Genericity and Inductive Inference

Abstract

We are often justified in acting on the basis of evidential confirmation. I argue that this is because inductive inference supports belief in non-quantificational—or generic—generalizations, rather than universally quantified generalizations. I show how this account supports, rather than undermines, a Bayesian account of inductive inference. Induction from confirming instances of a generalization to belief in the corresponding generic is part of a reasoning instinct that is typically (but not always) correct, and allows us to approximate the predictions that formal epistemology would make.

1. Introduction

If members of a kind F are observed to have some property G, this may confirm a general pattern. If sufficiently many confirming instances of this pattern are observed, this may be reflected in the actions and attitudes taken toward Fs. Observing that m-many robins are red or eating n-many poisonous holly berries may (given certain thresholds are met for m and n) influence the way an observer acts toward robins and holly berries in general.

In short, evidence concerning specific members of some group can shape the decisions that observers make with respect to that group as a whole: Stella looks for trails of red feathers when searching for robin eggs; Landon decides to pack lunch for his hiking trip rather than snacking on foraged berries. These patterns of action and expectation appear to be underwritten by generalizations about kinds.

Further, the decisions being made on the basis of such observations are often rationally justified. Let us consider these claims in connection with the following plausible principle about the relationship between an agent’s evidence and the justification they have for acting:

1. JUSTIFICATION–ACTION LINK: If a belief-forming method provides rational support for some action, then that method of belief formation provides doxastic justification for a belief that underwrites it. ¹

This principle represents a central methodological commitment: that we may reason backward from claims about justification for action to claims about justification for belief. ² If an agent is rationally justified in acting on the basis of some observation—if that observation figures essentially in an explanation of their rational behavior—then that observation provides rational support for a belief that underwrites their behavior. The goal of this article is to determine the output of a certain pattern of inference by considering the actions that are rationally justified by such inferences.

Combine this principle with the earlier claim that observing sufficiently many Fs that are G can be justification for a pattern of action that appears to be explained by a generalization linking Fs to G. ³ Call the belief-forming pattern whereby observations of specific instances of a pattern are used to support generalizations a generalizing inductive inference. ⁴

When someone makes a generalizing inductive inference, they form a general belief about Fs on the basis of observing a limited number of Fs. The standard question about such inferences—often called the problem of induction—is how they can be justified, given that there is no necessary connection between observed and unobserved instances of an event. How is it rational to suppose that the next observed F will be G, given only that previous instances have been? And how can such a rational transition reflect a prima facie epistemic connection between a generalization and its confirming instances (Hume 1748/1993)? ⁵

This article addresses a different question: What cognitive states do these inferences rationalize? This way of putting the question might seem confused: to describe a particular inference pattern just is to describe a particular maneuver from a certain set of propositions, E, to another set of propositions H. So debates about what sorts of beliefs an inference licenses are really debates about different kinds of inference patterns. But there is another—I think productive—way of thinking about (and individuating) inferences: as maneuvers from a certain evidential position to a certain rational position.

The thesis of this article is that inductive inferences support generic generalizations. More thoroughly: when inductive inferences justify (a change in) patterns of action that generalize with respect to some kind F, this is by way of providing doxastic justification for a belief in a generic generalization. ⁶ Inductive inference is a reasoning tool that allows us to produce nonquantificational thoughts about kinds—to characterize and organize our thoughts about those kinds. Call this the Generic View.

Traditionally, inductive inferences are taken to support universal generalizations. ⁷ The problem of induction is often treated as the problem of figuring out “how the discovery that a great number of Fs are Gs can make it rational to be confident that all Fs are Gs” (Bacon 2020, 354, emphasis mine). After setting up the Generic View in section 2, in section 3, I argue against the traditional view. In section 4, I attempt to incorporate the Generic View into Bayesian approaches to induction. On a Bayesian approach, decisions we make on the basis of generalizing inductive inferences are justified by probability judgments. I argue that the Generic View supports such probabalistic approaches to inductive confirmation. ⁸

2. The Generic View

I will start by saying some things about what generic generalizations are. The rest of the section will elaborate the connection between inductive inferences and generic generalizations.

