Justification as a dimension of rationality

Abstract

How are justified belief and rational belief related? Some philosophers think that justified belief and rational belief come to the same thing. Others take it that justification is a matter of how well a particular belief is supported by the evidence, while rational belief is a matter of how well a belief coheres with a person’s other beliefs. In this paper, I defend the view that justification is a dimension of rationality, a view that can make sense of both of these conflicting accounts. When it modifies belief, ‘rational’ is a multidimensional adjective, as there are multiple dimensions along which a belief can be rational. I will argue that one of these dimensions is justification, an account that can not only explain why philosophers give diverging theories of the relationship between justified belief and rational belief, but can also reveal why rational belief and justified belief are closely related despite being distinct.

1 Introduction

A number of epistemologists have thought that ‘rational belief’ and ‘justified belief’ are synonymous. Ralph Wedgwood says that, at least in the way epistemologists use the terms, “phrases like ‘rational belief’ mean exactly the same thing as ‘justified belief’,”¹ while Declan Smithies thinks that “to say that a belief is justified is to say that it is rational or reasonable.”² Sinan Dogramaci simply notes, as an aside, that the terms can be used interchangeably—“Rationality, justification, reasonableness: same thing. Use whichever word you like.”³ ‘Rational’ and ‘justified’ are now so commonly regarded as synonymous that many authors do not even bother to note that they use the terms interchangeably. Maria Lasonen-Aarnio captures this prevailing practice, pointing out that “as is rather standard amongst epistemologists, I have spoken about epistemic justification and epistemic rationality in one breath.”⁴ Thus, not only do a number of philosophers say outright that the rationality and justification of belief come to the same thing, many more simply treat it as the default position.

Despite the number of epistemologists who adopt this position, rational belief and justified belief do not come to the same thing, as their behavior diverges at the top of their scales. Consider, for example, the following case⁵:

Small Town Election

Warren and Greg live in a small, rural town with just over one thousand residents. Warren is counting the ballots from the recent mayoral election and finds that Naomi won the election 467–212. The next day, Greg also learns that Naomi won when he reads it in the town newspaper.

In this scenario, both Warren and Greg are justified in believing that Naomi has been elected mayor. They both have good evidence to think that she won, Warren through counting the ballots and Greg through reading the newspaper, such that the truth values for (1) and (2) coincide:

• (1) Warren and Greg are both justified in believing that Naomi won

• (2) Warren and Greg are both rational in believing that Naomi won

Even though it seems possible that ‘rational’ and ‘justified’ are synonymous in (1) and (2), this cannot be the case, as the truth values of (3) and (4) come apart:

• (3) Warren is more justified than Greg in believing that Naomi won

• (4) Warren is more rational than Greg in believing that Naomi won

While it is plausible that Warren is more justified than Greg in believing that Naomi won—after all, he was the one who counted the ballots—it seems obviously wrong to say that Warren’s belief is more rational than Greg’s. Rather, because they both adopted the belief that was justified for them, it seems that they are equally rational.

Even though Small Town Election makes a strong case that ‘rational belief’ and ‘justified belief’ are not synonymous, it also leaves a number of unanswered questions. It is not a fringe view to think that rational belief and justified belief come to the same thing – it might even be the dominant account. If ‘rational’ and ‘justified’ are not synonymous, though, then we need an answer to the Synonymy Question:

Synonymy Question—Why have so many philosophers taken ‘rational belief’ and ‘justified belief’ to be synonymous?

If it is not true that being rational and being justified are the same property, then the fact that a considerable number of philosophers think that ‘rational belief’ and ‘justified belief’ are synonymous could use some explaining. Philosophers are far more likely to posit multiple senses of a term than they are to declare distinct terms as synonymous. To see this, we need look no further than justification itself. Even if we limit ourselves to just epistemic justification, the types of justification that have been posited include propositional and doxastic justification, immediate and mediate justification, prima and ultima facie justification, and personal and objective justification, amongst others. This makes it particularly striking that a number of philosophers have thought that we do not need to distinguish between rational belief and justified belief. Why think that they are synonymous to begin with?

One reason, perhaps, that philosophers have regarded ‘rational belief’ and ‘justified belief’ as synonymous is that they seem closely related. Robert Audi has argued that rationality and justification are intertwined, saying that “a natural and promising way to begin to understand rationality is to view it in relation to its sources. The very same sources yield justification, which is closely related to rationality.”⁶ One theory, of course, for how the two are related is that they come to the same thing. Where does that leave us, though, if ‘rational belief’ and ‘justified belief’ are not synonymous? Thus, another unresolved issue is how exactly rationality and justification are connected:

Linking Question—Are rational belief and justified belief actually closely related? And if so, how?

The simple answer is that a belief’s being rational and being justified are the same property, but that account is undermined by cases like Small Town Election. If rational belief and justified belief are not equivalent, then how else might they be closely related?

