Dimensional Reliabilism

1. Introduction

In everyday contexts, epistemic reliability is widely used to assess the trustworthiness of several information sources: Informants, medical tests (e.g., SARS-COV-2 PCR and rapid antigen testing),¹ newspapers, blogs, websites, directory services, TV programmes, social media, intelligence agencies, sense modalities—the list is as long as the information channels people rely on. Over the past few decades, reliability has also become a central concept within the theoretical discipline of mainstream epistemology. Generic reliabilism and related views such as process reliabilism and virtue reliabilism assume that knowledge is true belief that is the product of a reliable belief-forming process or cognitive ability. While considerable disagreement exists between these views on what more is required from a process to count as knowledge-conducive, they all put forward the same definition of reliability:

Reliability

A process is reliable just in case “it leads to a sufficiently high preponderance of true beliefs over false beliefs” (TB >> FB).²

Given this straightforward definition, reliability appears to be, and so far has been implicitly treated by epistemologists as, a mono-dimensional concept. Nevertheless, by reference to widely used functions that statisticians have developed for assessing the reliability of binary classification processes, this paper argues that reliability is a multidimensional concept. Specifically, given the above definition of reliability, the notion is open to at least four different interpretations—what (following statisticians) we will here refer to as ‘Precision,’ ‘Negative Predictive Value’ (NPV), ‘Recall’ and ‘Specificity.’ Moreover (as the argument will go) each of these dimensions of reliability serves different epistemic goals and, depending on the agent’s epistemic goal, they can all take centre stage in assessing whether a belief-forming process is reliable, and thereby knowledge-conducive.

Pondering in this way on the multidimensional nature of reliability will bring to the fore two broad epistemic goals that correspond to two important kinds of knowledge (or epistemic states, if you like). The first goal is best captured by the familiar locution of ‘know-that.’ Though epistemologists do not specify how they interpret the above definition of reliability, due to their interest in ‘know-that’, their mono-dimensional focus seems to have been mainly directed at Precision alone (or, at best, at both Precision and NPV, but without distinguishing between the two).³ As it will transpire, however, the (entirely) neglected dimensions of Recall and Specificity are essential for guiding the satisfaction of another kind of epistemic goal, best captured by the locutions ‘know-most’ and ‘know-all.’⁴ Think, for example, of sentences such as ‘I know all movies by David Lynch’; ‘I know most subjects who have contracted the virus’; ‘I know most/all profitable investments’; and so on.

Though off the radar of reliabilist epistemology so far, the paper argues that ‘know-most/all’ and the dimensions of reliability that distinctively underly it—that is, high Recall and/or high Specificity—are important epistemic concepts that epistemologists should not neglect anymore. Various reasons can be offered in support of this claim: For example, manifesting high Recall and/or high Specificity is essential for alleviating a common kind of ignorance (to be specified later); from a reliabilist perspective, the associated epistemic states of ‘know-most/all’ seem irreducible to ‘know-that’; focusing on Recall and Specificity can provide significant insights concerning the debate over the validity of evolutionary reliabilist epistemology; and, perhaps most importantly, paying attention to Recall and Specificity can lead to useful theoretical and practical distinctions for assessing and understanding within epistemology the reliability of various information sources (including informants, medical tests and mass media)—distinctions, which are impossible to draw on the basis of a mono-dimensional approach to the concept of reliability.

For example—to appeal to an until recently topical distinction—we will see that if reliabilists only focus on the dimension of Precision and/or Negative Predictive Value, without any recourse to the dimensions of Recall and Specificity, they are unable to explain the most noteworthy and crucial difference between the reliability of PCR testing and the reliability of (at least certain) rapid antigen tests for SARS-CoV-2. And yet, as it is widely known, there is often supposed to be an important difference between the reliability of these two two kinds of medical tests for SARS-CoV-2. As we shall see, the present approach, with its explicit recognition of the multidimensional character of the notion of reliability, can provide reliabilism with the means for clearly accounting for this distinction—and many more besides.

Overall, then, the aim of the following is to highlight how each of the aforementioned dimensions of reliability can serve different epistemic goals and that, depending on the agent’s epistemic goal, they can all take centre stage in assessing whether a belief-forming process is reliable, and thereby knowledge-conducive. This observation, I will argue, invites us to upgrade reliabilism into what I will refer to as dimensional reliabilism.

To make the case for the above, the paper will proceed in the following order. To first familiarise us with the relevant dimensions of reliability, the paper will start with a nontechnical discussion of the target dimensions (Section 2), which will then be followed by a section offering mathematically rigorous definitions of them, drawing on widely used statistical tools (Section 3). With these definitions in place, the paper will then proceed to provide several examples that illustrate the central idea—that is, that different epistemic goals call for high scores across different dimensions of reliability and their combinations (Section 4). At that point, the discussion will then be paused to consider a technical worry: The dimensions of Precision and NPV seem to directly relate to ‘know-that’, whereas Recall and Specificity relate to ‘know-most/all’; could there be a way to reduce Recall and Specificity to Precision and NPV, such that there would be no need for epistemologists to look beyond ‘know-that’? Arguing that this seems impossible (Section 5) and that ‘know-most/all’ is not thereby reducible to ‘know-that’ (at least not from a reliabilist perspective), the paper will continue to highlight some of dimensional reliabilism’s key advantages: The view is in an excellent position to explain, in reliabilist terms, how knowledge can be the antidote to a very common kind of ignorance (Section 6). It can also prove particularly helpful in defending reliabilist approaches to evolutionary epistemology from a worrying counterexample (viz., the ‘rabbits counterexample’) (Section 7). Finally, the paper (Section 8) will demonstrate how the view offers the tools for a more nuanced understanding of the reliability of information sources, both in the theoretical domain (for example in our assessment of thought experiments) and in practice: For instance, dimensional reliabilism is in a unique position to explain the difference in the reliability of medical tests such as PCRs and at least certain rapid antigen tests for SARS-CoV-2 as well as to offer a detailed (and so far inaccessible) breakdown of the several ways in which online information sources and mass media might succeed (or fail) in being reliable.

