A Defense of Impurist Permissivism

Abstract

One famous debate in contemporary epistemology considers whether there is always one unique, epistemically rational way to respond to a given body of evidence. Generally speaking, answering “yes” to this question makes one a proponent of the Uniqueness thesis, while those who answer “no” are called “permissivists”. Another influential recent debate concerns whether non-truth-related factors can be the basis of epistemic justification, knowledge, or rational belief. Traditional theories answer “no”, and are therefore considered “purists”. However, more recently many theorists have argued to the contrary, claiming that impurist factors, such as practical stakes, can sometimes encroach or even override truth-related considerations. This paper bridges the two debates by presenting and defending what I call “Impurist Permissivism”. I support Impurist Permissivism by showing how it can resist Roger White's famous Argument from Arbitrariness (2005).

1. Introduction

One hotly debated issue in contemporary epistemology is whether evidence can be permissive. Essentially, the central question is whether there is always one unique epistemically rational way to respond to a given body of evidence. Generally, philosophers who propose a positive answer to this question are the proponents of the so-called uniqueness thesis. In contrast, epistemologists who reject uniqueness are identified as permissivists.

Another recent debate in epistemology centers around the issue of whether non-truth-related factors can be the basis of epistemic justification, knowledge or rational beliefs. Traditional theories jointly side on no to this issue. That is, they only consider truth-relevant factors, such as evidence or the reliability of belief-forming processes, to be the relevant factors when judging whether a belief is rational. Hence, they are purists about epistemic rationality. In contrast, in recent years, many have argued the contrary. For these theorists, epistemic justification is not purely about truth-relevant factors. Instead, pragmatic factors encroach or even override truth-related considerations at times. And these are the impurists.

This paper establishes and defends a view that I call impurist permissivism. I start with an introduction and a review of the permissivism–uniqueness debate. Then I argue all impurist views are by definition permissive in nature. The latter half of the paper is devoted to defending impurist permissivism. I reconstruct Roger White's famous Argument from arbitrariness (2005) and then show how impurist views are systematically resistant to his attack.

2. Background

2.1. Uniqueness and permissivism: epistemic conflicts and the epistemological orthodoxy

The debate between uniqueness and permissivism centers around the following question: Is there always one unique epistemically rational way to respond to a given body of evidence? Though this question itself is subject to certain ambiguities, roughly speaking, it is possible to give answers that pull in opposite directions as follows.¹

Proponents of the so-called uniqueness thesis are inclined to give a positive answer: given a body of evidence, there is just one unique epistemically rational attitude (hence “Unique-ness”). In contrast, permissivists tend to give a negative answer. Generally speaking, they deny the uniqueness thesis and propose cases in which there is more than one rationally permissible way to respond to a given set of evidence (therefore “Permissiv-ism”).

I shall discuss the ambiguities concerning the formulations of the exact theses that have appeared in the recent literature in section 2.2. Let us first look at the motivation behind both campaigns. Say that you were entering a bookstore to find a copy of Plato's Republic, which is normally displayed on the second floor. Unexpectedly, there was a sign on the ground floor suggesting that the second floor was temporarily closed. The sign looked authentic and there was no reason to suspect that it was a prank. Therefore, you formed a belief that the second floor was closed and then left the bookstore. Such a scenario seems quite ordinary. Without further information, it is natural to think that most people would judge your belief to be rational. The epistemologically intriguing question, however, is whether this is the only rational attitude to have. According to the long-standing philosophical orthodoxy, one's doxastic attitude is justified or rational only if one's attitude fits one's evidence. Therefore, it is tempting to think that if your belief that the second floor is closed is rational, then when anyone with the exact same evidence refuses to believe so – e.g., a person who sees the same arguably reliable sign but somehow strongly insists the second floor is open – they are being irrational. An intuition of this sort can be one motivation for accepting uniqueness.

