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Generics as Modals

Ariel Cohen
p. 63-82

Résumés

On conçoit couramment les génériques comme exprimant une quantification universelle sur des individus normaux. Je réfute cette approche et démontre que la quantification n’est ni universelle ni sur des individus normaux.
Concernant l’universalité, les génériques ne répondent pas aux tests standards de la quantification universelle. Je propose, comme alternative, que les génériques expriment des mesures de haute probabilité. Je formalise cette notion au moyen d’une extension modale de la logique probabiliste du premier ordre, et montre comment ce système peut rendre compte des génériques enchâssés et des inférences sur des génériques.
Quant à la normalité, je la mets en contraste avec une autre notion, celle d’uniformité : les génériques sont évalués par rapport à des mondes dont le futur ressemble à leur passé. En utilisant les tests standards de substitution pour l’intensionnalité, je démontre que les génériques sont évalués par rapport à des mondes uniformes plutôt que normaux.
Le résultat final est qu’un générique comme Birds fly (les oiseaux volent) ne signifie pas « tous les oiseaux normaux volent » ; il signifie plutôt que la probabilité pour qu’un oiseau pris au hasard vole est élevée, et qu’il est attendu que cette tendance perdure.

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1. The paradox of generics

1Generics are both more and less powerful than universals. They are more powerful, because they are lawlike : (1a) may be true as a contingent fact, but (1b) will not be true unless a law is enacted, requiring Supreme Court judges to have a prime Social Security number.

(1)

a. All Supreme Court judges have a prime Social Security number.

 

b. Supreme Court judges have a prime Social Security number.

2But generics are also less powerful than universals, because they tolerate exceptions : (2a) is false, while (2b) is true.

(2)

a. All birds fly.

 

b. Birds fly.

This paradox seems to be at the core of the problem of genericity. How can we solve it ?

3To solve the first problem, it is often proposed that generics are modal (Dahl 1975). Thus, (1a) is about actual Supreme Court judges, but (1b) is about possible Supreme Court judges. This is why (1a), but not (1b), can hold of a temporary, contingent generalization. But if generics are modal, what sort of modals are they ?

4In this paper I propose an answer to this question. I the next section I present a widely held view of generics, the “all normal” approach. In section 3 I consider whether, as the word “all” indicates, generics are really universal, or express probability judgments, as I suggest in section 4. Probabilistic accounts of generics have been subjected to various criticisms, especially regarding the ways they handle inference and embedded generics. I propose a theory that overcomes these difficulties. In the following section I proceed to examine whether generics really are about “normal” worlds, and conclude that they are not. Instead, I propose an account of generics as probability judgments over uniform worlds. Section 6 summarizes the main conclusions of the paper.

2. The “all normal” approach

5Modality is characterized by three components (Kratzer 1981):

  1. A modal base : essentially, the set of accessible worlds

  2. A modal force: universal, existential, or perhaps something in between

  3. An ordering source: roughly, a relation on worlds, s.t. w1 w2 indicates that w1 is “better”, in some sense, than w2.

A widely held view (references too numerous to mention, but see Greenberg’s article, this volume) is that generics express quantification over “all normal” individuals. The idea is that (2b) can be paraphrased as “All normal birds fly”. This view leads to the following specification of generics, in terms of the three components of modality :

  1. The modal base is, in fact, rarely discussed by proponents of this approach, but it is presumably circumstantial.

  2. The modal force is clearly a universal.

  3. The ordering source is stereotypical: w1 w2 means that w1 is closer to the stereotypical ideal than w2.

Thus, the meaning of (2b) can be expressed, somewhat inaccurately, as follows : “In all normal worlds, all birds fly.”

6This theory solves the first problem, i.e. accounts for the fact that generics are lawlike : since it is not an essential requirement for Supreme Court judges to have prime Social Security numbers, in normal worlds they may have composite (non-prime) Social Security numbers.

7But the theory also solves the second problem, namely the fact that generics tolerate exceptions : this is because exceptions are considered abnormal instances. Thus, penguins don’t fly, hence constitute exceptions, but that does not falsify (2b), because they are somehow abnormal.

8This theory, then, solves both sides of the paradox at one fell swoop, which explains its attraction. But is it correct ?