2. Dimensions of Reliability

Let’s start by familiarising ourselves with the several dimensions of reliability with a simple example. Think of a process whose function, say, is to identify cats—that is, a cat-identifying mechanism (C). For many, claiming that C is reliable will likely indicate the following:

• 1.

  If C outputs that an object is a cat, then it is highly likely that the target object is a cat.

This kind of reliability can be grasped in terms of a ‘high preponderance of true over false beliefs’—that is, in terms of the aforementioned, widely accepted definition of reliability—in the following way:

True beliefs of the type ‘object x is a cat’ >> False beliefs of the type ‘object x is a cat’

Indeed, this is an important way in which C can be reliable. It suggests that the mechanism will rarely misidentify objects that are not cats as cats. Nevertheless, there are further cat-related beliefs C is responsible for that are not guaranteed to be equally reliable:

• 2.

  If C outputs that an object is not a cat, then it is highly likely that it is not a cat.

This kind of reliability can be grasped in terms of a ‘high preponderance of true over false beliefs’ in the following way:

True beliefs of the type ‘object x is not a cat’ >> False beliefs of the type ‘object x is not a cat’

A mechanism that satisfies the first kind of reliability may not satisfy the second. For example, even if C is highly unlikely to misidentify objects that are not cats as cats, there might be lots of (strange-looking) cats that the mechanism mistakes for objects that are not cats.

• 3.

  C will detect most existing cats. For objects that are cats, C’s outputs that the target objects are cats are considerably higher than C’s outputs that the target objects are not cats.

Interestingly, this kind of reliability can also be grasped in terms of a ‘high preponderance of true over false beliefs’ in the following way:

True beliefs of the type ‘object x is a cat’ >> False beliefs of the type ‘object x is not a cat’

Again, it is easy to see how a mechanism that satisfies the first kind of reliability may fail to satisfy the third. There might be several cats in the vicinity, but the mechanism fails to categorise them as cats (because, say, they are strange-looking cats). As a result, a large percentage of cats will be ignored.

• 4.

  C will detect most objects, which are not cats. For objects that are not cats, C’s outputs that the target objects are not cats are considerably higher than C’s outputs that the target objects are cats.

This too can be grasped as a kind of reliability in terms of a ‘high preponderance of true over false beliefs’ in the following way:

True beliefs of the type ‘object x is not a cat’ >> False beliefs of the type ‘object x is a cat’

Though this case might be slightly trickier, it is not difficult to see how a mechanism that satisfies the first kind of reliability may fail the fourth kind. It could be the case that, in the vicinity, the number of cats is much larger than the number of objects that are not cats. In this case, the number of objects that are not cats (and thus the potential number of correctly identified such objects) will be close to the number of objects that are incorrectly identified as cats, even if—due to the first kind of reliability—this happens only rarely. In this scenario, true beliefs of the type ‘object x is not a cat’ will not be much higher than false beliefs of the type ‘object x is a cat’. In result, of all the objects that are not cats, a large percentage will be ignored.

The upshot is that defining reliability of a mechanism as the mechanism’s ability to lead to a ‘preponderance of true over false beliefs’ is too broad. According to the above, for any kind of epistemic belief-forming process whose function is to identify the presence of some quality ι (such as the quality of being a cat), there are at least four distinct ways to interpret mainstream epistemology’s generic definition of reliability, thereby revealing four different dimensions of reliability. What then is the way to decide which of the above interpretations is the correct one or whether any single one of them is correct? Put another way, which ‘sufficiently high preponderance of true over false beliefs’ should assessments of whether a belief-forming process is reliable, and thus knowledge-conducive, focus on? Could there be contexts where one should be preferred over the other?

3. Reliability Indicators

More precise definitions of the above dimensions of reliability can be provided by employing certain widely used functions that statisticians and computer scientists have developed for assessing the reliability of classification processes (see, for example, Tharwat 2021). Binary classification can be defined as a kind of categorisation process, whereby sampled items are divided into two distinct classes, depending on whether the target items bear or lack some qualitative property ι. As we go along we will explore various examples that demonstrate the potential practical applications of binary classification, but the following are common instances where this kind of categorisation categorisation process can be implemented in practice:

• Image classification: Assessing whether an image represents a certain visual pattern (e.g., a cat) (where ι is the quality of representing the target pattern).

• Spam detection: Assessing whether a message is a spam (where ι is the quality of being a spam)

• Medical screening: Assessing whether a subject has a target condition or pathogen (where ι is the quality of having the target condition or pathogen).

Binary classification is relevant to epistemology, because most (perhaps all) basic human belief-forming processes seem amenable to be construed as binary classification processes. Consider the following examples:

• Visual processes of colour perception (where ι is a specific colour).

• Visual processes of pattern recognition (where ι is a specific pattern).⁵

• Long term autobiographical memory (where ι is a past event in one’s life as opposed to confabulation).

• Long term explicit memory (where ι is a previously encoded piece of information as opposed to confabulation).

• Inference-making (where ι is a valid inference).

• Reception of testimony (where ι is a reliable testimony).⁶

Accordingly, the reliability of most human belief-forming processes can be assessed on the basis of classification functions.⁷ To understand how classification functions work as indicators of different kinds of reliability, the following terminology will be useful (see also (Tharwat 2021) for more details):

For any set of elements that might bear the property ι (e.g., being a cat):

• Positives, P, refer to the tested elements that bear ι (e.g., to actual cats).

• Negatives, N, refer to the tested elements that do not bear ι (e.g., to any object that is not a cat).