2.1. What are generic generalizations?

Generics express nonquantificational generalizations. Generics “express general claims about kinds,” but they cannot “be used to answer the question how much or how many” (Leslie 2012, 355). Generic sentences include “Dogs have four legs,” “Ravens are black,” “Ducks lay eggs,” and “Mosquitoes carry West Nile." ⁹ In a generic, a predicate denoting a property G is attributed to (a bare plural designator of) a kind F, without apparent quantification over individual members. ¹⁰

Generics are present in every known language, but in no language are generic sentences “marked” with an explicit generic operator. Generics are studied (by philosophers, linguists, and developmental psychologists) because of their abstruse formal properties and the important role they play in cognitive development. ¹¹

What sorts of beliefs do generics express? As Sorensen (2012) points out, “generics cannot be elliptical for universal generalizations or statistical generalizations” (445). This is a substantive assumption, but it is not difficult to motivate. As Leslie (2007a, 2017) notes, when we consider generic sentences to which we would assent, we do not think of what we’re doing in terms of a quantificational paraphrase. Young children are able to adopt and use generic generalizations years before they are competent with explicit quantification, further weakening the prospects for holding generic generalizations to be quantificational. As Sterken (2017) notes, generics do not “convey any stable or easily specifiable information about how many members of the given kind or group have the given property” (1).

A comprehensive survey of theories of generics would be too much to attempt, but I will consider two views of the beliefs that generic sentences are used to express. ¹²

2.1.1. Cognitive defaults

Most take the meaning of a generic sentence to involve a two-place operator, “Gen.” The logical form of a generic sentence ⌜ $F$ s are Gs⌝ is:

1. (1) $${\rm Gen} \,x \;[F(x)][G(x)].$$

According to an influential view, the “Gen” operator is a cognitive default generalization (Leslie 2007a, 2008): humans possess a primitive cognitive mechanism for forming general thoughts about kinds on the basis of experiences involving instances of those kinds. Generics express the cognitive state this mechanism produces.

Such defaults reflect a natural cognitive capacity for individuating kinds, often by linking them to apparently “essential” features (Leslie 2017). ¹³ Notably, we individuate kinds not only by the properties that adhere with the highest frequency among members but also properties that are striking or that adhere with more frequency in one group than another. The truth conditions for generics—now relativized to these cognitive defaults—track dimensions along which we sort the world that have historically benefitted us. ¹⁴ The grounds for accepting a generic blurs the line between epistemic and practical reason; generic beliefs will reflect our capacity to organize the world in a way that benefits us rather than merely a capacity to represent things as they are.

2.1.2 Direct kind predication

Liebesman (2011) defends the view that generics express direct predications of properties to kinds (see Leslie [2015] for a critical response). ¹⁵ Liebesman’s “simple” theory of generics shifts questions about the truth conditions of generics to questions concerning the metaphysics of kinds (Liebesman 2011; see Carlson 1982). ¹⁶ Generic statements report facts about the world, and the logical form of a generic like

1. (2) Tables have legs.

is $L(t)$ , where L denotes the property of leggedness, and t names the kind table. The truth of (2) is thus fixed in the same way as that of a simple subject–predicate sentence like

1. (3) Josh is a runner. ¹⁷

Both (2) and (3) are true just in case the subject of the statement instantiates the property. ¹⁸ To say that Josh is a runner is just to say that Josh is among the runners in our model. And what settles the question of whether it is appropriate to include Josh among the runners in our model is a matter for metaphysics.

Generic sentences are used to express thoughts about a kind rather than its members. “Cats meow” is about an individual cat in the way that “This chair is made of wood” is about the chair’s leg. Generics are helpfully thought of as singular thoughts about general objects.

2.2 Pragmatic features of generics

How can any claim be made about justification for a belief if what it takes for that belief to be true is not known? ¹⁹ Aren’t we owed a story about what it is for tables to have legs, for cats to meow? A semantic theory tells us how things have to be to make a sentence true, but only in the set-theoretic terms of a formal model—the semantic theory gives us a representation of the world but not an explanation of what worldly features make that representation accurate.

Relatedly, a theory of epistemic justification may give us the conditions under which the sorts of thoughts that are expressed by S are appropriate to have, but it can avoid questions about how the world has to be organized in order for S to be true. A theory of perceptual justification might provide an explanation for how the visual experience of a red apple is prima facie warrant for believing the apple is red, but the epistemologist does not owe us a story about what it is for an apple to be red. Likewise, we can claim that observing sufficiently many black ravens justifies the belief that ravens are black without offering a story about what it is for ravens to be black. ²⁰

As noted at the outset, the central methodological assumption of this article is that we can reason backward from an agent’s rational decisions to the belief contents that explain their decision. Rather than the truth conditions of generics, we might consider their inferential and action-guiding properties. What role do generics play in practical reason, and what are the properties generics have such that they play that role?