Against the thought that rational belief and justified belief are somehow intertwined, another view has developed that keeps rationality and justification strictly distinct. On this way of thinking, rationality and justification are actually quite different, with rationality picking out the coherence of a particular set of beliefs and justification referring to those beliefs which are supported by one’s evidence/epistemic reasons. Alex Worsnip exemplifies this alternate account, saying that “In my view, the term ‘justified belief,’ in contrast to ‘rational belief’, is best used simply to refer to a belief’s being supported by the evidence,” whereas “rationality is a matter of the right kind of coherence between one’s mental attitudes.”⁷ James Pryor gives a similar account, arguing that what beliefs are rational and what beliefs are justified can come into conflict—“I will count a belief as rational when it’s a belief that none of your other beliefs or doubts rationally oppose or rationally obstruct you from believing. This makes “being rational” a different quality than having justification. A subject can have some justification to believe p, but be unable to rationally believe p on the basis of that justification, because of some (unjustified) beliefs and doubts he also has.”⁸ Both Worsnip and Pryor treat rationality as merely a matter of how beliefs fit together, whereas justification concerns the evidence/epistemic reasons that a person has for their beliefs. This view would answer the linking question by saying that, though ‘rational’ and ‘justified’ can both be used to evaluate beliefs, they pick out distinct properties.

There is, thus, another way of characterizing ‘rational belief’ and ‘justified belief’ other than the synonymy account, a view which takes them to be quite distinct. But this is rather surprising. How could it be that, while a large number of philosophers thought that ‘rational belief’ and ‘justified belief’ were synonymous, another tradition sprang up that treated rationality and justification as strictly distinct, taking rationality to be merely a matter of coherence?

Coherence Question—Why have a number of philosophers taken rationality to just be a matter of coherence?

We, thus, have three outstanding questions about the relationship between justified belief and rational belief—why so many philosophers took them to be the same thing, why a separate tradition arose on which rationality refers only to the coherence of a set of beliefs, and how justification and rationality are actually related.

In this paper, I plan to defend answers to all three of these questions. I will argue that justification is a dimension of rationality, a position that can explain not only why some philosophers have thought that ‘rational’ and ‘justified’ are interchangeable while others have held that rationality is purely a matter of coherence, but can also show how rationality and justification are related. In Sect. 1, I will distinguish between unidimensional and multidimensional adjectives, arguing in Sect. 2 that ‘rational’ is multidimensional. Just as there are multiple dimensions on which a person can be healthy, there are multiple dimensions on which a belief can be rational.⁹ I will then argue in Sect. 3 that justification is one dimension of rationality, an account that opens up a strategy for providing answers to the Synonymy Question, the Linking Question, and the Coherence Question. After introducing this account of rational belief, I will then consider two potential objections in Sects. 4 and 5 – Scanlon’s argument that only coherence considerations contribute to irrational belief and the externalist view that it is possible to describe someone as rational but not justified. Whether a belief is justified is a dimension of whether a belief is rational, an insight that offers a definitive link between the justification and rationality of belief.

A brief note before we begin. Some epistemologists may treat terms like ‘rational’ and ‘justified’, not as picking out the properties of rationality and justification, but simply as tools for referring to some general positive epistemic status. Take, for instance, Pryor’s claim that his “main interest when doing epistemology is in the conditions, nature, and ‘logic’ of a status or quality that folk language may have no unambiguous direct expression for. I can direct the attention of theorists to this status by calling it ‘prospective justification or warrant to be more confident’ that something is the case.”¹⁰ For the purposes of this paper, I will consider how we should understand the relationship between rationality and justification if we treat ‘rational’ and ‘justified’ as actually picking out these properties rather than being a rough way of referring to some other, distinct epistemic status.

2 Multidimensional adjectives

2.1 Unidimensional and multidimensional adjectives

A number of adjectives are multidimensional in that there are multiple underlying dimensions that affect whether or not they apply.¹¹ Compare the adjectives ‘tall’ and ‘healthy.’ Whether someone is tall is a function of a single dimension, height, whereas whether someone is healthy is a function of multiple dimensions. A person can be made unhealthy by having high blood pressure, broken bones, a contagious virus, or a weakened immune system. This, of course, is not to say that there is no contextual variation in who counts as tall. The height required to count as tall amongst basketball players is greater than the height that is required amongst elementary school students, but what makes ‘tall’ unidimensional is that this contextual variation occurs only along the dimension of height. ‘Healthy,’ on the other hand, is multidimensional, as it involves more than just one underlying component. As we can see in Fig. 1, the primary characteristic that distinguishes multidimensional from unidimensional adjectives is that they have multiple underlying dimensions that are used to determine when they apply.

Fig. 1

Uni- vs. Multi-dimensional adjectives

A number of linguistic tests can be used to reveal whether an adjective is uni- or multidimensional. Multidimensional adjectives, for example, permit sentences that quantify over all of their dimensions:

• (5) Joe is healthy in every respect

• (6) The boxes are identical in every respect

• (7) Susan is honest in every respect

Due to their multiple underlying dimensions, ‘healthy,’ ‘honest,’ and ‘identical’ all easily accept the “every respect” construction. Just as it is possible to be healthy in a number of respects, it is also possible to be identical in a number of respects. Two boxes can be identical with respect to their color, weight, height, length, width, etc. The same is true of honesty. In his recent work on the virtue of honesty, Christian Miller has pointed out that honesty involves more than just avoiding telling lies. In particular, it can count against someone’s honesty if they act deceitfully, break their promises, or cheat their employer.¹² The dimensional aspect of these adjectives is also on display with interrogatives:

• (8) In what ways is Joe healthy?

• (9) In what ways are the boxes identical?

• (10) In what ways is Susan honest?

Just like we can say that someone is healthy or honest in every respect, we can also inquire as to what ways they are healthy or honest. It may be that a person is healthy or honest in every way, or it could be that they are only healthy or honest in a few ways. Regardless of how healthy or honest someone is, though, multiple dimensions are required to assess whether they possess these characteristics.