9The “all normal” theory assumes a definition of normality, according to which, for example, non-flying birds are abnormal. But what does it mean to be abnormal ? What is abnormal about the penguin ? It is a bird just like any other bird, perfectly adapted to its environment, so why would we want to say that it is abnormal ?

10Of course, we cannot define normal birds as birds that fly, for then (2b) becomes trivial : it would simply say that all birds that fly, fly. Hence, a non-circular definition of normality is necessary. But despite much work on the “all normal” theory, no such definition seems to be forthcoming.

11In addition to this conceptual problem, the “all normal” approach suffers from substantial empirical difficulties. This view constitutes of two major claims : one is that the modal force is universal, and the other is that the ordering source is stereotypical. Let us examine each one of these claims in turn.

3. Is the modal force universal?

12There are several acknowledged tests for universal (or negatively universal) quantifiers. We can use them to determine whether the modal force is universal.

13The first test involves the adverb absolutely, which can only modify universals. Thus, (3a) is fine, whereas (3b) is bad.

(3)

a. Absolutely everyone/nobody was there.

 

b. *Absolutely some/few/three/many/most people were there.

Generics do not behave like universals: (3c) is bad.

 

c. *Absolutely birds fly.

The second test makes use of exceptive phrases, which allow only universal or negatively universal quantifiers (Moltmann 1995; Zuber 1998):

(4)

a. Every/No bird except for Tweety is sad.

 

b. *Some/Few/Three/Many/Most birds except for Tweety are sad.

Again, generics pattern with the non-universal, rather than universal, quantifiers:

  • 1 This sentence is improved with comma intonation preceding except, but this kind of intonation also (...)

 

c. *Birds except for Tweety/penguins fly.1

The third test concerns even which also combines only with universal quantifiers (Zuber 2004) :

(5)

a. Every bird, even Tweety, is sad.

 

b. No bird, not even Tweety, is sad.

 

c. *Some/Few/Three/Many/Most birds, even Tweety, are sad.

Once again, generics pattern with the non-universal quantifiers, and cannot combine with even :

 

d. *Birds, even Tweety/penguins have wings.

14The fourth test was not originally developed as a test for universal quantification, but makes use of an interesting property of speech acts, discussed by Krifka (2001). He notes that (6) is ambiguous

(6)

What did everyone bring to the party?

  • 2 Krifka notes that (6) has yet a third reading, which does not concern us here.

Under one reading, (6) asks which x is such that everyone brought x to the party. A possible answer can be : Beer. Under the second reading, (6) asks, for each individual y, what y brought to the party. A possible answer would be : Mary brought beer, John brought white wine, Fred brought cookies…2

15Krifka notes that only universal quantifiers are ambiguous in this way. If we replace the universal with a different quantifier, we get only the first type of interpretation. Thus, (7) can only receive an answer such as Beer, but not Mary brought beer, John brought white wine, Fred brought cookies…

(7)

What did some/few/three/many/most people bring to the party ?

16When we test generics, they, once again, do not behave like universals : an acceptable answer to (8) is Honey ; but the following is not a felicitous answer : Pooh likes to eat honey, Teddy likes to eat meat, Yogi like to eat everything…

(8)

What do bears like to eat ?

17Based on all these tests, we must conclude that the modal force of generics is not universal: (2b) simply cannot mean All normal birds fly.

18One might suppose that this is not such a significant setback. Perhaps, instead of a universal quantifier, we just use a different one, say most. Then (2b) would mean Most normal birds fly. However, since generics are assumed to be modal, it is not clear how to interpret this. How does one define most over infinitely many possible worlds ?

4. Probability

4.1. Probability as a measure function over worlds

  • 3 It must be noted, however, that this was not the main point of their paper.

19In order to define a non-universal quantifier over possible worlds, we need some measure function over possible worlds. A natural choice suggests itself. In fact, it has already been suggested by Schubert and Pelletier (1989).3 They propose that the generic quantifier is most, and that it quantifies over pairs of worlds and individuals, and explain :

most” is to be interpreted in terms of some probability distribution favouring worlds w′ similar to w [the actual world], with regard to the “inherent” or “essential” nature of things (p. 259-260)

20That is to say: Schubert and Pelletier propose a probability function that respects the stereotypical ordering source. Hence, (2b) is interpreted as saying that the probability that a normal bird flies is high.