2.2.1. Generality

Both the universal generalization $ \ulcorner $ Every F is $G \urcorner $ and the generic generalization $ \ulcorner F$ s are Gs $ \urcorner $ can be said to express something about Fs in general. But these constructions put expression to different sorts of thoughts.

What is it to ascribe “generality” to a thought in the first place? This can be explained in terms of the inferences and actions such thoughts dispose us to make. Namely, to have a general belief about a class is to be able to reason, in a certain way, about arbitrary members of that class. ²¹ When you believe that every raven is black, this disposes you to act in a certain way toward any potential future raven you encounter. If you believe that every raven is black but you fail to act as though the next raven you encounter will be black, then you are not rational.

As Sorensen (2012) notes, “[belief] in a generic disposes one to believe that an arbitrary member of a kind will have the relevant [property]” (444)—generic propositions dispose us in at least one of the same ways that universals do. ²² To think about Fs in general is to reason to conclusions about arbitrary members of F. The exact route from a generic to our treatment of arbitrary members of a kind may depend on—among other things— the semantic theory we accept. For instance, we might insist on a normative understanding, such that a generic is about Fs in general because it tells us something about what any F ought to be like (Nickel 2016), ²³ or a dispositional understanding where a generic is about Fs in general because belief in that generic disposes us to treat arbitrary members of F in a particular way.

2.2.2. Flexibility

Generic sentences express “general propositions without being committed to full generality” (Liebesman 2011, 409). A generic of the form $ \ulcorner F$ s are Gs $ \urcorner $ expresses something about Fs in general without making a commitment to the presence of G in every instance of F. Generic sentences like “Ravens are black” and “Dogs have four legs” can be felicitously uttered even though there are albino ravens and three-legged dogs. In other words, the existence of non-G members of F does not undermine an assertion of the generic $ \ulcorner F$ s are Gs $ \urcorner $ .

You would like to get a pet, and your only criterion is that it be able to fly. I can felicitously utter, as a reminder, “Birds fly” and not have said something misleading (even though we may both be able to think of many flightless birds). Birds fly, but cats don’t; cats are clean, but dogs aren’t. Such statements are understandable and play an action-guiding role. What I have done is I have prompted you to consider, in your search for the ideal pet, the kind bird. Some mammals fly, but ’‘Mammals fly” does not—to us—seem as appropriate a thing to utter. ²⁴ Some mammals fly, but many more do not; it is not appropriate to think of the kind mammals (in this context, at least) as among the flying things. ²⁵ This flexibility means that you can take actions that generalize over kinds, without committing you to generality in full.

2.2.3. Nonquantifiability

Generics express something general about a kind, but the fact that G is true of many or most members of a kind F is neither a necessary nor sufficient condition for the generic $ \ulcorner F$ s are $G \urcorner $ to be felicitous to state. Against necessity: we can note the apparent felicity of statements like “Ducks lay eggs” (egg laying is a property that is instantiated by many, but certainly not most, ducks) and “Mosquitoes carry West Nile” (not true of many mosquitoes). ²⁶ Against sufficiency: we can note the apparent infelicity of statements like “Books are paperbacks” (true of most books) and “Humans are right-handed” (true of most humans). ²⁷

Sally Haslanger notes that generics let us sort kinds by their “striking features,” perhaps by the features that strike us as most important (Haslanger 2011, 185). The fact that many individual dogs are four-legged might strike us as an important feature for distinguishing dogs from other sorts of things (e.g., humans, birds, insects). ²⁸ Likewise, the fact that mosquitoes have the capacity to transmit viruses like West Nile might strike us as an important feature for distinguishing mosquitoes from “less dangerous” insects. This is in spite of the fact that very few mosquitoes are West Nile carriers.

2.2.4 Role in inference

It has been observed that generics often license the following sorts of (nonmonotonic) inferences: ²⁹ (P1) Birds fly, (P2) Tweety is a bird, and therefore, (C) Tweety should fly. That Tweety should fly does not entail that Tweety does fly. And although learning that Tweety is a bird may license actions taken on the basis of the belief that Tweety flies, this is a defeasible belief. That Tweety flies is a proposition we can accept for the purpose of deliberation and action, but it remains to be seen whether it is true.

The connection between such epistemic “ought” claims and rational deliberation and action is not well understood. But what ought to happen—epistemically—presumably has some impact on how one is justified to act. For instance, if you justifiably believe—or know—that it should rain tomorrow, then you seem to be justified in (among other things) acting as though it will rain tomorrow (for instance, by packing your umbrella or canceling your outdoor plans).