Unlike multidimensional adjectives, unidimensional adjectives sound much less natural in “every respect” constructions:

• (11) ?Dan is tall in every respect

• (12) ?The cup is empty in every respect

• (13) ?The rope is long in every respect

The issue with (11–13) is that ‘tall,’ ‘long,’ and ‘empty,’ pick out just one dimension. ‘Tall’ picks out where someone falls on a scale of height, ‘empty’ picks out how much substance there is in a container, and ‘long’ picks out where an object falls on a scale of length. This is not to say that these terms can never be used in any other sense. ‘Long,’ for instance, has both a temporal and a spatial sense—just as a rope can be (spatially) long, a shift at work can be (temporally) long. What differentiates multidimensional adjectives, however, is that they encode a number of characteristics within just one sense of the term. I need to consider multiple dimensions before I can dub a person healthy, but I only need to consult one dimension in order to call a rope long. Because unidimensional adjectives only encode one dimension, we also encounter issues with interrogatives:

• (14) ?In what ways is Dan tall?

• (15) ?In what ways is the cup empty?

• (16) ?In what ways is the rope long?

All of (14–16) sound amiss. If we know that Dan is tall, there is no further information to be gained about the ways in which this is so. There is only one way which this could be true—whether he meets the contextual standard for height in a given scenario. Likewise, there are not multiple ways in which the cup can be empty. The only dimension that ‘empty’ picks out is how much of a particular substance there is in the cup. And even though ‘long’ has different senses, only the spatial sense is under consideration when we are talking about a rope. Thus, unidimensional adjectives do not allow discussing various underlying dimensions in the same way that multidimensional adjectives do.

Even though multidimensional adjectives involve multiple dimensions simultaneously, it is possible to specify which dimensions we care about in a particular situation. Consider the following:

• (17) With respect to his cardiovascular health, Joe is healthy

• (18) In terms of their height and weight, the boxes are identical

• (19) When it comes to keeping her promises, Susan is honest

All of (17–19) allow for dimensional specification. Not only can we speak of being healthy or identical in general, but we can single out certain respects in which someone can be healthy or honest. Instead of just talking about whether two objects are identical in general, we can specify the ways in which they are identical, in this case their height and their weight.

Dimensional specification need not always be explicit. Oftentimes, context limits the dimensions under consideration. Take, for instance, a nurse who, removing a cast from a patient’s arm declares, “It looks like you’re healthy!” If the doctor disputes the nurse’s claim, saying that the patient still has high blood pressure, the nurse can maintain that they were only talking about the patient’s fractured arm. Or suppose that an interior decorator is asked about the color of the two bedrooms in a newly renovated home. If in response they say, “The bedrooms are identical,” it would be strange indeed to disagree by remarking that the rooms have different widths and lengths. Context can, thus, help specify which dimensions are under consideration with particular uses of multidimensional adjectives.

Whereas multidimensional adjectives allow for dimensional specification, unidimensional adjectives, once again, behave somewhat differently:

• (20) ?With respect to his _________, Dan is tall?

• (21) ?In terms of its _________, the rope is long?

• (22) ?When it comes to _________, the cup is empty?

With all of (20–22), it is unclear how we would sensibly complete them. For instance, suppose that we completed (21) by saying that, in terms of its length, the rope is long. Even though this would not be ungrammatical, it does not further specify the dimension of longness to which we are referring, as only multidimensional adjectives allow for dimensional specification.

2.2 Multidimensional adjectives: conjunctive, disjunctive, and additive

We can also distinguish between conjunctive and disjunctive forms of multidimensional adjectives. Conjunctive adjectives quantify over all of their contextually relevant underlying dimensions. If two boxes are the same size but differ in color, it is acceptable to say that they are not identical, revealing that ‘identical’ is a conjunctive, multidimensional adjective. In order to be identical, two boxes must be identical with respect to all of the relevant underlying dimensions. This is not to say that we must always consider every dimension. As we have already seen, context can specify the particular dimensions that are at issue. In the case of the interior decorator, only color is relevant for whether the rooms can be described as ‘identical’. However, when they are not used in a way that specifies a particular dimension for consideration, conjunctive adjectives require that all of their dimensions fall in the appropriate range.

Disjunctive adjectives, on the other hand, only require that one of their underlying dimensions falls in the appropriate range. Consider, for example, the multidimensional adjective ‘nonidentical’. There are a number of dimensions along which two boxes can be nonidentical, but it only requires one of these to judge that the two boxes are nonidentical simpliciter. Two boxes can fail to be identical because they are different colors, different lengths, or different heights. As seen in Fig. 2, conjunctive multidimensional adjectives must rise above the necessary contextual threshold in all of their relevant dimensions, while disjunctive multidimensional adjectives only need to fall below the threshold in at least one of their relevant dimensions.

Fig. 2

Conjunctive vs. Disjunctive multidimensional adjectives

If we were to represent this a bit more formally, where DIM is a function from contexts c and predicates P to predicates p, DIM(P, c) picks out all the relevant dimensions of P at context c, e.g. DIM(identical, c) picks out all the contributing features of similitude that are relevant in context c. Thus, a multidimensional adjective is conjunctive if and only if it satisfies the universal quantifier such that $\lambda$ x.$\forall$ Q $\in$ DIM(P, c):Q(x). On the other hand, a multidimensional adjective is disjunctive if and only if it satisfies the existential quantifier such that $\lambda$ x.$\exists$ Q $\in$ DIM(P, c):Q(x).