• True Positives, TP, refer to the elements that the test identified as bearing ι and they bear ι indeed (e.g., to those elements that they were identified as cats and they are cats indeed).

• True Negatives, TN, refer to the elements that the classification process identified as not bearing ι and, indeed, they do not bear ι (e.g., to those elements that they were identified as objects that are not cats and indeed they are not cats).

• False Positives, FP, refer to the elements that the test identified as bearing ι but they don’t (e.g., to those elements that they were identified as cats when in fact they aren’t).

• False Negatives, FN, refer to the elements that the classification process identified as not bearing ι but in fact they do (e.g., to those elements that were identified as objects that are not cats but in fact they are).

Given the above, the following also holds:

• P = TP + FN

• N = TN + FP

With the above terminology in place, we can now present the basic functions for assessing the reliability of binary classification processes, as these have been introduced by statisticians and computer scientists (indicatively, see Tharwat 2021). In addition to being clear about the following reliability indicators, it is also important to keep in mind that these indicators are distinct from one another in that a mechanism’s scoring highly with respect to one of the following indicators does not entail that it will score highly with respect to any of the other indicators. Below, I offer the statistical definitions of the dimensions of reliability that the paper focuses on, without listing the reasons for which each kind of reliability is distinct from the others. Interested readers can find a detailed list of these reasons in the Appendix.

4. Dimensions of Reliability and Epistemic Goals

The above offers precise definitions of the dimensions of reliability we are here going to focus on, and Appendix A demonstrates how they are distinct from one another. In the introductory section, we also noted that these distinct kinds of reliability may serve different epistemic goals. That is, differences in what agents aim at knowing call for high scores along different dimensions of reliability. It is also the case that certain epistemic goals may require a combination of them. A direct consequence of these points is that a shift in the agent’s epistemic goal may render an otherwise reliable and knowledge-conducive process entirely inappropriate with respect to the epistemic task at hand. To get a better grip on this, it is worth considering a few examples of how certain epistemic goals may call for high levels of reliability along several dimensions.

First, take high Precision, which is required when it is important to be mostly correct about positively identified elements, but one can afford to ignore a significant percentage of positives (i.e., exhibit low Recall), does not care about frequently misidentifying positives as negatives (i.e., exhibit low NPV) and can afford to ignore a significant percentage of negatives (i.e., exhibit low Specificity). Say the epistemic agent is an art collector who wants to know whether some painting is an original Picasso in order to buy it:

EG_AC: When judging that an object x is a Picasso, know that x is a Picasso

With respect to this epistemic goal, all the agent needs is that the relevant belief-forming process exhibit high Precision. But a change of her epistemic goal can easily change Precision’s efficiency in rendering the relevant mechanism knowledge-conducive. Say the agent wants to know every painting that is an original Picasso, because she wants to buy them all:

EG_AC’: When judging that an object x is a Picasso, know that x is a Picasso; and know most (ideally all) Picassos

To achieve this new epistemic goal, the relevant belief-forming process would also need to exhibit high Recall. What this means is that if we focused on Precision alone to judge whether the agent’s belief-forming process is reliable and thereby knowledge-conducive, we would have to conclude that it is, no matter what her epistemic goal is. Yet, when the agent wants to also know all original Picassos (i.e., when her epistemic goal is EG_AC’, rather than EG_AC), high Precision alone would fail her, as she would be prone to missing out on many of them.

Now, take NPV. High NPV is appropriate when one needs to have a high success rate with respect to negatively identified elements but can afford to ignore a significant percentage of negatives (i.e., exhibit low Specificity), does not care about regularly misidentifying negatives as positives (i.e., exhibit low Precision) and can afford to ignore a significant percentage of positives (i.e., manifest low Recall). Say the epistemic agent wants to know whether incoming emails are not important in order to delete them:

EG_E: When judging that email x is not important, know that x is not important

With respect to EG_E, all the agent needs is that the relevant belief-forming process exhibit high NPV. But a shift in her epistemic goal can easily change NPV’s efficiency in rendering the relevant belief-forming process knowledge-conducive: Say that now she wants to also know all stored emails that are not important in order to delete them all (perhaps the memory of her email account is running full). In this case, her epistemic goal would be as follows:

EG_E’: When judging that email x is not important, know that x is not important; and know most emails that are not important.

To satisfy this new epistemic goal, the relevant mechanism would also need to exhibit high Specificity. Moreover, notice that having the relevant mechanism exhibiting only high Precision would be irrelevant to either of the above epistemic aims. Why should it matter that the agent is correct most times she thinks an email is important (i.e., manifest high Precision)? Even if Precision is high, she may still often claim that emails are not important when in fact they are (i.e., manifest low NPV), thus failing her first epistemic goal. Similarly, when manifesting high Precision, it can still be the case that a big percentage of the emails that are not important is incorrectly judged to be important (i.e., manifest low Specificity), thereby also failing her second epistemic goal.⁹ So again, judging whether the agent’s belief-forming process is reliable and thereby knowledge-conducive by focusing on Precision alone would deliver the wrong result.

Next is Recall. High Recall is useful when one cannot afford to ignore a significant percentage of positives, but can afford to ignore a significant percentage of negatives (i.e., exhibit low Specificity) and does not so much care about frequently misidentifying negatives as positives and vice versa (i.e., exhibit low Precision and NPV). Say the epistemic agent is a doctor who must know most (ideally all) patients who have contracted a virus in order to give them a cheap medicine that is amply available:

EG_D: Know most (ideally all) individuals with the virus

For EG_D to be satisfied, it is necessary that the relevant mechanism exhibit high Recall.¹⁰ But, again, a change in the agent’s epistemic goal can easily affect the corresponding mechanism’s ability to deliver knowledge. Say that the relevant medicine is in shortage, such that the doctor needs to know most individuals who have contracted the virus and needs to also know, for each positively identified individual, that they have contracted the virus indeed:

EG_D’: Know most (ideally all) individuals with the virus; and when judging that individual x has the virus, know that x has the virus

In this case, the relevant mechanism must also exhibit high Precision. And yet notice that with respect to either of the doctor’s epistemic goals, using Precision alone to judge whether her belief-forming process is knowledge-conducive would be insufficient. Even if the doctor is most times correct when judging one to be a patient (i.e., manifest high Precision), there can still be a lot of patients that she mistakes for healthy individuals. To avoid this, it is necessary to check whether her belief-forming process also manifests high Recall.