2.3. Generics and generalizing inferences

Imagine a rational agent who observes a large group of robins for the first time. All of the robins they observe are red. What are they in a position to conclude about robins in general on the basis of this observation? My claim is that they are in a position to conclude that robins are red.

In a generalizing inductive inference, one moves from an observation of some Fs to a conclusion about Fs in general. The evidence collected leaves open the possibility that there are unobserved Fs, but the conclusion drawn is, in part, about those unobserved members of the group. A standard way of understanding inductive inferences is as a reasoning mechanism that allows us to draw conclusions about the unobserved by virtue of what we have, in fact, observed.

We can identify two characteristic properties of generalizing inferences:

1. a. The evidence used in a generalizing inference is compatible with the feature observed in a group of Fs not holding for every F. Observing n-many Fs as having the property G is always compatible with some individual $n + x$ th F not having the property G (and the action taken with respect to the inference is taken in full view of this compatibility).

2. b. The belief justified by a generalizing inference is general: the belief that an agent comes to hold on the basis of their observation of a group of n-many Fs is a belief about Fs in general, not just a belief about n-many Fs.

Generic generalizations express something general about arbitrary members of a kind. We can take it for granted that the generality consideration in (b) is met by the Generic View and does not need to be elaborated. ³⁰ Later, I elaborate on the claim that inductive generalizations are compatible with disconfirming evidence and discuss how we might treat this as an explanatory desideratum for a theory of inductive inference. I also explain how it is that such disconfirming evidence, despite potentially overwhelming the confirming evidence, is not itself to be taken as evidence for a different generic claim.

2.3.1. Compatibility with “defeaters”

One way of putting the problem of induction made famous by Hume (1748/1993) is as a problem of reconciling the compatibility of an inductive base (an observation) with some proposition p, with the fact that p is not compatible with the conclusion of the inductive inference, which was made only on the basis of the observation. In an inference from A to B, A is compatible with p, and B is not. But the problem of induction is a problem of uncertainty. It is the problem of explaining how evidence can justify an expectation of regularity without the possibility of deductive certainty. What Hume pointed out is that we cannot be deductively certain of the regularity that we come to expect, and those who have since defended the rationality of induction have sought to defend the claim that our confidence in this regularity is nevertheless warranted.

Induction is fallible because the expectations it produces are fallible. A belief with a generic character produces expectations that can be defeated by evidence, but this evidence does not defeat the belief. In the Generic View, the object of your full belief is a generic. Generics are compatible with there being disconfirming instances of the generic (i.e., the generic $ \ulcorner F$ s are $G \urcorner $ is compatible with an F that is not G). Consider generic sentences like “Dogs have four legs” or “Ravens are black”; these can be asserted and believed despite known counterexamples (three-legged dogs, albino ravens). The generic generalization is not one of which you are going to be deductively certain (it is possible to be deductively certain of a generic, but the source of the inference should not change how you are licensed to deploy it). ³¹

2.3.2 Justified generic beliefs

The view that induction has a generic character is supported by plausible claims about when beliefs in generics are appropriate to form. When do we say that a belief in a generic is reasonable or justified? Do generalizing inferences provide this justification? (If so, under what circumstances?) To answer this first question, we can consider what it takes for an assertion of a generic to be warranted and to warrant action. ³²

Mel and Vic are searching for a piece of jewelry that has been lost somewhere on the street. They both know that the object is bronze, but nothing else. Mel has no idea what bronze looks like, so she asks Vic what to look out for. Vic has never seen the ring, but she knows what bronze looks like. Vic tries to think about what kind of thing she could tell Mel that would help; Vic reflects on bronze objects she’s seen and forms a belief that she reports to Mel:

1. (4) Bronze shines.

Vic’s assertion is justified; it even seems as though it is plausibly confirmed by what she knows about instances of bronze jewelry. Even if she knows that tarnished or oxidized bronze loses its luster, she is justified in making this assertion. Mel is then justified in acting on Vic’s assertion, by way of looking out for something that shines. The basis for Vic’s assertion (and Mel’s action) is an inductive inference.