It is also important to acknowledge a third variety of multidimensional adjective, lying between the conjunctive and the disjunctive. Additive multidimensional adjectives are like the conjunctive in that they require more than one dimension to fall in the appropriate range. At the same time, though, it is not necessary that all dimensions must do so. Take, for example, our earlier example ‘healthy’. If I am slightly unhealthy along one dimension, say by having high blood pressure, it seems too strong to conclude that I am unhealthy simpliciter. In order to count as unhealthy, I would need to be very unhealthy along a single dimension or somewhat unhealthy along several. Thus, it is possible to be healthy overall even though I am not healthy in every respect, making ‘healthy’ an additive multidimensional adjective.

3 ‘Rational’ as a multidimensional adjective

Now that we have laid out the characteristics of multidimensional adjectives, I will argue that ‘rational’ is a multidimensional adjective, making the case that it is either additive or conjunctive. From recent work in epistemology, it should already be familiar that a number of authors have proposed that there are multiple respects in which a belief can be rational, structural and substantive rationality. The distinction goes roughly as follows. Structural rationality is what gives rise to coherence requirements, norms that govern the way that beliefs should hang together. Popular norms of structural rationality include that beliefs should be logically consistent or that lower and higher-order beliefs should be enkratic. Whereas structural rationality might require that particular sets of beliefs be logically consistent, substantive rationality requires that you respond correctly to your reasons or evidence. If your beliefs are due to bias or wishful thinking instead of strong evidence, you are violating the requirements of substantive rationality. When applied to individual beliefs, a belief is substantively rational if it is supported by someone’s evidence and it is structurally rational if it coheres with their other beliefs.¹³ In the remainder of this section, I will argue that, for a belief to be fully rational, it must be both structurally and substantively rational, making ‘rational’ a multidimensional adjective.

A number of recent authors make use of the distinction between structural and substantive rationality. Daniel Fogal says that he “take(s) there to be two threads in our thought and talk about rationality” both “responding correctly to the reasons one has” and “having the right structural relations hold between one’s attitudinal mental states.”¹⁴ Pryor notes that, when it comes to discussions of the normativity of coherence and the normativity of reasons, there is a trend for epistemologists to “use ‘rationality’ to refer to the whole genus.”¹⁵ Worsnip has also moved from equating rationality with structural considerations to recognizing that both “structural and substantive rationality are two distinct but equally genuine kinds of rationality.”¹⁶ And even though the language of structural and substantive rationality may be fairly recent, the distinction itself has historical precedent. In their book Evidentialism, Earl Conee and Richard Feldman speak of both types of rationality, saying on the one hand that “it is quite credible to suppose that rational belief formation at least partly consists in adopting beliefs because they fit well with other things that the person thinks” while also maintaining that “the epistemically rational thing to do at any moment is to follow the evidence.”¹⁷ Audi argues that rationality is composed of more than just coherence requirements,¹⁸ while Scanlon acknowledges that ‘rational’ is often applied to both structural and substantive rationality before arguing that its use should be limited to cases of structural rationality.¹⁹

‘Rational’ is multidimensional in that substantive and structural rationality both contribute to the overall rationality of a belief. One characteristic of multidimensional adjectives that we saw in Sect. 1 is that they permit sentences that quantify over their different respects. The same is true of ‘rational’. Take, for example, the following case:

Precipitation Prediction

Mary is researching precipitation figures in the northwestern United States. She learns that, over the past ten years, there has never been a year that Seattle has had less than 30 inches of rain. From this, she infers that Seattle is very likely to get 30 or more inches of rain in the coming year.

So long as it does not conflict with any of her other beliefs, Mary’s belief p, that Seattle is very likely to get 30 or more inches of rain next year, is both substantively and structurally rational. Not only is p supported by her evidence, but it is reasonable for Mary to infer p from her belief that Seattle has never had less than 30 inches of rain in the past ten years. Because Mary’s belief is both substantively and structurally rational, that makes (23) a very natural assessment of her belief:

• (23) Mary’s belief that p is rational in every respect

Not only is (23) a natural evaluation of Mary’s belief, but because there are multiple respects in which her belief is rational, (24) is also a sensible request:

• (24) In what ways is Mary’s belief rational?

Unlike with the unidimensional adjectives in (14–16), it seems like there are sensible answers we could give to (24). We could say that she has strong evidence that Seattle typically gets more than 30 inches of rain, or we could say that this belief fits well with her other beliefs about Seattle rainfall. Thus, we can see that ‘rational’ is like other multidimensional adjectives in that it allows quantifying over multiple respects.

Not only is ‘rational’ multidimensional, as it passes these tests of quantification, but ‘rational’ is also additive or conjunctive, as serious failures of either substantive rationality or structural rationality are enough to prevent a belief from being fully rational. Consider the following vignette:

Southside Sluggers

Bill is a committed fan of his favorite baseball team, the Southside Sluggers. This week, the Sluggers are playing their rival, the Hometown Hitters, in a seven game series. Because he is biased in favor of the Sluggers, Bill forms the belief that the Sluggers will win the series even though there is strong evidence that they are less talented than the Hitters. Later in the week, the Sluggers have lost three games and have only won once, making it very improbable that they will come back to win the seven game series. Nevertheless, Bill stands by his belief that the Sluggers will win the series, reasoning that, because they will win the series, that also means that they will be victorious in each of the next three games.