21It should be emphasized that the use of probability is not essential, and some other measure function might perhaps have done just as well. However, probability has the enormous advantage that it has been heavily studied for several centuries, and there is a wealth of useful observations, techniques, and theorems regarding probability.

22However, it has been argued that probability is not an appropriate tool for dealing with generics. Let us consider some of these arguments.

4.2 Probability and inference

23Let us suppose that the logical form of the generic As are Bs is genx [A(x)] [B(x)], so that the logical form of (2b) is genx [bird(x)] [fly(x)]. An important question in the study of generics is this : when can we conclude one generic from another ? For example, consider the following general inference pattern :

genx [A(x)] [B(x)] ⇒ genx [A(x) ∧ C(x)] [B(x)]

24The question is: for which properties C is the inference valid?

25It has been argued (e.g., Pearl 1988) that probabilistic theories cannot answer this question satisfactorily. Pearl himself proposes that the inference is valid if we know that genx [A(x)] [C(x)]. However, this would get us too few inferences. For example, we will not be able to conclude from the truth of (2b) that red birds fly, because (9) is not true.

(9) Birds are red.

26But surely this is counterintuitive.

27Pelletier and Asher (1997) propose a different solution, which is based on the idea of defeasible strengthening of the antecedent. They argue that the inference pattern in question is always valid, unless it is defeated, i.e. unless we know that

genx [A(x) ∧ C(x)] [¬B(x)].

However, this move would get too many inferences. For example, suppose we don’t know whether (10) is true or not.

(10) Injured birds do not fly.

Then, according to Pelletier and Asher, we must conclude:

(11) Injured birds fly.

28But we clearly shouldn’t: it may be that (10) or (11) is true, depending on the nature and extent of the common injuries that birds suffer.

29How does probability fare ? In a later paper, Pearl (1991) admits :

I have speculated that this [phenomenon] is more in line with the rules of [Pearl’s theory] than with those of “support” or “majority” logics [i.e., probability logic]. I am now in the opinion that this agreement is more reflective of tacit assumptions of independence.

The idea is that we can conclude that red birds fly on the basis of the truth of (2b), and that’s because the properties of being red and flying are independent of each other. However, we cannot conclude from (2b) that injured birds fly, and that’s because being injured and flying are clearly not independent of each other.

30To represent these facts, we can use the mathematical notion of conditional independence. Two properties, α and β, are conditionally independent given ĸ if :

P(α ∧ β | ĸ) = P(α | ĸ) × P(β | ĸ)

It can easily be shown that if red and fly are conditionally independent given bird, the inference is valid :

P(fly | bird ∧ red) = P(fly | bird)

4.3. Reasoning with exceptions

31Another important question is the influence of exceptions on inferences. For example, suppose we believe (12a-c) ; can we conclude (12d) ?

(12)

a.

Mammals bear live young.

 

b.

Mammals have a uterus.

 

c.

Platypuses don’t bear live young.

 

d.

Platypuses have a uterus.

32According to the “all normal” approach (see, e.g., Pelletier and Asher 1997), we shouldn’t: (12c) has demonstrated that platypuses are abnormal; but (12b) is only about normal mammals, hence we are not licensed to conclude that platypuses have a uterus.

33This appears to be a desirable result ; indeed, platypuses do not have a uterus. But now consider, instead of (12b) and (12d), the following :

(12)

b′.

Mammals have hair.

 

d′.

Platypuses have hair.

34For the same reason, the “all normal” approach predicts that we cannot conclude that platypuses have hair, since (12b′) is, presumably, only about normal mammals. But this is intuitively wrong.

35The crucial factor, once again, appears to be conditional independence. Bearing live young and having a uterus are not independent given the property of being a mammal, hence (12d) does not follow. But bearing live young and having hair are independent given the property of being a mammal, hence (12d′) does follow. The probabilistic approach, far from being unable to handle such inferences, in fact captures them naturally without the need for additional assumptions : conditional independence is an integral part of the theory of probability.

4.4 Embedded generics

36Embedded generics are sometimes claimed to pose a problem for probabilistic accounts of generics. Consider (13), for example.

(13) Movies that critics love are boring.

37According to the probabilistic approach, (13) means that a movie that a critic is likely to love is likely to be boring; hence the interpretation of (13) calls for higher order probability. How is it to be interpreted ?