This is not just practical justification, either. If Mel and Vic were looking for their friend’s ancient bronze armlet, which Vic knows to be oxidized, then it could be helpful for her to say, “Bronze is dull and greenish” because this belief would play a practically appropriate action-guiding role for Mel. Yet this assertion does not seem justified: in fact, Vic seems to retain justification for uttering “Bronze shines” (perhaps with an addendum like “but this armlet does not” or “but this armlet is probably green”). “Bronze shines” is assertable because it corresponds to Vic’s judgments about what bronze objects are usually or typically like; “Bronze is dull and greenish” is not assertable because it does not match Vic’s inductive base.

At least in some scenarios, then, we say that an assertion of a generic—and a corresponding belief—is justified on the basis of observations of a general pattern. It will be reasonable in such scenarios to say that generalizing inductive inferences can provide us with justification in asserting a generic.

This raises some questions about the scope of the Generic View. First: If an inductive base of n-many Fs that are G allows for counterinstances (Fs that are not G), then why shouldn’t those counterinstances form an inductive base of their own, especially given that they may outnumber the Fs that are G (as is the case for generics like “Ducks lay eggs”)? And second: Are we really meant to believe that any inductive base serves to justify a generic generalization? If the inductive base included only instances of oxidized bronze, would we be justified in asserting “Bronze is green”? What if the inductive base included only paperback books?

A lot of our judgments will depend on what information is already part of our evidence. In the case of green bronze, we theorists are in a position to know that this is an unusual feature with what Leslie calls a positive counterinstance (i.e., a counterinstance that is a “concrete alternative property” adequate for characterizing the kind [Leslie 2007b, 66]). But if we weren’t aware of this, and if all the bronze in our inductive base was oxidized, then—I claim—there would indeed be prima facie warrant for generic generalizations that match what we’ve observed. ³³ Likewise, if your inductive base included only paperback books and you did not have a great grasp of the concept of a book, you would—I take it—be justified in beliefs that books are soft, bendable, and made entirely from paper: all the properties of paperbacks.

A similar claim can be made for cases where the confirming instances of a generalization are outnumbered by its defeaters. The majority of ducks do not lay eggs, nor do most have egg-laying capacities (there is actually a sex-ratio imbalance favoring males). And yet we can be confident in stating that ducks lay eggs. But the property of being an egg-laying kind of thing—and what gives such a generalization its explanatory value—is one that requires little adherence among its members. The majority of instances of Josh are such that he is not running, but we cannot infer—on these grounds alone—that Josh does not run ever, and this is because such instances are compatible with the most plausible ways for it to be the case that Josh is a runner, and we are aware of this. Likewise, the observation that many ducks do not lay eggs does not serve for us as the inductive base for a generic because we are in a position to know that the observations we are making adhere with the same regularity in worlds where ducks do and do not lay eggs.

Observing an egg-laying duck and observing a non-egg-laying duck do both give us confirmation of (contradictory) generics. However, what it takes for these observations to confer justification may be different. This is because what it is for a predicate F or G to be true of a kind is different from what it is for that predicate’s negation to be true of the kind. The conditions under which it is true that ducks lay eggs and the conditions under which it is true that they do not are not parallel. But this means that we should not expect the conditions under which we are justified in believing each of these things to be parallel, either, given an abundance of background knowledge.

Further, although claims about the absence of properties may be hard to justify, things that entail those absences for particular individuals are not: “Ducks have penises”; “Josh naps”; “Ravens are affected by albinism.” These are all claims we seem to be perfectly justified in making on the basis of our evidence.

3. The standard picture, revisited

The standard picture of inductive confirmation is that observing sufficiently many Fs that are Gs, under the right circumstances, makes it rational to believe in a universal generalization: that every F is G. In this section, I will argue that this standard account does worse than the Generic View when it comes to explaining how an agent’s behavioral patterns are justified on the basis of inductive inferences. First, consider the following case from Bacon (2020): “It is a law that emeralds are either blue or green, but the distribution of colors is otherwise determined randomly. By chance it happens that all the emeralds in the actual world are green” (354). According to Bacon, someone who observes 100 emeralds in a row, under these conditions, is “not in a position to infer that the next emerald will be green” (354). ³⁴

Absent knowledge of the law governing the distribution of colors, I think they nevertheless are in a position to treat emeralds as green objects. ³⁵ They are justified in acting as though the next emerald will be green: that is, looking out for green things if their goal is to find more emeralds; avoiding emeralds if they have some deep aversion to green objects. This justification does not come from a belief about any particular emerald with which they might be confronted, that it is green, but instead from the fact that it ought to be—based on what’s been observed—and is thus rationally treated as such. Believing that every arbitrary F is G is irrational, but treating arbitrary Fs as G may not be.