Bill’s belief q, that the Sluggers will win the series, rationally commits him to the belief r, that the Sluggers will win the next three games. Unless he gives up q, it would be a violation of structural rationality for him to also believe that the Sluggers will lose one of the next three games. However, unlike Mary’s belief p in Precipitation Prediction, Bill’s belief r is not rational in every respect. In particular, r is not supported by the evidence. Not only are the Hitters more talented than the Sluggers, but the Hitters have already won three of the required four games to win the series. Because Bill’s belief r is substantively irrational, it seems like a mistake to dub it as rational, full stop. Instead, because his belief does not appropriately respond to the evidence, this alone seems sufficient to describe it as not fully rational.

The same phenomenon occurs with failings of structural rationality. With Southside Sluggers, we had a situation where Bill’s belief r was structurally rational but not substantively rational. Now consider a case that’s reversed:

Timid Tester

Jane is skilled at math, routinely getting good marks on her tests at school. Sadly, Jane’s older brother routinely second-guesses her abilities, saying that she is just getting lucky and that she will do poorly on the next exam. Jane knows that he does not have any good reason to think this, but he still regularly undermines Jane’s confidence in her mathematical abilities with his remarks. After Jane’s next test, she immediately finds herself believing that she got a high score – she breezed right through all of the questions and finished before anyone else in the class. Then, however, she experiences a moment of self-doubt. Even though she believes that she scored highly on the exam, because of her brother’s comments, she cannot shake the belief that her belief is irrational.

Jane is in an epistemically akratic state. On the one hand, she believes s, that she scored highly on her exam, the proposition that her evidence supports. On the other other hand, she also believes that her belief s is irrational. Due to this unjustified higher-order belief, s is substantively but not structurally rational.²⁰ As before, even though Jane’s belief succeeds along one dimension of rationality, this is not enough to describe it as rational simpliciter. Despite the fact that s is supported by the evidence, her higher-order belief creates rational pressure for her to give up s. So long as Jane maintains the belief that her belief s is irrational, her belief is not yet fully rational.

If all of this is correct, then ‘rational’ is either an additive or a conjunctive multidimensional adjective. Being rational by the lights of a single dimension, whether that be substantive or structural rationality, is not enough to make a belief rational overall, preventing ‘rational’ from being a disjunctive multidimensional adjective. Instead, a belief must be either rational on all dimensions of rationality (conjunctive) or many of the dimensions of rationality (additive) in order to be rational. Now, even if it is correct that ‘rational’ is either additive or conjunctive, this is not to say that we have identified all of the dimensions of rationality, a possibility that is left open in Fig. 3. All that is necessary for our purposes is whether structural and substantive rationality are dimensions of rational belief, which it seems like there is good evidence to think that they are, but we will leave it open whether there are more respects in which a belief must be rational in order to be rational simpliciter.²¹

Fig. 3

The dimensions of rational belief

4 Linking rationality and justification

Now that we have seen that the rationality of belief is multidimensional, we are now in a position to propose a link between rationality and justification. In this section, I will outline the view that justification is a dimension of rationality, showing how this account can answer the Linking Question, Synonymy Question, and Coherence Question, as well as explain why justified belief and rational belief come apart in Small Town Election.

Not only is substantive rationality a dimension of the rationality of belief, but some recent work has drawn close comparisons between substantive rationality and justification.²² Worsnip thinks that “substantive rationality is concerned with being reasonable, or justified,”²³ while Fogal says that substantive rationality generates justificatory pressure to adopt particular beliefs.²⁴ Fogal even goes so far as to define substantive rationality in terms of justification: “For our attitudes—i.e., our beliefs, intentions, preferences, and the like—to be rational in this sense is for them to be justified or reasonable. Call this substantive rationality.”²⁵ This potential connection is not surprising. After all, we have already seen substantive rationality and justification described in much the same ways, as both involve responding appropriately to the evidence/one’s epistemic reasons.

This close relationship between justification and substantive rationality naturally gives way to the following proposal: Instead of taking it that justified belief and rational belief come to the same thing, maybe justified belief is actually the same thing as substantively rational belief. If, for the time being, we assume this proposal is correct, then we are in position to advance a link between full rationality and justification. ‘Rational’ is a multidimensional adjective, and one of its underlying dimensions is justification:

The Link

Rational belief and justified belief are linked as follows:

• (i) S’s belief that p is fully rational only if S’s belief that p is substantively rational, and

• (ii) S’s belief that p is substantively rational if and only if S’s belief that p is justified

There are several things to point out here. To begin with, note that the first conditional only holds from left to right. S’s belief that p is fully rational only insofar as it is substantively rational, but more is required for p to be completely rational. At the very least, S’s belief that p must also be structurally rational before it can be considered perfectly rational, and perhaps more if there are further dimensions to rational belief. The second conditional, on the other hand, holds in both directions. Being substantively rational in a belief requires being justified in that belief and vice versa.

Another thing worth noting is that The Link stops short of saying that being justified and being substantively rational are identical properties. Unlike the view on which rational belief and justified belief are the same thing, The Link is merely committed to the view that when speaking of substantive rationality, ‘justified belief’ and ‘rational belief’ are co-extensive, not that justified belief and substantively rational belief are the same thing. My own view is that, once a belief has enough justification to be considered justified, it is then substantively rational, but that further increases in justification do not make the belief more substantively rational.