It is a widely perceived phenomenon that people disagree. The topics that are susceptible to disputes range from daily doxastic commitments to moral or religious convictions. For example, in the case above, your friend standing next to you who was also in need of the Republic might have suggested that you should go above the stairs and see for yourselves just in case: “It's only 8 o'clock. Maybe they just forgot to retract the sign from yesterday.” For some reason, she just brought up a legitimate possibility and hinted that she needed more conclusive evidence before forming the same belief as yours. It seems natural that instead of calling her unreasonable just because of your initial differences, you might consider her proposal or even follow it. Perceived this way, at least on an intuitive level, it is hard to see why either one of you has to be irrational given your diverse responses, even though you have access to the same evidence. In addition, it is imaginable that she is a Buddhist and vegan, while you are a Christian who does not have a particular stance regarding vegetarianism. But you hardly think she is an irrational person – otherwise, you would not have been to the bookstore with her and even enjoyed chatting with her over lunch afterward. If you think this kind of friendship is possible or even exactly a part of your daily life, then it might be worthwhile to entertain the plausibility of permissivism.

Broadly construed, epistemic conflicts could be of a pure intellectual nature, but they could also happen to serve as the bases for practical deliberation and decision-making. They can be cases that lie between individuals such as you and your friend, but they could also be disputes at a societal, national, or cultural level. Sometimes they happen in one instant without any overt verbal cues in addition to a raised eyebrow; in other occasions, they are expressed as carefully crafted arguments to contest views that were thoroughly developed in the previous course of history. All in all, these phenomena have led to some serious attention to the debates between uniqueness and permissivism in contemporary philosophy.

Theoretically, the back and forth arguments between the two sides are closely connected with other debates in the vicinity, e.g., the epistemology of peer disagreement (Christensen 2009). But in addition to their contribution to these more locally connected debates, the increased attention to the tension between uniqueness and permissivism is also due to their intriguing connections with other epistemological theories within a broader picture (for examples, see Kelly 2014; Kopec 2015; White 2005).

2.2. Formulating the thesis: ambiguities and disambiguation

While the tension between the two campaigns of ideas can be easily spotted, when examining the relevant literature closely, neither one of the sides has an agreed-upon formulation of their favored position. Moreover, the ambiguities about their scope and strength come in multiple dimensions. In this section, I explain the ambiguities and disambiguate the theses in pairs, and I will also point out the formulations that I prepare to work with in the later sections.

Let me start with White's presentation of the uniqueness thesis:

White's uniqueness thesis: Given one's total evidence, there is a unique rational doxastic attitude that one can take to any proposition.

According to Kopec and Titelbaum (2016), there is a scope ambiguity regarding White's thesis. Here are the two potential readings: (1) we fix first upon a cognitive subject, and then, for that subject in particular, White's uniqueness thesis holds that for any proposition, there is one unique rational doxastic attitude she can have based on her evidence; (2) we fix first upon a set of evidence, and then, for any subject with this set of evidence, White's uniqueness thesis holds that for any proposition, there is one unique rational doxastic attitude any subject with this set of evidence can have.

The second reading is logically stronger – if based on the same evidence, there is only one rational doxastic attitude toward a proposition anyone can have, then surely, for any particular subject, that attitude is the only rational attitude to have. As a matter of comparison, the first reading is recognized as an intra-personal reading, while the second an interpersonal one.

Intra-personal uniqueness: For any subject S, given their body of evidence E regarding a proposition p, there is always at most² one unique rational doxastic attitude for S to take with respect to p.

Inter-personal uniqueness: Given a body of evidence E, about a proposition p, there is at most³ one unique rational doxastic attitude for any cognitive subject S to take with respect to p.

As explained above, inter-personal uniqueness entails intra-personal uniqueness.

In the literature, permissivism is usually defined as the denial of the uniqueness theses. Therefore, I formulate the corresponding permissivist theses as follows:

Intra-personal permissivism: It is possible that for a subject S with total evidence E, there is more than one rational doxastic attitude for S to take toward p.

Inter-personal permissivism: It is possible that for two subjects S and S′ with total evidence E, S and S′ could adopt different rational doxastic attitudes toward p.

As it stands, intra-personal permissivism entails inter-personal permissivism. Following White, I shall call these potentially possible scenarios permissive situations or permissive cases (White 2005). Although White does not make these two dichotomies explicit, others have suggested that they may be worth attention (see, e.g., Kelly 2014).

Another explanation about the four theses at our disposal is about how doxastic attitudes should be cashed out. The relevant literature covers both coarse-grained and fine-grained attitudes. The former attitudes are usually considered to include belief, disbelief, and some potential neutral attitude candidates such as suspension or withholding judgment. They are the primary focus of traditional epistemologists; while the latter attitudes are under the category of credence, which is the subject matter of formal epistemology and decision theory. Some classic arguments within the uniqueness–permissivism debate are considered to be about both kinds of attitudes (see White (2005) and Kelly (2014) for examples). Therefore, I leave the formulations to be compatible with both interpretations. However, in this paper, I limit the scope of my discussion to outright-belief level doxastic attitudes. This is partly because there is a lack of consensus among theorists of how belief and credence relate to each other. Moreover, given my purpose of providing one route for defending permissivism, I find it unnecessary to step into this controversy.