Finally, think of Specificity. High Specificity is fitting when one cannot afford to ignore a significant percentage of negatives, but can afford to ignore a significant percentage of positives (i.e., manifest low Recall) and does not so much care about her success rates with respect to either negatively or positively identified elements (i.e., exhibit low NPV and Precision). Say the agent is an investment consultant whom her client is relying upon to know most investments that are not profitable.

EG_IC: Know most (ideally all) investments that are not profitable.

With respect to this goal, it is necessary that the relevant belief-forming process exhibit high Specificity (i.e., ignore a small percentage of the investments that are not profitable).¹¹ But, once again, a change in the agent’s epistemic goal can easily affect the corresponding mechanism’s ability to deliver knowledge. Say her client is likely to be dissatisfied with being often advised against investments that are in fact profitable. In this case the consultant would also need to know, for each negatively identified investment, that it is not profitable indeed:

EG_IC’: Know most (ideally all) investments that are not profitable, and when judging that investment x is not profitable, know that x is not profitable.

To satisfy this new epistemic goal, the relevant mechanism would also need to exhibit high NPV. Moreover, notice, once again, that judging whether the relevant belief-forming process is knowledge-conducive on the basis of Precision would be entirely misleading. Being most times correct when judging investments to be profitable (i.e., manifest high Precision) could still expose the consultant to ignoring a big percentage of the investments that are not profitable, thereby failing her first epistemic goal.¹² Similarly, high Precision, in this case, won’t prevent the consultant from often judging that investments are not profitable when in fact they are (i.e., manifesting low NPV), thereby failing her second epistemic goal.

Now, if the above is correct, there are good reasons for thinking that different epistemic goals—that is, what the agent aims at knowing—call for varying levels of reliability along different dimensions. This observation points to the need for upgrading reliabilism to dimensional reliabilism. According to this multi-dimensional approach to reliabilism, different epistemic goals call for high levels of reliability along different dimensions (and perhaps their combinations too); thus, assessing whether a process is knowledge-conducive depends on whether it manifests high reliability along the appropriate dimension(s), given the epistemic goal at hand.¹³

5. Correctness and Breadth of Scope: Know-That and Know-Most

The above examples in support of dimensional reliabilism are meant to indicate that different epistemic goals require varying scores of reliability across different dimensions; moreover, certain goals may require combinations of high scores across multiple dimensions. At the same time, however, the foregoing examples also reveal an interesting pattern that one may attempt to use against dimensional reliabilism: On one hand, high Precision and high NPV are most clearly associated with epistemic goals that relate to ‘know-that’; on the other hand, high Recall and high Specificity seem to mostly serve epistemic goals that relate to a different kind of knowledge that is best captured by the ‘know-most’ and ‘know-all’ locutions. This observation raises two important worries for dimensional reliabilism.

First, given that mainstream epistemology has traditionally focused on ‘know-that,’ are Recall and Specificity of any importance to mainstream epistemology? Secondly, even if Recall and Specificity do have important roles to play, could it be the case that a belief-forming mechanism that manifests high Precision and/or NPV—that is, the two dimensions that relate to know-that’—ensures that high Recall and high Specificity are also manifested? If that’s the case, then one could argue that there is a single ‘master’ notion of reliability—one that covers either high Precision or high NPV (or maybe both simultaneously)—which relates directly to ‘know-that’ and which can do all the relevant epistemic work, including the work of high Recall and high Specificity. In that case, high Recall and high Specificity would not seem as important after all and the associated ‘know-most/all’ would seem easily reducible to ‘know-that.’

In this section, I will take up the second question concerning the reducibility of ‘know-most/all’ to ‘know-that’. The rest of the paper will then deal with the first question regarding the epistemic importance of the dimensions of Recall and Specificity.

To start answering the second issue, let us return to the following pressing question: Could there be a ‘master’ notion of reliability, upon which—pace dimensional reliabilism—all assessments of reliability and knowledge may depend? Given epistemologists’ long-standing focus on ‘know-that’ and the aforementioned pattern between the different dimensions of reliability and the kinds of epistemic goals they seem to primarily serve, a promising candidate for playing this role is what we may here refer to as ‘Correctness.’ Think of Correctness as the common denominator between Precision and NPV. A belief-forming process with high Precision will likely be correct with respect to positives. When it outputs that an element is a positive, it is highly likely that it is a positive indeed. Similarly, a belief-forming process with high NPV will likely be correct with respect to negatives. When it outputs that an element is a negative, it is highly likely that it is a negative indeed. In contrast, we can see that the common denominator between Recall and Specificity is what we may here refer to as ‘Breadth of Scope.’ A process with high Recall has high Breadth of Scope with respect to positives in that it will not ignore a big percentage of the existing positives. Similarly, a process with high Specificity has high Breadth of Scope with respect to negatives in that it will not ignore a big percentage of the existing negatives.

With the above in place, a promising way to resist the need for upgrading to dimensional reliabilism would be to claim that, given epistemologists’ focus on ‘know-that’, what they may have so far had in mind when they thought that a process was reliable was the dimension of Correctness with respect to either positives or negatives. If we can also demonstrate that high Breadth of Scope (in the form of either high Recall or high Specificity) can be reduced to high Correctness, then we may have a strong argument against the upgrade to dimensional reliabilism.