We now have a possible answer to our Linking Question, but what reasons do we have to think that The Link is plausible? Along with the fact that a number of epistemologists think that substantive rationality and justification both involve evidential reasons, there are a number of other grounds for thinking that The Link correctly describes the relationship between rational and justified belief. To begin with, The Link can give a natural answer to the Synonymy Question. We began by wondering, if ‘rational belief’ and ‘justified belief’ are not synonymous, then why ever think that they are in the first place? Here we can say that, because ‘rational’ can be used to pick out the dimension of justification, there are certain contexts in which it looks like rational belief is identical to justified belief. Suppose that I present someone with Precipitation Prediction and ask the following question about Mary’s belief p, that Seattle is very likely to get 30 or more inches of rain in the next year:

• (25) Given Mary’s evidence, is her belief that p rational?

In (25), I specify the dimension of rationality that I am interested in—whether Mary’s belief is rational given the evidence. This limits my question to considerations of substantive rationality. And if substantive rationality is the same as justification, then (25) ultimately asks the same thing as (26):

• (26) Given Mary’s evidence, is her belief that p justified?

If The Link is correct and ‘rational’ is a multidimensional adjective, both (25) and (26) ask whether Mary’s belief is substantively rational, creating a context in which ‘rational’ and ‘justified’ pick out the same thing and, thus, appear to be synonymous.

We now have the beginning of an answer to the synonymy question. ‘Rational’ and ‘justified’ can be used in such a way that they both pick out substantive rationality, and if this sort of use is common within epistemology, then it is unsurprising that a number of theorists have taken them to be the same thing. As it turns out, ‘rational’ is regularly used in a way that limits it to only picking out whether a belief is substantively rational. In Evidentialism, Conee and Feldman say that “one traditional problem in epistemology concerns the relation that must hold between a body of evidence and a proposition for it to be rational.”²⁶ Roger White’s definition of uniqueness—“Given one’s total evidence, there is a unique rational doxastic attitude that one can take to any proposition”—centrally features substantive rationality.²⁷ Kevin Dorst invokes substantive rationality while discussing evidential uncertainty: “if you should be uncertain what your evidence warrants, then learning facts about your evidence can give you new evidence—and so can change what it’s rational to think.”²⁸ Dealing with cases of deception, Stewart Cohen argues that “subjects in the matrix can have such rational beliefs. These subjects clearly have lots of evidence for their beliefs.”²⁹ In laying out common uses of ‘rational’, Jack Lyons says “that was the rational thing to believe, based on the evidence you had at the time.”³⁰ Lasonen-Aarnio points out that “a flourishing literature in epistemology is largely concerned with […] what it is rational to believe given one’s evidence.”³¹ All of these discussions of rationality focus on substantive rationality, the type of rationality that evaluates whether or not someone believes what their evidence supports. These types of uses of ‘rational’ occur regularly across the philosophical literature, making it unsurprising that so many philosophers treat ‘rational’ and ‘justified’ as synonymous.³²

What about the Coherence Question? Why have so many philosophers theorized as if rationality is merely a matter of coherence? Here, we can also appeal to dimensional specification. Just like it is possible to create contexts where ‘rational’ only picks out substantive rationality, it is also possible to create contexts where ‘rational’ only refers to structural rationality. With (25), we asked whether Mary’s belief is rational given her evidence, but we can also single out whether her believe is rational given her other beliefs:

• (27) Given that Mary thinks Seattle gets over 30 inches of rain each year, is her belief that p rational?

We have already seen that a number of philosophers often use ‘rational’ in a way that isolates whether a belief coheres with other beliefs. Dimensional specification explains why this is possible—just like, in certain contexts, philosophers can use ‘rational’ to pick out whether a belief is supported by the evidence, in other cases, they can use ‘rational’ to pick out whether a beliefs fits appropriately with other beliefs. Thus, it is not a surprise that some philosophers theorize as if rationality is primarily focused on coherence constraints, because it is possible to use ‘rational’ in such a way that it only applies to whether beliefs fit together in the right way.

Beyond answering the Linking Question, the Synonymy Question, and the Coherence Question, the thought that ‘rational’ is a multidimensional adjective can also explain the behavior of ‘rational’ and ‘justified’ in Small Town Election. Recall that, in Small Town Election, both Warren and Greg were rational and justified in their belief that Naomi won, but, even though Warren’s belief was more justified than Greg’s, their beliefs were equally rational. According to the multidimensional view of ‘rational,’ once a belief is substantively rational and the other dimensions of rationality are satisfied, that belief is fully rational. Just like two boxes that are identical in all respects are completely identical, a belief that is rational in all respects is completely rational. This is what we see in Small Town Election. Warren and Greg are both justified (and thus substantively rational) in their belief that Naomi won the election, as they both have sufficient evidence that she did. So long as they do not fail along any other dimensions of rationality, and Small Town Election does not indicate that they do, then their beliefs are also fully rational. It is true that Warren’s belief is more justified than Greg’s given that Warren has stronger evidence that Naomi won, but this does not make Warren’s belief more rational than Greg’s. Because they are both justified in their belief, Warren and Greg both have a fully rational belief, making their beliefs that Naomi won the election equally rational.

5 Monistic views of rationality

This concludes my argument for The Link. Not only do a number of authors describe justification and substantive rationality as involving evidence/epistemic reasons, but taking justification to be a dimension of rationality can provide answers to the Linking Question, the Synonymy Question, and the Coherence Question as well as explain why rational belief and justified belief behave differently at the tops of their scales. One worry worth addressing is whether monistic views of rationality, accounts that explain structural rationality in terms of substantive rationality or vice versa, are a challenge to the thesis of this paper.³³ Do views like these threaten our argument for The Link, specifically the thought that ‘rational’ has multiple dimensions?