Relatedly, the distinction between what White calls extreme permissivism and moderate permissivism also demands clarification. In my opinion, they should simply be read as specifications of the theses defined above. The former is a permissivism over believing p and believing not-p, while the latter is over believing p (or believing not-p) and some neutral attitude. In White's terminology, permissivism over different credence is also considered moderate. But as mentioned, this will not be my focus, hence it will not be included in moderate permissivism.

Potentially, the permissivist results can be realized in a number of different ways. One widely considered possibility in the current literature concerns epistemic standards: roughly speaking, the different permissive results considered rational are each evaluated against a distinct permissible epistemic standard. Schoenfield (2014) provides several examples of what an epistemic standard might be like: they can be in the form of rules such as “Given E, believe p,” or simply beliefs about how other beliefs should be formed. I believe that epistemic standards can also be expressed in probabilistic terms, such as “Believe p, if the evidential probability is greater than 0.7,” which is equivalent to “Believe p, if Pr(P|E) ≥ 0.7.” Crucially, Schoenfield suggests that “we can just think of a set of standards as a function from bodies of evidence to doxastic states which the agent takes to be truth-conducive” without getting into the controversy of how epistemic standards are fleshed out. (For a more general discussion on permissivism over epistemic standards, see Ru Ye 2019.)

3. Establishing impurist permissivism

In this section, I aim to establish the connection between the uniqueness–permissivism debate and the so-called purism–impurism debate (which I will introduce shortly). The goal is to point out the big-picture links and show the logical relations between these theses.⁴

3.1. Purism and the orthodox view in epistemology

In the traditional analysis of knowledge prior to Gettier (1963), justified true belief (henceforth JTB) is considered to be the necessary and sufficient condition for knowledge. Gettier cases revealed how JTB is not sufficient for knowledge. Later, a large amount of literature has been devoted to establishing a connection between justification and truth. In a way, this then shaped a tendency to perceive truth as the most important goal of epistemological inquiries. This is why knowledge or justified beliefs are considered to solely be based on truth-relevant factors, and such an orthodox view that purely allows veridical considerations, is recognized as purism. In addition, another motivation for purism roots in the consideration that truth is the constitutive aim of belief (see Shah and Velleman (2005) for related discussion).

Here is a summary of purism by Jeremy Fantl and Matthew McGrath (2009):

Purism about knowledge: For any subjects S and S′, if S and S′ are just alike in their strength of epistemic position with respect to p, then S and S′ are just alike in whether they are in a position to know that p.⁵

Some clarifications on Fantl and McGrath's notion of epistemic position will make this clear: according to Fantl and McGrath, your epistemic position with respect to some proposition p is your standings on the truth-relevant dimensions such as how reliable your belief-forming process for p is (see Goldman (1979) for instance), or how strong your evidence about p is, or how strong your counterfactual relations to the truth-value of p are. Naturally, each of these factors corresponds to some first-order epistemological theories, i.e., reliabilism, evidentialism, and safety or sensitivity analyses of knowledge, and that is what makes purism about knowledge a meta-claim.

A terminological clarification is in order here. Since according to Fantl and McGrath, epistemic position just labels one's profiles on truth-relevant dimensions, I consider it better⁶ to just call it one's truth-relevant profile.

Historically, purism about knowledge has been the orthodox epistemological view. However, knowledge is not the only central notion in contemporary epistemology, especially not in the post-Gettier era. Quite a lot of attention has been drawn to concepts such as (epistemically) justified beliefs and (epistemically) rational beliefs. That is why I consider the following thesis also captures a significant disposition of orthodox epistemology.

Purism about rational belief: For any subjects S and S′, if S and S′ are just alike in their truth-relevant profiles with respect to p, then S and S′ are just alike in whether they are rational in believing p.

3.2. What impurism is

Evidently, Impurism about rational belief will be the denial of purism about rational belief.

Impurism about rational belief: There are two subjects S and S′, S and S′ are alike in their truth-relevant profiles with respect to p, but S and S′ are not alike in whether they are rational in believing p.