Of course, in some cases, a very inductive-looking leap from one’s evidence to a universal generalization is rationally possible. If I observe 35 South China tigers and I see that they are all striped, I may be justified in believing that all South China tigers are striped if I also have the justified belief that there are roughly 35 to 40 South China tigers living in the wild.

This kind of likelihood is generated by the antecedent knowledge that there are roughly n-many such tigers in the wild. This seems to provide an expected regularity for my observation, which gives certain hypotheses a statistical advantage. The same thing can be found in a case where I observe 100 ravens and have a background belief that ravens do not vary in color (I would, in fact, be wrong to hold this belief because there are albino ravens). I have an expectation that future instances of gravity’s pull that I observe will behave in roughly the same way as all the instances of it I have observed. I have only observed a small fraction of all the instances of gravity’s pull there will ever be, but I have a strong and justified expectation of regularity.

Bacon’s example provides some insight into when a universal generalization might be justified to believe. Surely, there is always some expectation of regularity that constrains our observation. Even if the very moderate skepticism I am advocating is correct, there will always be a universal generalization that can be rationally believed on the basis of confirming evidence. If I make an observation of some Fs, and those Fs are all G, there will always be a universal generalization of the following form that we can justifiably believe:

1. (5) $\forall x((Fx \wedge \Delta x) \to Gx),$

where $\Delta $ is the set of properties provided by the regularity. For example, if I observe several koalas in a zoo, and they all have sharp teeth, I would plausibly be justified in believing that all koalas I have seen in the zoo have sharp teeth. The restricting property of having been seen by me in the zoo is provided by the expectation that perceptual deliverances are an adequate guide to reality. ³⁶

These $\Delta $ -restricted generalizations, as I will call them, satisfy the compatibility feature discussed in section 2.2.1. ³⁷ If we take F to be the group that the belief is about, then a generalization of the form in (5) is compatible with there being members of the group F not having property G. The existence of koalas without sharp teeth is compatible with the fact that every koala in the zoo has sharp teeth. But this comes at the cost of giving up generality with respect to all members of the group F.

There are also certain cases in which the generic offers an explanation of your action and an action-governing universal generalization does not.

Ginger and Mel B. are camping in a national park. They learn something interesting from two other groups of park patrons: that on two separate occasions, in two different parts of the park, these groups had their campsites ransacked by foxes that only took one thing, cold chicken sandwiches. Ginger and Mel B. are reasonably sure that it is not very likely that every fox in the park has a taste for cold chicken sandwiches. And the park is vast enough that they can also be reasonably sure they will not run into the particular foxes that stole from these other park patrons.

The only universal generalization that Ginger and Mel B. are justified in making on the basis of the information they have is one that takes scope over a small portion of the park’s foxes. The domain over which they generalize does not plausibly include the next fox they will encounter. Thus, although they are capable of making some sort of restricted generalization, they are not justified in forming any belief about the next fox they will encounter on the basis of that restricted generalization.

But Ginger and Mel B. see this as evidence of a trend among the park’s foxes, and intuitively, they are justified in a decision not to pack cold chicken sandwiches on the basis of the information they got from the other park patrons; they are justified in acting on the basis of something they learned when they heard that two groups of foxes had developed a taste for cold chicken sandwiches. (Consider that if they had been in a park without any instances of this phenomenon, their concerns would have been different.) Further, this action takes the form of patterns of behavior that seem to generalize with respect to the park’s foxes.

When you act on the basis of an inductive generalization, and you are justified in acting this way, what best explains your taking the action you do is a belief with a certain set of properties. If we take this to be a matter of full belief, then the only beliefs that have these properties are beliefs in generics. Whatever explains your behavior in this case has a number of relevant features. (a) It is a general belief about foxes in the park: you believe something about foxes in this park as a kind (that they have a taste for chicken sandwiches). It is a belief about the whole group of foxes, but it is not a belief about the sum of individual foxes that make up that whole. (b) It seems immune to “counterexample”: the fact that some foxes are known or presumed not to have developed a taste for cold chicken sandwiches is not a defeater for your belief. Finding a fox that does not have such a taste does not necessarily change your opinion of foxes in the park generally. (c) It seems sensitive to features that are relevant for distinguishing this group from others: learning that some small number of foxes have developed this taste motivates you in acting, but learning that two of the park’s coyotes are male should not lead you to take action to prepare for the park’s coyotes to be male. (d) It has no associated quantity: although you may have antecedent reason for believing that some number of foxes have a taste for cold chicken sandwiches, that is not what motivates your actions. What motivates your actions is a belief about foxes that you have in spite of this quantity.