38It is sometimes suggested that higher order probability is interpreted epistemically (Gaifman 1988), but this won’t do here : generics, embedded or not, have objective truth conditions.

39However, higher order probabilities do not have to be epistemic : they can get a natural objective interpretation. Suppose in some country the national mint is very old and in bad shape, and 80 % of coins manufactured there are crooked. Then (14) is true.

(14) A coin manufactured in this mint is likely to be crooked.

40This is a statement of higher order probability:

P(P(a coin manufactured in this factory comes up “heads”) ≠ 0.5)) is high

41In words, (14) means the following: pick at random a coin manufactured in this mint; it is likely that the probability that it comes up heads is not 0.5. Note that both probabilities are objective, not epistemic.

4.5. Probability logic

  • 4 It might seem that 0.5 is too low a threshold, and that generics are much closer to universals, so (...)

42In previous work (Cohen 1999), I proposed that probability applies at the level of interpretation. That is to say, the logical form of (2b) is genx [bird(x)] [fly(x)], which is true iff P(fly | bird) > 0.5.4 But in order to account for embedded generics, probabilities ought to be introduced at the level of logical form—hence the need for a logic of probability.

  • 5 These logics are different, but for our purpose we can treat them as one.

43I will follow the logics of Baachus (1990) and Halpern (1990).5 First order logic is augmented with arithmetic operators, and with square brackets, whose intended interpretation is probability.

44Unconditional probability is represented as, for example : [even(x)]­x = 0.5. This means that the probability that some individual is even is 0.5. Conditional probability is represented as, for example : [fly(x) | bird(x)]x > 0.5. This says that the probability that something flies, given that it is a bird, is greater than 0.5.

45Formulas are evaluated with respect to a structure M = O, θ, μ, where O is a set of individuals—the domain ; θ is an interpretation function, defined as usual (except for probabilities, to be discussed anon), and μ is a discrete probability function on O.

46The probability function μ is extended to subsets of the domain as follows :

for every AO, μ(A) = μ(a).

47For every expression α, structure M, and assignment function υ :

⟦α⟧(M,υ) = μ({a : (M,υ[a/x]) ⊨ α})

48This definition can be straightforwardly extended to multiple variables, using product measures.

49The meaning of conditional probability can now be defined in the normal way :

[α | β]x × [β]x = [α ∧ β]x.

50There is, however, an obvious problem with this definition, if we want to apply it to generics: it is extensional, while generics, as we have seen, are intensional. In order to solve this problem, we can intensionalize the definition, by making the domain, instead of a set of individuals, a set of pairs of worlds and individuals, following Schubert and Pelletier (1989 ; cf. Gallin 1975) : O = W × D.

  • 6 We could also place additional constraints on μ. For example, Kratzer (2009) requires μ to respect (...)

51The interpretation function θ is now, of course, relativized to worlds. The probability function μ is now defined on pairs of worlds and individuals. We may require μ to respect the stereotypical ordering source : if w1 is more normal than w2, then, for all d ∈ D, μ(w1, d) ≥ μ(w2, d).6 Of course, since μ is discrete, all except for a denumerable number of worlds will have zero probability.

52Now (2b) has the following logical form : [fly(x) | bird(x)]x > 0.5 Its interpretation is, roughly : the probability that x flies in w, given that w is a normal world and x is a bird, is high.

53We can now provide a natural account of embedded generics. Consider (13), repeated below as (13a). Its logical form is (13b) which, in probability logic, becomes (13c).

(13)

a.

Movies that critics love are boring.

 

b.

genx [movie(x) ∧ geny [critic(y)] [love(y,x)]] [boring(x)]

 

c.

[boring(x) | movie(x) ∧ [love(y, x) | critic(y)]y > 0.5]x > 0.5

The interpretation of (13) is that the probability that x is boring in w is high, given that w is normal and x is a movie s.t. the probability that y loves x in w′ is high, given that w′ is normal and y is a critic. While this is a mouthful, it nicely captures the meaning of the sentence, assuming that the ordering source is stereotypical.

4.6. Generic comparisons

54Treating embedded generics in this way can help solve a thorny problem, involving generic comparisons (Cohen 1996; Nickel 2010). Consider the following perfectly natural sentence :

(15) Girls do better than boys in grade school.