In other words, on the surface, to stand as the negation of the purism thesis, impurism merely has to state that two subjects who are alike in their truth-relevant profiles with respect to p can still differ in their rationality status in believing p. In this sense, it is a fairly minimal and abstract position.

However, in concrete notions, as we shall see in section 5, all impurist views on the market cash out the non-truth-directed dimensions in terms of practicality (and not, say, as aesthetic concerns or biological constraints). In other words, according to impurist epistemologies, a cognitive subject's practical environment or pragmatic considerations can make a difference in regard to her rationality or knowledge status even if all truth-directed factors are held constant.

We will be looking at the detailed impurist theses and their motivations in section 5. But roughly speaking, there are generally two reasons to entertain the plausibility of impurist views. First, our cognitive commitments play a significant role in practical decision-making. We rely on the beliefs and knowledge that we have in choosing the right course of action. It is generally recognized that the threshold of how much information we need in order to rationally act varies according to the occasions. Impurists are sympathetic to the idea that at times such a variation in the threshold for how much information is required for action also reflects on our epistemic rationality requirements – we cannot know or rationally believe a proposition that we are not willing to act upon. And second, it has long been recognized that words like know are context-sensitive, and impurist theories are able to account for such data.⁷

We will look at this in detail in section 5. Now I shall begin my establishment of impurist permissivism by arguing that all impurist views are permissivist views by definition.

3.3. Why impurism is a type of permissivism

Recall the purism about rational belief thesis in section 3.1 and inter-personal uniqueness thesis in section 2.2:

Purism about rational belief (PRB): For any subjects S and S′, if S and S′ are just alike in their profiles on truth-relevant dimensions with respect to p, then S and S′ are just alike in whether they are rational in believing p.

Inter-personal uniqueness (IPU): Given a body of evidence E, about a proposition p, there is at most one unique rational doxastic attitude for any cognitive subject S to take with respect to p.

Crucially, inter-personal uniqueness entails purism about rational belief: if, according to IPU, S and S′ are alike in their evidential status with respect to p, then they will be alike in whether they are rational in believing p. (Why? Believing p is either the only rational attitude for anyone with their evidential profile to adopt or not. If it is, then both subjects are rational; if it isn't, then both are irrational.) Meanwhile, PRB provides a stronger antecedent: it declares that S and S′ are alike in all their truth-relevant standings with respect to p (which entails that they are alike in the evidential status regarding p). And it is under this stronger premise, they will be alike in whether they are rational in believing p.⁸

Consequently, impurism (at times also labeled as non-intellectualism ⁹), as a denial of purism, shall also be a denial of uniqueness. Conceptually, since uniqueness and permissivism are jointly exhaustive, all impurisms are therefore permissivisms.¹⁰

Impurist permissivism: For some subject(s) S and S′, even if S and S′ are just alike in their truth-relevant profiles with respect to p, S and S′ are still rationally permitted to adopt different rational doxastic attitudes toward p. (S and S′ can be two different subjects or different time-slices of the same subject.)¹¹

Let's briefly reflect on what has been included in the aforementioned formulations of the uniqueness and permissivism theses in section 2.2, and what has been left out. To do so, compare these abstractions with our concrete examples of conflictual situations introduced in section 2.1. Regardless of your stance, you may notice the following about our definitions of permissivism: we do not distinguish cases where the differences in attitudes are overtly expressed through verbal channels and the ones where the conflict is never put on the table; nor do we attribute any significance to whether the differences in attitudes happen synchronically or diachronically. We also have no systematic way to address or categorize the propositions involved, and we ignore other aspects of the agents' identities and circumstances.

My opinion is that we should be cautious about what has been left out in our abstractions. The parameters that successfully made their way to these definitions or their commonly assisting explanations are more or less merely a reflection or consequence of the currently well-explored aspects of epistemic conflicts. They may be important parameters or postulates we imported from other prominent territories in epistemology, e.g., type of doxastic attitudes, or an observational result from naturally imposed partitions, e.g., the intrapersonal/interpersonal dichotomy. But as we have observed in section 2.2, at a more concrete level there are more distinctive features to each disagreement.

In section 4, I will introduce and analyze arguably the most famous argument that has allegedly systematically threatened all permissive views. I will then, in section 5, argue that impurist permissivism (i.e., impurism as a kind of permissivism) is systematically resistant to White's argument.

