the literature for the claim that these disjuncts are false; see, for example, Carlson (
For discussion of other versions of the kind-predication approach that also entail GEM, see von Fintel (
To remain neutral between competing versions of the quantificational approach, and different ways if dividing sentence material between the restrictor and matrix clauses, I simplify the LF representation by leaving tacit the variables bound by
For other semantic theories that predict truth-value gaps arise from undefinedness, see the Frege–Strawson theory of definite descriptions which holds that sentences containing definite descriptions are truth-valueless when their definite descriptions are undefined due to presupposition failure (
An analysis of the notion “well-established kind” is not attempted here, since the distinction seems real enough given the strikingness of the example sentences.
‘#’ indicates infelicity of some sort.
Of course, this consideration will have less dialectical weight for theorists, like those mentioned in ft. 6, who judge the counterexamples to GEM to be merely unassertable, rather than false.
Recall that it is common ground amongst most, if not all, three-valued logics that a disjunction is neither true nor false if both its disjuncts are neither true nor false.
Here and throughout, I make the harmless idealisation assumption that the extensions of declarative English sentences can be modelled as (the characteristic functions of) sets of worlds.
Dialectically speaking, I think my use of quantificational glosses on the propositions expressed by generics is unobjectionable, since Liebesman helps himself to quantificational glosses on the truth-conditions of generics and argues at length that doing so doesn’t commit him to the claim that generics are themselves quantificational; see Liebesman (
See Dorr (
Even worse, this approach predicts that ‘Mosquitoes carry WNV’ and ‘Mosquitoes don’t carry WNV’ are both true, and so it invalidates an extremely plausible principle governing generics,
See Hoeltje (
For other reasons to be cautious about theories that predict property gaps in this way, albeit in a different context, see Williamson (
There are other reasons to be cautious about this notion of property inheritance. For example, kinds often seem to inherit some, but not other, properties from their members, even though exactly the same members instantiate both properties. For example, consider (i) seems true and (ii) to be true, even if all and only the male cardinals are the red ones.
(i) Cardinals are red. (ii) Cardinals are male.
Explaining the difference in truth-value between these sentences is a general problem for theories of generics. But the present concern is that, while property inheritance is not guaranteed by a certain proposition of a kind’s membership having a certain property, proponents of the kind predication approach do not offer an explanation for these facts.
Alternatively, one may retain full commitment to the view
For arguments against Cohen (
For present purposes, I will focus on Greenberg’s theory, but what I have to say generalises to other versions of the view. For other proponents of the normality-based approach, see, e.g., Asher and Morreau (
Actually, Cohen proposes a slightly more complicated truth-conditions in order to accommodate what he calls ‘relative generics’. We will focus on a simplified version of his view, since nothing that I have to say here is impacted by relative generics.
A wrinkle. It is physically possible, though exceedingly rare, for a flipped fair coin to land on its side. Taking this into account,
For further discussion of Cohen’s homogeneity principle, see Cohen (
Cohen’s actual statement of his truth-conditions is complicated by (i) his treatment of relative generics (see ft. 23) and (ii) his treatment of alternatives. For present purposes, I assume a simplified treatment of alternatives, though, see Cohen (
Interestingly, Cohen (
See also Löbner (
For the sake of argument, I follow von Fintel in assuming that, for a generic
As mentioned in ft. 27, Cohen (
(i) The generic [ 1. for every psychologically salient partition 2. for every psychologically salient partition
On a natural understanding of this view, a generic
It’s unclear whether von Fintel must assume that Homogeneity is a presupposition for his theory of
Numerous places in Nickel’s informal remarks strongly suggest he intends his homogeneity principle to be an entitlement, such as the following: “The principle to enforce the sort of homogeneity I just described informally is simply the inference from claims of the form instantiated by [(5a)] to claims of the form instantiated by [(8)] are
Note the relevant reading of (13) involves a disjunctive matrix clause, rather than as a disjunction of generics. That is, the logical form of (13) is
For a related argument that Nickel’s view contradicts
I should like to thank Annie Bosse, Sam Carter, Daisy Dixon, Paul Elbourne, John Hawthorne, Ofra Magidor, Brian Rabern, Daniel Rothschild, and Timothy Williamson for helpful comments and discussion on previous drafts of this paper, as well as to two anonymous reviewers for Philosophers’ Imprint for invaluable comments. This research was partially supported by the Arts and Humanities Research Council Doctoral Studentship (AH/L503885/1) and a Jacobsen Studentship provided by the Royal Institute of Philosophy.