4. Bayesian decision theory

The discussion so far has been framed in the terms of traditional debates about confirmation: debates about how we justifiably come to believe propositions on the basis of our confirming evidence. Whereas it is traditionally thought that observing a sufficient number of Fs that are G justifies a commitment to the claim that all Fs are Gs, I have argued that such observations are more appropriately taken to justify a commitment to the proposition expressed by the generic sentence $ \ulcorner F$ s are $G \urcorner $ .

Bayesian accounts of confirmation eschew talk of “justification” in favor of rational probabilities for hypotheses, given our evidence and prior probabilities. Bayesian accounts treat inductive inference in terms of incremental increases in the probability we are rational to assign some proposition (a hypothesis H) on the basis of our evidence (E) that lend probabilistic support to that proposition, where that support is measured in terms of an agent’s prior probabilities relating E and H.

Consider the proposition that all ravens are black (H): observing a black raven (E) raises your degree of confidence in the overall proposition, based on the following rules:

1. 2. ${P_{{\rm{new}}}}(H) = {P_{{\rm{old}}}}(H|E)$ .

2. 3. $P(H|E) = P(H){{P(E|H)} \over {P(E)}}$ .

Given that the proposition that all ravens are black entails that any given raven will be black, $P(E|H)$ will necessarily be 1 (by the Kolmogorov axioms of probability theory). Thus, as long as an agent has fixed prior probabilities in H and E, we can determine their probability assignment for H given E and thus what their change in credence ought to be, given that they have observed a black raven (namely, that their new credence in H should be their prior conditional credence in H given E). ³⁸

According to the Bayesian, we start with a background probability assignment linking any given member of some kind to a property. Let’s say we assign a prior probability of n (where $0 \lt n \lt 1$ ) to any given F being G. Observing any F that is G raises this probability by a predictable amount—exactly what amount will depend on an agent’s priors.

How can the Bayesian strategy be reconciled with my proposal? I will suggest two such strategies of reconciliation: one strategy ties the justification conditions for generic beliefs more directly to norms of instrumental rationality, which is explained by Bayesian methods. Another strategy implicates generics more directly in the Bayesian methodology, as either the objects of credence or the sources of our prior probabilities.

4.1. Compatability

It is possible that Bayesian and traditional full-belief models for action have distinct, but complementary, explanatory aims. Weisberg (2013) argues that Bayesians and traditionalists are after different things when talking about rational action. The aim of Bayesian decision theory is to tell us what is ideally rational; the aim of a traditional account of confirmation is to tell us what assumptions we are justified in relying on when we act. Presumably, we would like to do what is rational. However, we may not always have the cognitive tools necessary to do so at our disposal.

This difference can be highlighted by analogy: Imagine a perfect food pyramid, which says exactly what portions of which foods one ought to eat in order to maximize their health and well-being. The food pyramid tells us, more or less definitively, what it is good to eat. Of course, we do not have access to such a food pyramid. So, we have developed (via selective pressures) our own sets of tools for determining the healthiness of foods (how they make us feel, their taste, color, etc.). This is how, without having tasted poison, I am able to tell that something tastes wrong. The goodness of our diet can be measured against the health ideal of the food pyramid; however, the tools that we use to pick the foods we eat bear almost no resemblance to the food pyramid. ³⁹

So, there is some rational condition, elucidated by Bayesian methodology, but that rational condition is hard for us to achieve. Rationality is too demanding when it comes to certain kinds of reasoning, especially statistical reasoning that measures the prevalence of a property in a group. But we can shortcut this with certain sorting techniques. Our set of cognitive tools can provide us with judgments that enable a rough behavioral approximation of the Bayesian ideal, but at the cost of being much less accurate. Such simple heuristical reasoning is what we typically put to use in decision-making. Bayesians tell us what it is rational to do, but the Generic View tells us what sorts of mental representations enable us to justifiably act.

As Weisberg notes, there is a “massive research program in psychology dedicated to determining what methods we use, when we use them, and how effective they are at generating expected-utility-maximizing choices” (Weisberg 2013, 6). ⁴⁰ One upshot of this research has been the discovery that we seem to favor “economical” methods, like making decisions on the basis of full beliefs, rather than more “expensive” Bayesian methods. This way of dividing things up seems to make Bayesian decision theory a theoretical tool for determining rational action and full belief a practical tool that we actually use. This is not quite how we should draw the line. It is obviously possible, even if it is not likely, that someone will use a decision-theoretic method to make a decision. We might instead think of the division as drawing the line between what people ought to do (ideally) and what people generally do to match the ideal. What you do in reasoning is a low-powered way of matching what decision theory (a high-powered method) says is rational.