This is not a simple matter, however. High Correctness with respect to positives (i.e., high Precision) does not entail high Breadth of Scope with respect to positives (i.e., high Recall). There might still be a significant percentage of positives that are incorrectly identified as negatives, and which are thus ignored. Similarly, high Correctness with respect to negatives (i.e., high NPV) does not entail high Breadth of Scope with respect to negatives. There might still be a significant percentage of negatives that are incorrectly identified as positives, and which are thus ignored.¹⁴

Now, at this point, one might re-join by denying that epistemologists have so far focused either on Precision or on NPV. Rather, they may suggest, when epistemologists claim that a process is reliable and thereby knowledge-conducive what they mean is that it manifests high overall Correctness—that is, high Correctness with respect to both positives and negatives. This is entirely possible given that the subtle distinction between Precision and NPV has so far gone unnoticed. But then, if we grant this assumption, we have to revisit the reducibility question and, this time, ask: Can high overall Correctness ensure high overall Breadth of Scope (i.e., high Breadth of Scope with respect to positives and high Breadth of Scope with respect to negatives)?

As it happens, the answer is again negative. Take a mechanism that exhibits both high Precision and high NPV. Even if the mechanism does not often misidentify negatives as positives (due to high Precision), and even if the mechanism does not often misidentify positives as negatives (due to high NPV), it could still be the case that either Recall or Specificity are low. In cases where the number of positives in the population is much higher than the number of negatives, the number of negatives that can be correctly identified (i.e., the number of TN) will be close to the number of FP (despite the fact that, due to high Precision, the mechanism very rarely misidentifies negatives as positives).¹⁵ Consequently, a large percentage of negatives will be ignored (i.e., Specificity will be low). Conversely, in cases where the number of negatives in the population is much higher than the number of positives, the number of positives that can be correctly identified (i.e., the number of TP) will be close to the number of FN (despite the fact that the mechanism, due to high NPV, very rarely misidentifies positives as negatives).¹⁶ Consequently, a large percentage of positives will be ignored (i.e., Recall will be low).¹⁷

Therefore, it does not seem possible to reduce high overall Breadth of Scope (i.e., both high Recall and high Specificity) to high overall Correctness (i.e., both high Precision and high NPV). This indicates that the largely ignored locutions of ‘know-most/all’ may not be reducible to ‘know-that’—at least not from a reliabilist perspective. The reason is that ‘know most/all’ require that the underlying belief-forming mechanism manifests high scores across certain kinds of reliability that cannot be ensured by high scores in the kinds of reliability required for ‘know-that.’ Put another way, ‘know-most/all’ seems irreducible to ‘know-that’, because having both the requisite justification for knowing that p and the requisite justification for knowing that not-p does not entail that one possesses the justification required for knowing most (ideally all) ps and not-ps.

But if ‘know-most/all’ does not reduce to ‘know-that,’ could it at least be the case that ‘know-that’ is a necessary component of ‘know-most/all’? It may be pointed out, for example, that if one were in a position to detect most ps and not-ps, but manifested low Correctness by manifesting low Precision and/or low NPV, it would be inappropriate to claim that they nevertheless know (just because of high Recall and Specificity) most ps and not-ps. In other words, it may be pointed out, low Precision and low NPV are incompatible with ‘know-most/all.’

Consider for example the cat-identifying mechanism of Section 2 and a population consisting of 1090 animals that are not cats—of which 1000 are correctly identified as not-cats (i.e., TN=1000 and FP=90)—as well as of 11 cats—of which 10 are correctly identified as cats (i.e., TP=10 and FN=1). In this case, Recall ≈ 0.91, Specificity ≈ 0.92, NPV ≈ 0.99, but Precision = 0.1. Despite the high Recall of this mechanism, one could object that it is not possible to know-most cats on the basis of this mechanism, because, on its basis, when one judges that an animal is a cat one cannot know that the target animal is a cat—claiming that something is a cat, after all, turns out to be correct only one out of ten times (i.e., Precision = 0.1). In other words, the worry may go, such a mechanism cannot be said to know most cats because there seems to be something wrong with the ‘idea’ of cats it is operating on—there simply are too many animals that it mistakes for cats. And if one can be so easily mistaken about what a cat is, they cannot really know most cats, even though, were they interested in obtaining as many cats as possible, due to promiscuous ordering, they would miss out on very few of them. Put simply, judging to be a cat anything that remotely looks like a cat, so that, in the end, very few cats will be ignored, prevents one from knowing most cats: Knowing most cats, the suggestion is, does not only require that one miss out on very few cats—in doing so, one must also be in a reasonably good position telling cats from cat-looking animals apart.

Admittedly, the above suggestion is not without merit.¹⁸ But even if we accept it, it does not directly lead to the conclusion that ‘know-that’ is necessary for ‘know-most/all.’ Knowing that p requires a sufficiently high level of Precision—presumably, most people would consider 0.9 as sufficient and anything below 0.8 would likely be unacceptable, though, depending on the process, different levels might be deemed acceptable each time. It is not clear, however, that the same level of Precision is required for knowing most ps. Say one is in a position to miss out on very few cats by manifesting very high Recall, but the precision of their cat-identifying mechanism, while well above chance, falls short of the reliability required for knowing that something is a cat—say it is only 0.7. Or say that one can list most Michelin-starred restaurants in their city, but only seven out of the ten restaurants that they list are indeed Michelin-starred. Wouldn’t in these cases still be appropriate to claim that the agent knows most cats or that they know most Michelin-starred restaurants, even though the moderate Precision of the underlying mechanisms would not support them in knowing that something is a cat or knowing that a restaurant is indeed Michelin-starred? Intuitively, the answer here seems to be positive; claiming, in such cases, that agents ‘know-most’, even though they do not quite ‘know-that,’ sounds fair and unproblematic. If that’s correct, however, then not only is it not possible to reduce ‘know-most/all’ to ‘know-that’ but ‘know-that’ may not even be necessary for ‘know-most.’ Rather, ‘knowing most/all’ may only require a reasonable level of Correctness (perhaps, considerably above chance).