55The “all normal” approach faces a problem here, since (15) clearly does not mean that all normal female pupils do better than all normal male pupils.

56Nickel (2010) attempts to solve this problem, by proposing, essentially, that (15) expresses a number of generalizations over different subsets of the pupil population. According to him, (15) means something like : All normal excellent girls do better than all normal excellent boys, all normal ok girls do better than all normal ok boys, all normal weak girls do better than all normal weak boys….

57However, Nickel’s proposal leads to incorrect predictions. Suppose there are few weak girls, but they are weaker than all the boys ; most girls are excellent, and better than all the boys. Then (15) is true, but it is predicted false according to Nickel’s account.

  • 7 Most is, of course, interpreted probabilistically, as above.

58In earlier work (Cohen 1996) I suggested that generic comparisons express quantification over pairs. For example, (16) says that “most7 pairs x,y s.t. x is a dog and y is a cat are such that x is bigger than y.

(16) Dogs are bigger than cats.

59However, now I am of the opinion that although this reading may be available, it is not the dominant one.

60Consider, for example, a situation where one third of the dogs are huge, and bigger than all cats ; while two thirds of the cats are bigger than the rest of the dogs. This situation is depicted in figure 1.

Figure 1 : Cats vs dogs

Figure 1 : Cats vs dogs

61Given this scenario, (16) is false, although in most pairs (5 out of 9) the dog is bigger than the cat. Intuitively, the reason is that most dogs are not bigger than most cats.

62Now consider the situation depicted in figure 2.

63This time, one third of the cats is bigger than all dogs, but the rest are smaller than two thirds of the dogs. Now (16) is true, although in most pairs (5 out of 9) the dog is not bigger than the cat. But again note that most dogs are bigger than most cats, which, intuitively, accounts for this judgment.

64These interpretations of generic comparisons can be accounted for in a natural way if we take them to be embedded generics. Specifically, the idea is that (16) means that “most” dogs are bigger than “most” cats. Formally, its logical form is

genx [dog(x)] [geny [cat(y)] [bigger(x, y)]].

65In our logic of probability, we get

[[bigger(x, y) | cat(y)]y > 0.5 | dog(x)]x > 0.5.

66Thus, (16) means that a randomly chosen dog is likely to be such that a randomly chosen cat is likely to be smaller than it. This cumbersome paraphrase captures the intended interpretation.

Figure 2: Cats vs dogs

Figure 2: Cats vs dogs

5. Is the ordering source stereotypical?

5.1. Theoretical considerations

  • 8 Or remain unconvinced by the arguments above, and still maintain that the modal force is a universa (...)

67We have seen evidence that the modal force of generics is not a universal, and that it is best represented as a probability measure. Recall that the modal force is only one leg of the “all normal” approach ; the other leg is the claim that the ordering source is stereotypical. These two claims are orthogonal : one can agree that the modal force is not a universal, yet still maintain that the ordering source is stereotypical.8 Yet, such a stance would have unappealing consequences.

68Recall that normality was introduced in the first place to account for the problem of exceptions : exceptions are presumed to be abnormal, while generics only quantify over normal individuals. But if, indeed, the modal force is less than a universal, exceptions arise naturally, simply by the nature of non-universal quantification. If (2b) means something like “Most normal birds fly”, then naturally this is compatible with the fact that some normal birds do not fly. Hence there is no need to make the problematic stipulation that penguins are somehow abnormal, and the notion of normality is unnecessary.

69In fact, the notion of normality cannot explain exceptions : something can be normal, yet constitute an exception. This can be seen directly in the case of adverbs of quantification (Q-adverbs).

70Q-adverbs, like generics, are lawlike :

(17) Supreme Court judges usually/often/sometimes/seldom have a prime Social Security number.

71Sentence (17), just like (1b), is odd, because there is no law relating to the Social Security number of judges. However, Q-adverbs (except for always) are clearly not universal.

72One might want to propose that Q-adverbs quantify over normal individuals, with a non-universal modal force. But then (18) would mean that some normal birds are incapable of flying.

(18) Birds are sometimes incapable of flying.

73Since (18) is true, it follows that exceptions can be normal. Hence, the notion of normality cannot account for exceptions, which was the sole reason for introducing it in the first place.