So, the Generic View can be situated within the project of discovering a “psychologically plausible notion of rationality” (Gigerenzer et al. 2000). This makes the claims of this article (and of research on the links between full belief and action in general) conditional: given that we use economical methods to reason, you are justified in believing a generic about Fs on the basis of a generalizing inference from your evidence base.

I think this reconciliation is promising. We can explain what it is instrumentally rational for an agent to do by appeal to the complex principles of a robust decision theory. What it is instrumentally rational for an agent to do may sometimes involve behaviors that appear to be or depend on generalizations about certain kinds. A natural shortcut for limited agents like ourselves would be to represent those generalizations.

Generics may express what Kahneman and Tversky call System 1 judgments (Leslie 2007a); these are the judgments produced quickly and with little deliberative effort. ⁴¹ Leslie treats generics as cognitive default generalizations—according to Leslie, generics “give voice to our most primitive, default generalizations, while explicit quantifiers, in contrast, require our conceptual system to actively diverge from this default” (Leslie 2007a, 382). Empirical evidence that this is the case comes from experiments involving young children, who are able to recall quantifiable information generically but struggle with abstract quantificational characterizations. ⁴²

4.2. Humean views

Bayesianism is not immune to Humean skepticism. In the Bayesian story, our probabilities are relativized to prior beliefs and credences, and the prospects of reducing all of these to a priori judgments are slim. For instance, the agent’s prior probability concerning the likelihood of H given E is dependent on the probability they assign to E (in this case, the probability that a particular raven will be black). But isn’t the Humean point exactly that this probability cannot ever be known? That is, there is no way of working out from first principles how likely it is that any given raven will be black, unless those first principles are stipulated. Substantive principles matching our prior probabilities to various features of the world have been proposed, but—reasonable as many of them sound—they still fall prey to the Humean skeptical argument.

But the Generic View can be incorporated into the Bayesian solution in a different way, too: we might, for instance, hold that the contents of our probability assignments are generic sentences (see Silva [2020] for an interesting suggestion along these lines). Having a credence of 0.6 that all ravens are black means taking it to be 60% likely that any unobserved raven will be black. But the problem of induction is one of showing how exactly this sort of prediction—a prediction about the likelihood of some unobserved thing happening—can be made. ⁴³ We have no more reason—based on what we’ve already observed—to take this to be 60% likely than we do to take it to be 2% likely, or so the Humean will claim.

But taking it to be 60% likely that ravens are black need not have this implication. If we hold that such beliefs are not nestled in the probabilistic structure of the universe, then we need not posit any relationship here at all. The “simple” theory of generics discussed earlier holds that generic sentences like “Ravens are black” express “bare” facts about the world: the kind raven instantiates the property of being black. And there is no reason to think that this sort of thing can’t be more or less directly observed.

This is not to say that there is no connection between generic sentences and probabilities concerning their instances. As Silva (2020) notes, the observation of instances of a generic should make us more confident in that generic. This picture of reconciliation between Bayesian and generic approaches to induction can be extended to operator views as well. Here, the precise relationship between the generic operator and probabilities is important. To give just one example, an operator view that ties the metaphysical truth conditions for generics to something like normality (Nickel 2016) or contextually fixed probabilities (Sterken 2015b) will “explain quantificational variation as an epiphenomenon” (Sterken 2017, 4).

More generally, if we think of epistemic space as corresponding to a set of probability spaces, then any modal claim will supervene on probability distributions, even if there was no way of reading from the modal to a particular probability distribution (claims of the form $ \ulcorner $ Might $p \urcorner $ are true by virtue of some probability space[s] being salient). So generics qua “Gen” will always correspond to probabilistic learning of one kind or another. A full story of how this is still needs to be worked out. But the point is that having any particular credence in a generic does not commit you to precise probabilities concerning unobserved instances of that generic. Thus, incorporating genericity into our Bayesian explanations may allow us to address one of the problems of induction.

5. Conclusion

The role of generics in reasoning has been underexplored. This article is a programmatic attempt at correcting this by exploring some of the advantages of the Generic View over standard views of induction.