In any case, whatever the answer regarding the necessity of ‘know-that’ for ‘know most/all’ may be, the above indicates that there are good reasons for thinking that ‘know-most/all’ cannot be dealt with merely by appealing to ‘’know-that.’ This leaves us with the less technical worry that ‘know-most/all’ and Breadth of Scope might not be epistemically important—at least not important enough to warrant the attention of mainstream epistemology. Is this true?

6. Correctness, Breadth of Scope, Knowledge and Ignorance

As we have seen, it does not seem possible to do away with Breadth of Scope and ‘know-most/all’ by reducing them to Correctness and ‘know-that.’ Yet there might be another way to resist the shift to dimensional reliabilism: Instead of seeking to reduce Breadth of Scope to Correctness, one could argue that, from a reliabilist perspective, Breadth of Scope is unrelated to knowledge assessments. Arguing in this direction would clearly reinforce the mainstream epistemological status-quo, whereby the focus has been primarily on ‘know-that.’ But is it correct to claim that Breadth of Scope is irrelevant to knowledge assessments? After all, as we have already seen, on many occasions, knowing most ps or not-ps is at least as important as knowing that p or not-p, and on other occasions it is crucial to know both that p or not-p and most ps or not-ps. So how might one deny that Breadth of Scope is relevant to knowledge assessments such that reliabilists, qua reliabilists at least, should not be concerned with it?

To see how such a strategy might go, consider Goldman’s (1986: 122) notion of ‘power’, which sounds similar to Breadth of Scope, though, as I will shortly explain, it is not quite the same:

Reliable cognitive mechanisms are an antidote to error, but not necessarily an antidote to ignorance. Reliable processes guarantee a high truth ratio among the beliefs they generate. But they may generate very few beliefs indeed; they may leave the cognizer with very little information, even on the issues that interest him or her the most. The antidote to ignorance is not reliability, but (intellectual) power. Powerful cognitive mechanisms are (roughly) mechanisms capable of getting a relatively large number of truths. An intelligent cognitive system, it seems clear, is not simply a reliable system.

Goldman’s power and Breadth of Scope are similar in that they are both concerned with alleviating ‘ignorance.’ Nevertheless, we should be clear that the two epistemic notions are by no means the same. As Goldman (1986: 123) further notes: “Power [is] a function of the proportion of questions it [a cognitive system] wants to answer that it can answer (correctly), or the proportion of problems undertaken that it can solve correctly.” So, on one hand, Goldman’s power refers to a system’s ability to address a big proportion of the questions and problems it is interested in. Breadth of Scope, on the other hand, refers to the ability of a process to detect a high percentage of the positives or negatives it is looking for. Thus, the two notions seek to alleviate ignorance in different senses of the term. On one hand, power is meant to prevent cognitive systems from being reliable but highly specialised in the sense of being capable of generating correct beliefs in a few narrow domains, while failing to generate (thus ignoring) true beliefs in other important domains. On the other hand, Breadth of Scope is meant to prevent belief-forming processes from failing to detect (and thus ignore in another sense of the term) a significant percentage of the items they are meant to be looking for.

Despite the fact that the two notions are not the same, I here mention Goldman’s discussion of power because I am interested in his strategy for accommodating it within epistemology. Notably, Goldman does not associate power with knowledge but with the distinct notion of ‘intelligence.’ Presumably, the reason for this move is Goldman’s programmatic commitment to analysing knowledge and justification in terms of reliability. Since Goldman does not have a way to account for power in terms of reliability (i.e., in terms of a ‘high preponderance of true over false beliefs’), he avoids claiming that power is directly relevant to knowledge. So, the question we need to address here is whether one could deny that Breadth of Scope is directly relevant to knowledge in a similar manner.

In response, the preceding indicates that Breadth of Scope can be readily captured in terms of the standard definition of reliability as a ‘high preponderance of true over false beliefs.’ From reliabilism’s perspective, it would therefore seem arbitrary to discount Breadth of Scope as the kind of reliability that can be directly relevant to knowledge—especially when, as we have already demonstrated, high Breadth of Scope (i.e., high Recall and/or Specificity) is at least necessary for obtaining knowledge in a number of different cases (think of EG_AC’, EG_E’, EG_D, EG_D’, EG_IC, EG_IC’ as discussed in Section 4). Overall, then, accounting for knowing most ps (or not-ps) can be as important as accounting for knowing that p (or not-p), and reliabilism (or, more precisely, its upgraded version of dimensional reliabilism) is now in a position to analyse and assess attempts to satisfy both kinds of epistemic goals (and their combinations).

What is more, expanding reliabilism’s purview in this way should be a welcome result from a folk-psychological perspective. For, while Goldman might be correct in claiming that the antidote to the kind of ignorance he has in mind is ‘intellectual power,’ it is also widely assumed that the opposite of ignorance is knowledge. So, being in a position to explain how reliability in the form of high Breadth of Scope is crucial to knowing a sufficiently big percentage of what one is looking for is a promising way for spelling out, in reliabilist terms, this (at least) equally common assumption: That the way to alleviate (a common kind of) ignorance is through having knowledge—the kind of knowledge that is best captured by the locutions ‘know-most/know-all’, and which necessarily requires that the underlying belief-forming mechanisms manifest high Breadth of Scope.¹⁹

7. The Evolution of Reliability and Its Different Dimensions

According to evolutionary biology all species have evolved to exhibit traits that are conducive to coping within their natural environments. Instead of being the result of some intelligent design, these traits have, in brief, evolved by means of a long process of natural selection, which extends far in the past of the evolutionary history of each species. Likewise, according to evolutionary epistemology, organisms' epistemic capacities are the products of the same evolutionary process. (see also Bradie and Harms, 2023).