74We can conclude that the “all normal” theory fails, on both its claims. The quantifier is not “all”, but is rather a probability measure, and the idea of “normal” cannot account for exceptions.

75There are, in fact, not only theoretical considerations, but also empirical evidence against the normality approach. This evidence is seen most clearly when we compare the normality approach with an alternative.

5.2. Uniform worlds

76We have seen that the modal force of generics is a probability measure. How do we get the value of this probability ? In real life, statisticians extrapolate probabilities from past events. This is a case of induction : drawing a generalization based on individual instances.

77David Hume (1748) has established that in order for induction to work, we have to assume that the world is uniform, in the sense that future events resemble past and present ones. Even if we have observed the sun rising every morning, from the beginning of time, this does not provide evidence that it will also rise tomorrow : we can conclude this only if we assume that the future will resemble the past.

78Although this assumption is probably not warranted in general, when statisticians infer probabilities, they have to make the methodological assumption that the future resembles the past. In other words, they assume that the world we live in is uniform.

79Based on this idea, I propose that generics are evaluated with respect to a uniform ordering source : an ordering source that prefers worlds whose future resembles their past. Thus, w1w2 means that w1 is more uniform than w2.

80As usual, future and past are determined relative to the reference time : generics are evaluated with respect to an ordering source that places a constraint on the future of worlds : the time after the reference time resembles the time before it. A natural thing to ask is whether generics also place requirements on what happens before the reference time. This, I suggest, is determined by the modal base, which deserves more careful consideration than it usually receives.

81Condoravdi (2001) considers worlds to be complete histories through time. Two worlds are historical alternatives if they have the same past but possibly different futures. She defines a metaphysical modal base, which is the set of historical alternative to the actual world.

82I suggest that generics are evaluated with respect to a metaphysical modal base and a uniform ordering source. In other words, they are evaluated with respect to those worlds among the metaphysical alternatives to the actual world that are preferred by a uniform ordering source. I call such worlds uniform worlds.

83Uniform worlds share the history of the actual world up to the reference time. But from this point on, no significant change occurs : the future resembles the past. In such worlds it is true that “There is no new thing under the sun” (Ecclesiastes 1 :9).

84Hence, uniform worlds retain the stable properties of the actual world : non-stable properties will change in the actual world, but will remain the same in a uniform world.

85Note that, crucially, uniform worlds are not normal worlds. Uniform worlds do not change, whereas normal worlds do change, albeit in ways that are lawlike and follow the essential nature of things.

86Hence, normal worlds retain the essential properties of the actual world : non-essential properties may be different in a normal world.

87Which theory is correct ? Are generics evaluated with respect to normal or uniform worlds ? This question should, and can, be settled empirically.

5.3. Empirical considerations

88The decision between the two theories is not a matter of taste: it is an empirical question. The two theories make different predictions. According to the normal theory, generics are sensitive to what happens in worlds in which essential properties of the actual world are preserved. According to the uniform theory, generics are sensitive to what happens in worlds in which stable properties of the actual world are preserved.

89Let us first convince ourselves that generics are sensitive to stable properties. The following example is due to Carlson (1989) :

(19) A computer computes the daily weather forecast. (Carlson 1989)

90Carlson says (p. 179):

“the daily weather forecast” requires an intensional interpretation, where its meaning cannot be taken as rigidly referring to the present weather forecast, e.g. the one appearing in today’s copy of the Times predicting light rain and highs in the upper thirties.

91To see that this is indeed the case, suppose today’s weather forecast predicts a severe blizzard, and is consequently the main news item. However, we cannot conclude (20) from (19).

(20)

A computer computes the main news item.

92The reason is that being the main news item is not a stable property of the weather forecast: on other days the weather forecast will not be the main news item.

93Note that being the main news item is also not an essential property of the weather forecast. One might, therefore, claim that generics are sensitive to essential, rather than stable properties, and that this is the reason why (20) does not follow from (19). However, it can be easily shown that generics are not sensitive to essential properties.

94Suppose the weather report is John’s favorite newspaper feature in the actual world. Liking the weather report is a stable property of John, since such preferences do not change quickly. However, it is not an essential property of John, under any conceivable conception of essences. Hence, worlds in which he is not interested in the weather are perfectly normal. And yet, from (19) we can conclude :

(21)

A computer computes John’s favorite newspaper feature.