The first thing to say is that, on their own, monistic views of rationality need not conflict with the thesis that ‘rational’ is multidimensional. This is for a couple reasons. To begin with, we have already seen linguistic evidence that ‘rational’ behaves like a multidimensional adjective when it modifies belief. Any theory that says that the rationality of belief actually only has one dimension conflicts with this evidence, making multidimensionality a desideratum of an account of rational belief. If these monistic accounts do not allow that ‘rational’ is multidimensional, then so much the worse for those theories.

The other reason is that, even if it there is a deeper explanation of what links structural and substantive rationality, this is compatible with the thought that ‘rational’ is multidimensional. Take, for instance, the multidimensional adjective ‘healthy.’ There is likely a deeper explanation for why all of the different dimensions of health that we have mentioned—cardiovascular health, immune health, mental health, etc.—are all relevant to being healthy. Such an account would be consistent with the fact that we can use ‘healthy’ to pick out different dimensions of health, and likely explains why all of those factors contribute to being healthy overall. There would be strong reason to think that this so-called deeper explanation is incorrect if it reached the verdict that blood pressure and cholesterol levels are not relevant to health after all. The same is true for ‘rational’. Even if there is a deeper, monistic account of what makes a belief rational, this should itself explain why ‘rational’ is multidimensional, not reveal that rationality only has one dimension.³⁴

Even though monistic views of rationality, in and of themselves, are compatible with a multidimensional account of ‘rational,’ they can make trouble for the multidimensional proposal when they explicitly deny that we use ‘rational’ and ‘irrational’ to refer to both substantive and structural rationality. On one way of interpreting T.M. Scanlon, for example, failing to be responsive to evidence does not actually affect whether or not a belief is irrational Rather, talk of irrationality should be limited to just the ways in which a person’s judgments hang together. According to Scanlon, “irrationality in the clearest sense occurs when a person’s attitudes fail to conform to his or her own judgments,” and that ordinary usage of the term ‘irrational’ does not suggest that disregarding one’s evidential reasons, or failing “to accept certain considerations as reasons” is enough to make a belief irrational.³⁵ Now it is not entirely clear if Scanlon’s claim can be understood using our terminology of structural and substantive rationality. Scanlon was writing before these categories were explicitly introduced, though he later describes this distinction using the structural/substantive terminology.³⁶ If Scanlon has a different distinction in mind, then it may not undermine the arguments of this paper.

But for the sake of argument, if it is true that failures of substantive rationality cannot result in irrational beliefs, then this comes as a challenge to the thought that both failures of structural and substantive rationality can render a belief irrational. In order to argue his point, Scanlon considers two cases of a person who believes, despite the scientific evidence to the contrary, in the reality of extrasensory perception. In the first case, the person does not accept the scientific evidence, while in the second case, they judge that the scientific experiments may undermine their belief in extrasensory perception:

Let us stipulate that the person who believes in extrasensory perception is clearly mistaken; his conclusions violate the relevant standards of statistical reasoning and good scientific procedure. This alone does not seem to me to make these conclusions instances of irrationality. We might call them irrational if certain further things were true: if, for example, the person admitted that the established scientists’ experiments would, if valid, count against [extrasensory perception], and admitted that he could see no flaw in the methods used, but still kept insisting that there must be some flaw, without being able to cite any reason for this conclusion.³⁷

Here, Scanlon points out a crucial difference in the way that the believer in extrasensory perception processes counterevidence. In the first case, even though they are aware of it, they might not judge that the scientific evidence undermines their belief in extrasensory perception—a failure of what we have called substantive rationality. In the second case, they might judge that the experimental evidence does count against their belief in extrasensory perception, but neglect to change their belief structure because of this—a failure of structural rationality. Scanlon thinks that only the second case is a clear instance of irrational belief, while the first “does not seem to me to make these conclusions instances of irrationality.” So let’s consider the possibility that only structural rationality can make one’s belief irrational.

One way to respond to this view is to argue that it need not undermine the position that we have staked out in this paper. Scanlon makes it clear that he does not think that beliefs which fail to respect the evidence are fully rational. It is just that, on Scanlon’s view, we should “draw a distinction between an attitude’s being irrational and its being […] open to rational criticism.”³⁸ It may be possible to accept all of this and leave The Link intact. After all, the first conditional of The Link just says that, in order for a belief to be fully rational, it must also be substantively rational. Based on what Scanlon has said, it seems like he may be open to the possibility that beliefs that are not substantively rational are also not fully rational, given that they still may be open to rational criticism. This would allow that substantive rationality is a dimension of rationality and that failures of substantive rationality can still undermine the full rationality of one’s beliefs.

Even though this may be enough to preserve The Link in the face of Scanlon’s views on irrationality, it seems to me that we can also go a step further. After all, Scanlon says that his view “fits better with ordinary usage.”³⁹ In order to test if this account fits best with ordinary usage, a study was conducted with 50 participants via Amazon Mechanical Turk. All subjects were located in the United States, had graduated from high school, and were native English speakers. Study participants were first presented with the control case Precipitation Prediction, an example where the belief in question was both structurally and substantively rational, and asked whether Mary’s belief p was rational. As displayed in Fig. 4, 88 $\mathrm{\%}$ of participants responded that her belief was rational, 10 $\mathrm{\%}$ responded that her belief was irrational, and 2 $\mathrm{\%}$ responded that her belief was neither rational nor irrational. Participants were then presented with Southside Sluggers, a case of structural but not substantive rationality, and asked whether Bill’s belief r was rational. As seen in Fig. 5, 78 $\mathrm{\%}$ of participants responded that his belief was irrational, 18 $\mathrm{\%}$ responded that his belief was neither rational nor irrational, and 4 $\mathrm{\%}$ responded that his belief was rational.