Conceiving of epistemic cognitive processes as the product of natural selection provides evolutionary epistemologists with a simple yet plausible argument for the reliability of naturally evolved belief-forming processes. Briefly, if a belief-forming process is not reliable, then any organisms bearing the relevant process will be unlikely to survive until the age of reproduction. In result, the unreliable process will not be passed on to later generations. Conversely, any belief-forming process that has passed the test of natural selection is a process that is in fact reliable.

This is an important claim for evolutionary epistemology and especially reliabilist approaches to it, such as proper functionalism. For example, in defending this claim, Peter Graham notes: “This matters a great deal to me, as I believe perceptual epistemic warrant is constitutively associated with perception having the etiological function of inducing reliably true perceptual beliefs, where biological functions are a species of etiological function” (2014a: 2).²⁰ Nevertheless, the tight connection between evolution and epistemic reliability has also been the target of much criticism over the years, with Stich (1985), Kitcher (1992) and Pernu (2009) all raising objections against it (or close formulations of it). While it is beyond the scope of this paper to fully defend the claim that evolved belief-forming processes are reliable against all existing objections, it will be useful to demonstrate how dimensional reliabilism can come to its rescue with regards to what has come to count as a pressing counterexample.

The counterexample I have in mind was first introduced by Tyler Burge (2010) and later discussed by Graham (2014a). Burge considers the case of rabbits and their capacity to accurately represent danger. The worry is that rabbits appear to be easily frightened in that they often behave as though danger is present when in fact it is absent. In his attempt to deal with this potentially worrying counterexample, Graham (2014a: 22) writes: “such [danger-detection] mechanisms are often unreliable, for false positives (‘danger is present’ when there is nothing to fear) outnumber true positives (‘danger is present’ when it’s time to run).” Accordingly, there appears to be a naturally selected belief-forming process, which is unreliable. Nevertheless, even if unreliable, Graham notes that the rabbit danger-detection mechanism is effective. Specifically, he writes (2014a: 26):

Many predator detectors work like this, where the representation of danger is not very reliable; it often represents the presence of danger when there is nothing to fear. Though effective—they “fire” almost every time danger is present and so keep the organism safe from harm, or at least give the animal a fighting chance—they frequently fire when danger isn’t present, and so are not very reliable. Nature has settled on such a way of avoiding predators because false negatives (“there is no danger present; I’m safe” when danger is lurking) are so much worse than false positives (“danger is present, run!” when there’s nothing to fear). If the animal overestimates the chances of danger and runs away at the slightest sign, it will effectively avoid predators when they are present, even if it frequently runs away when, in fact, it is perfectly safe. [. . .] Nature settled on an unreliable but effective device.

So, let us ask: Is Graham correct in thinking that such a danger-detecting mechanism is unreliable? And what does he mean when he says that it is, at least, effective?

Graham judges rabbits’ ability to detect danger as being unreliable, because “false positives (‘danger is present’ when there is nothing to fear) outnumber true positives (‘danger is present’ when it’s time to run).” Given the terminology introduced in Section 3, it seems clear that Graham refers to Precision. This shouldn’t really come as a surprise, given the preceding points that high Precision is clearly required for ‘know-that’. Nevertheless, as Graham further notes, such danger-detection mechanisms, though they fail to exhibit high Precision, they are at least effective. “They ‘fire’ almost every time danger is present and so keep the organism safe from harm, or at least give the animal a fighting chance.” So, given these points, Graham (2014a: 26) concludes his discussion of Burge’s counterexample, in the following way:

Nature settled on an unreliable but effective device, effective because accurate often enough. Most of our perceptual states and systems, however, are not like this. Most are reliable, and contribute to fitness by being reliable. Unreliable danger detectors are the exception that, so to speak, proves the rule.

Now, it is doubtful that proponents of evolutionary reliabilist epistemology would find this response particularly appealing—admitting, after all, there is an exception to the rule (that the evolution of epistemic mechanisms ensures their reliability) is to admit that the rule is potentially wrong. But does Graham need to concede this much? Is it actually correct to admit that the mechanism that keeps rabbits safe is unreliable on the grounds that it manifests low Precision?

I want to suggest that dimensional reliabilism may provide Graham with the means to offer a better response to the ‘rabbits counterexample.’ To see how, we only need to pay attention to what Graham means when he claims the mechanism is effective. If we invoke the terminology of Section 3, we will come to see that Graham’s points essentially amount to claiming that the relevant mechanism exhibits high Recall. That is, when Graham points out that rabbits’ danger-detection mechanisms are at least ‘effective’, he is effectively making a claim that is far more helpful to his view (and to evolutionary epistemology more generally) than it may initially sound. From the point of view of dimensional reliabilism, he is, essentially, making the claim that rabbits’ danger detection mechanisms are reliable, because they exhibit high Recall.

This may sound problematic if it is assumed that Precision is all there is to reliability. But from an evolutionary perspective, focusing, in this case, on Recall rather than Precision makes sense. Rabbits are vulnerable creatures that need to stay safe. So long as they are reliable by exhibiting high Recall with respect to danger, they can live a long and happy life—even if they often misrepresent safe situations as dangerous ones. Put another way, given their vulnerable nature, it makes sense that they have evolved a danger-detection mechanism that is epistemically reliable in such a way that it allows them to be ‘better safe than sorry.’ (see also Stich 1985: 125).