95My claim that generics are not sensitive to essential properties is an important one, as it provides a powerful argument against the normality approach. Hence, it requires further evidence to substantiate it. As it happens, such evidence is easily obtained.

96Suppose John fears all bats but no other animal. This is a stable property of John, but not an essential one. Hence, worlds where he likes bats are perfectly normal. And yet (22a) and (22b) have the same truth value :

(22)

a.

Bats fly.

 

b.

Animals that John fears fly.

97For another example, consider the fact that, in the actual world, the whale is the largest animal on earth. This is a stable property of the whale, but not an essential property : perhaps being large is an essential property of the whale, but it’s a contingent fact that no larger animal exists. And yet, (23a) and (23b) have the same truth value.

(23)

a.

The whale suckles its young.

 

b.

The largest animal on earth suckles its young.

98The final example involves the quetzal, which is Guatemala’s national bird. This is a stable property of this bird (the designation of a national bird remains for a long time, presumably forever), but this is not an essential property of the quetzal. And yet (24a) and (24b) have the same truth value.

(24)

a.

The quetzal has a magnificent, golden-green tail.

 

b.

Guatemala’s national bird has a magnificent, golden-green tail.

99From all of the above we can conclude that the ordering source is uniform, not stereotypical, and that generics are evaluated with respect to uniform worlds, not normal ones.

6. Generics as probability measures over uniform worlds

100We can now characterize generics in terms of the three components of modality. Their modal base is metaphysical—worlds that share the history of the actual world. The ordering source is uniform—it prefers worlds that do not change. And the modal force is a measure of high probability.

101Thus, (2b) means that a pair b,w, where b is a bird and w is a world that shares the history of the actual world, and whose future resembles the past, is likely to be such that b flies in w. In other words : for a relatively long period of time it has been the case that most birds flew, and this pattern is expected to continue.

102This view of generics explains how observations in the actual world affect the truth value of a generic, but do not determine it. In contrast, this fact is a problem for the normality approach, because it only considers normal worlds, so what happens in the actual world, which is not normal, should not affect the truth of a generic.

103We can now provide a natural solution to the generic paradox. Generics are lawlike, because laws are stable properties. Sentence (1b) is odd because in the future, it is expected that new judges will be appointed, whose Social Security number will not be prime.

104Generics tolerate exceptions, because they require high probability, but do not require that the value of this probability be equal to 1.

105To recap the main points of this paper : generics do not express universal quantification over normal worlds. Rather, generics quantify over worlds that resemble the actual world at the reference time, but do not evolve further. The quantificational force over such worlds is not universal, and can most naturally be formalized as a probability function. Using an extended probability logic, this system accounts for several problems of reasoning with generics and embedded generics. And , last but not least, it provides a solution to the generic paradox.

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Notes

1 This sentence is improved with comma intonation preceding except, but this kind of intonation also improves (4b).

2 Krifka notes that (6) has yet a third reading, which does not concern us here.

3 It must be noted, however, that this was not the main point of their paper.

4 It might seem that 0.5 is too low a threshold, and that generics are much closer to universals, so a higher number is necessary. However, 0.5, coupled with the presupposition that the domain is homogeneous, suffices to bring about this quasi-universal effect (see Cohen 1999 for the details). At any rate, in this paper nothing hinges on the value of 0.5, and the reader is free to assign a higher number if it seems more appropriate.

5 These logics are different, but for our purpose we can treat them as one.

6 We could also place additional constraints on μ. For example, Kratzer (2009) requires μ to respect her constraint of comparative possibility.

7 Most is, of course, interpreted probabilistically, as above.

8 Or remain unconvinced by the arguments above, and still maintain that the modal force is a universal, yet deny that the ordering source is stereotypical.

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Titre Figure 1 : Cats vs dogs
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Titre Figure 2: Cats vs dogs
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Référence électronique

Ariel Cohen, « Generics as Modals », Recherches linguistiques de Vincennes [En ligne], 41 | 2012, mis en ligne le 01 septembre 2014, consulté le 30 août 2016. URL : http://rlv.revues.org/2068 ; DOI : 10.4000/rlv.2068

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Auteur

Ariel Cohen

Ben-Gurion University of the Negev

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Droits d’auteur

© Presses universitaires de Vincennes

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