Fig. 4

Is Mary’s belief rational?

Fig. 5

Is Bill’s belief rational?

From the results of this study, we can see that our interpretation of Scanlon’s account, that only failures of structural rationality can make a belief irrational, is not an accurate description of ordinary usage. On this view, because Bill’s belief r is structurally but not substantively rational, it is best described as neither rational nor irrational. It is open to rational criticism, though not bad enough to be dubbed ‘irrational’. The majority of study participants, however, were willing to call the belief irrational due to its lack of substantive rationality, undermining the thought that failures of substantive rationality are not enough to make a belief irrational. We, thus, have two ways of responding to the challenge. On the one hand, we could incorporate our interpretation of Scanlon’s views in a way that is compatible with The Link, characterizing beliefs that are not substantively rational as less than fully rational even though they might not be positively irrational. On the other hand, we could also reject the view altogether, appealing to the survey data here to argue that ordinary usage suggests that not being substantively rational is enough to make a belief irrational.

6 Rational but not justified?

Another concern someone might have about The Link is that it predicts that some sentences should be contradictions when they are clearly not. Consider, for example, a common claim by externalists about victims of global deception. In cases where subjects might be trapped in the matrix or deceived by an evil demon, internalists about justification tend to say that such victims are nevertheless justified in their beliefs.⁴⁰ One route to answering this worry for externalists is to concede that, though these victims may be rational in their beliefs, they are nevertheless not justified.⁴¹ Here, I am not concerned with taking either the internalist or externalist side. Instead, I am concerned with the externalist claim captured in (28):

(28) The beliefs of victims of global deception are rational but not justified

If The Link is correct, wouldn’t we expect (28) to be a contradiction? After all, according to The Link, in order for a belief to be fully rational, it must also be justified, suggesting that there should be some tension in saying that a belief is both rational but not justified. So why does (28) not sound contradictory?

One way to avoid this worry would be told hold that ‘rational’ is an additive rather than a conjunctive multidimensional adjective. When a multidimensional adjective is additive like our example ‘healthy’, then it can still be possible to be healthy overall despite a failure along a particular dimension. Even if my blood pressure is technically in the unhealthy range, I can still qualify as healthy simpliciter if I am healthy along a sufficient number of other dimensions. Likewise, it may be possible for a belief to be unjustified but for it still to be rational overall if it is rational enough in a number of other ways, preventing (28) from being contradictory.

A potential concern for this approach is that, even with additive multidimensional adjectives, a serious failing along any one dimension typically prevents the application of the multidimensional adjective. If my cholesterol is extremely high, making me at imminent risk of heart attack, then I do not qualify as healthy simpliciter even if I am healthy in a number of other ways. And if we take externalism about justification to be correct, then the victims of the matrix or the evil demon are seriously unjustified. Their beliefs about the world are wildly inaccurate, making their failure of rationality a significant one. In this case, even if ‘rational’ is an additive rather than a conjunctive multidimensional adjective, then we would expect a conflict to arise from (28).

Nevertheless, even if ‘rational’ is a conjunctive multidimensional adjective, there is still a strategy for making sense of sentences like (28) by appealing to dimensional specification. Thus far, we have picked out particular dimensions of multidimensional adjectives by using phrases such as “with respect to” or “in terms of”, but this is not the only way to limit the dimensions under consideration. Consider, for instance, the following sentence:

• (29) The boxes are identical, but they are different colors

Because ‘identical’ is a conjunctive, multidimensional adjective, (29) falls under the same criticism as (28). Shouldn’t it be contradictory to say that two boxes are identical but are different colors, since color is one of the dimensions of being identical? Even though this might be a reasonable expectation, it turns out that sentences like (28) and (29) can be used for dimensional specification. If someone says (29), they communicate that, even though they are different colors, the boxes are identical in terms of their other dimensions. The same can be said to account for the non-contradictory nature of (28). Even though being justified is part of what it is to be rational, we can nevertheless use (28) to describe beliefs that satisfy only some of the dimensions of rationality. Now, perhaps the externalist hypothesis is mistaken and victims of global deception are both structurally and substantively rational, but regardless of whether externalists are right about justification, dimensional specification can explain why a sentence like (28) can be used without contradiction. The important lesson is that, when used with conjunctive, multidimensional adjectives, sentences like (28) and (29) can be used to limit the dimensions under consideration, making sentences acceptable that would otherwise appear to be contradictory.

7 Conclusion

We started this essay with a couple of theories about the relationship between rational and justified belief. The central question was whether rational belief and justified belief are connected, and if they are, how exactly they are linked. On one popular theory, rational and justified belief are identical, making it possible to talk of rational belief and justified belief interchangeably. On a rival view, rationality is only concerned with whether beliefs fit together in the right way, while justification is focused on whether beliefs are supported by the evidence. In this paper, I have tried to shed light on what each of these theories has going for it while also arguing that neither fully captures the relationship between justification and rationality. Justification is a dimension of rationality, explaining why rational belief involves more than just coherence, but fully rational belief must be both substantively and structurally rational, showing why ‘rational belief’ and ‘justified belief’ are ultimately not synonymous.