The present approach therefore can be used to defend the claim that evolved belief-forming processes are reliable against the rabbit counterexample. It demonstrates that even though rabbits’ danger-detection mechanism manifests low Precision, this is not sufficient grounds for thinking that the relevant mechanism is overall unreliable. Given rabbits’ epistemic goal—that is, detect most (ideally all) situations that are dangerous—Precision is not the right dimension of reliability to prioritise when assessing whether their danger-detection mechanism is reliable. Being most often correct when judging a situation to be dangerous but being unable to detect most dangerous situations would be disastrous for them. Instead, rabbit’s danger-detection mechanism needs to manifest high Recall—which in the case of rabbits is remarkably high. Thus, given their epistemic goal, rabbits’ danger detection mechanism is reliable after all and, contrary to Graham’s concession, they do not represent an exception to the rule that evolution ensures epistemic reliability.²¹

Of course, it may be further pointed out that the debate on evolutionary epistemology may have been framed, for the most part, in terms of a general notion of reliability or accurate representation, but, really, participants to the debate have been interested in the kind of reliability that can ensure knowledge. This suggestion could explain, for example, why the debate seems to have so far focused on Precision—the narrative should be familiar by now: Mainstream epistemologists have been primarily interested in ‘know-that’, and high Precision, as we have seen, is intricately related to ‘know-that.’ This may well be true, though it hardly justifies the debate’s exclusive focus on Precision. As it has been here argued, it is questionable whether Precision, or, more broadly Correctness, and the associated ‘know-that’ are all that should matter epistemically. ‘Know-most/all’ appears to be an equally important epistemic goal and the debate on evolutionary epistemology should pay equal attention to it.

And yet, it may be further argued, even if we grant that the debate on evolutionary epistemology should not exclusively focus on ‘know-that’ and high Precision, but should, instead, also focus on ‘know-most/all’ and Breadth of Scope, Precision may still play a role in assessing whether evolution can ensure the kind of reliability required for ‘know-most.’ As noted toward the end of Section 5, in addition to high Breadth of Scope, some degree of Correctness may also be necessary for ‘know-most,’ just not to the same level required for ‘know-that’—perhaps ‘know-most’ requires that Precision be only considerably above chance. With that in mind, the debate on evolutionary epistemology would then need to revisit the case of rabbits and ask: Can evolution ensure the kind of multidimensional reliability required for ‘know-most’? In other words, while we may grant that rabbits are able to detect most instances of danger (due to the high Recall of their mechanism), are they also in a position to know most instances of danger? The answer to this question will largely depend (a) on how much higher than chance (if that) we need Precision to be for claiming that a mechanism can deliver ‘know-most’ and (b) on the answer to the further empirical question regarding the extent to which rabbits actually misrepresent danger.²² While their Precision might be insufficient for knowing that danger is present, perhaps it would not be all that surprising to find out that it is good enough for knowing (as opposed to merely detecting) most instances of danger. And should this turn out to be correct, then the case of rabbits would not only fail to count as a counterexample against the claim that evolution ensures epistemic reliability; it would also fail to raise doubts against the stronger claim that evolution ensures reliability that is sufficient for (at least an important kind of) knowledge.

At any rate, the above should make clear that dimensional reliabilism can help us retain the general, causal link between evolution and epistemic reliability on the face of the rabbits example; what is more, introducing the suggested additional dimensions of reliability can add significant nuance to our understanding of the claims put forward by evolutionary epistemology. More generally, and relatedly, the preceding also highlights a broader point that has already been introduced in previous sections: Employing a mono-dimensional approach to epistemic reliability, whereby one is more likely to prioritise Precision (or, more broadly, Correctness) over other dimensions of reliability is misguided. Given epistemologists’ keen interest in ‘know-that,’ it is hardly surprising that this may have been the case (at least implicitly) so far. But as the foregoing suggests, mainstream epistemology may need—and now has the means—to get past this. To do so, it needs to stay aware of the fact that different epistemic goals—that is, what the agent aims at knowing—seem to call for varying levels of reliability across different dimensions. This is the core message of dimensional reliabilism.

8. Applications

So far, we have seen that mainstream epistemology’s implicit assumption that reliability is a mono-dimensional concept has been called into question. Functions for assessing the reliability of classification processes reveal that mainstream epistemology’s definition of reliability is open to at least four different interpretations: Precision, Negative Predictive Value (NPV), Recall and Specificity. It has also become evident that, depending on the agent’s epistemic goals, these dimensions of reliability and their combinations can all play a direct role in assessing whether a process is appropriately reliable and thereby knowledge-conducive. This observation invited us to upgrade reliabilism to dimensional reliabilism, according to which, assessing whether a process is knowledge-conducive depends on whether it manifests sufficiently high reliability along the appropriate dimension(s), given the epistemic goal at hand. As a final attempt to motivate the upgrade to dimensional reliabilism, this section highlights a few ramifications of the view, across both the theoretical and the practical domain.

9. Conclusion

By reference to functions for assessing the reliability of binary classification processes, the paper has argued that the popular epistemological approach of reliabilism stands to significantly benefit from the upgrade to what I have called dimensional reliabilism. Some of the theoretical advantages of this move involve bringing to the fore the importance of knowledge captured by the ‘know-most/all’ locutions, which, from a reliabilist perspective, do not seem reducible to ‘know-that.’ Moreover, the paper has demonstrated that by paying attention to ‘know-most/all’ and the underlying reliability dimensions of Recall and Specificity, we can defend evolutionary reliabilist epistemology from the ‘rabbits counterexample’ as well as provide the means for more nuanced analyses of several theoretical matters, including questions within evolutionary epistemology and the results of epistemological thought experiments. Additionally, and perhaps most importantly, on the practical side, dimensional reliabilism offers epistemologists the tools for analysing and better understanding the reliability of various information resources—from medical tests and individual informants to mass media and online information sources—by drawing important comparisons and distinctions that are inaccessible to a mono-dimensional approach to the notion of reliability. The upshot is that dimensional reliabilism has the potential to significantly expand the purview of reliabilism.