4. White's argument from arbitrariness: an impurist permissivist response

4.1. A reconstruction of White's argument

As far as my interpretation goes, the argument from arbitrariness takes the form of a reductio ad absurdum. It first comes across as an alleged threat to what we now read as an extreme intra-personal permissivism (by the definitions introduced in section 2.2) and then purportedly spreads its undermining power over all forms of permissivism by generalization on multiple dimensions. We start with White's formulation of his first target:

Extreme permissivism: There are possible cases in which you rationally believe P, yet it is consistent with your being fully rational and possessing your current evidence that you believe not-P instead.

Let us start with White's favored legal example. Suppose S is a jury member presiding over the criminal trial People versus Sam. Before she had access to the evidence, S abided by the presumption of innocence principle as instructed by the court. Then after carefully examining the relevant evidence, she formed the belief that Sam was guilty of murder. So she voted Guilty accordingly during jury deliberation. This sounds like a legitimate way of belief-forming and decision-making. In comparison, the following hypothetical scenario, not so much:

Hypothetical: Suppose instead of viewing her evidence, S decided to choose her attitude toward whether Sam is guilty on the basis of the result of coin-flipping. Heads for a Guilty verdict, tails for a Not-Guilty one. She got heads, so she believed and voted accordingly. Alternatively, for someone who thinks it is impossible to have voluntary control over one's belief-forming, consider a more radical imaginary case in which there are some belief-inducing pills: some make you inclined for a Guilty verdict and others for a Not-Guilty verdict. S picked one randomly, swallowed it, and found herself having the belief that Sam is guilty. What's more, she was fully aware of how her attitude was formed, and yet she still acted upon it and voted Guilty.

Repress your immediate anger for the irresponsibility and ridiculousness just witnessed for a moment, and return to our original narrative. Recall that S's current belief that Sam is guilty is carefully formed on the basis of evidence. However, suppose there were some details I left out just now – under the influence of some permissive epistemology, S also comes to believe that this is an extreme (intra-personal) permissive situation, that is, she believes that were she to have the doxastic attitude of believing Sam was not guilty based on exactly the same set of evidence, she would also be equally rational. In short, she acknowledges that from the point of view of forming a rational belief, there is no difference between believing and disbelieving Sam's guilt. Yet, she still holds that Sam is guilty.

Now, here is the question White raises: if both attitudes are equally rational, what exactly is the factor that determined S's current attitude of believing? By the definition of permissivism, it could not have been the evidence S examined – because this is equally consistent with S rationally believing not-p. So it must have been something else – something non-evidential and arbitrary.

But that is troubling. That means it was something arbitrary that had decided the end product of S's belief-forming process. So, when S came to acknowledge this (and by hypothesis she does), can she still rationally hold on to her original commitment? The proper answer seems to be “No.” For if we agree to the opposite, it means we are allowing arbitrariness in rational-belief-forming. With more concreteness of this case, it means that we would be allowing a jury member to knowingly base her decision on coin-flipping-like randomness as rational.

If being aware of the arbitrariness involved, S still does not question the rational status of her belief, isn't it just as problematic as in hypothetical? Initially, one might think there is a difference there – in hypothetical, S's belief is formed purely on an arbitrary basis. She did not even look at the evidence. That is why we have a strong intuition for not calling it a rational way of belief-forming. In contrast, for S's actual belief that Sam is guilty, she did carefully examine her evidence.

But here is White's point. In S's line of reasoning, although the arbitrariness is just a part of the whole belief-forming process, it is the decisive factor. It is able to swamp the result of evidential support. To be more elaborate, suppose, for instance, the current evidence in the criminal court points to Sam being not guilty, but instead of following the presented evidence and believing Sam is not guilty of murder, S consciously let whatever arbitrary factor overturn the result of evidential support, and ended up believing otherwise. Shouldn't this induce the same kind and even the same level of rage as we had for hypothetical? Once the reasoning has this arbitrary determinant embedded, it also does not seem to be less worrisome even if S's conviction just happened to coincide with the result of evidential support. The bottom line here is that in effect there really is not any difference between pure arbitrariness and partial (but decisive) arbitrariness.

From a theoretical perspective, we could refine the above line of thought further. It has been a widely agreed-upon position that one ought to follow one's total evidence in forming doxastic attitudes. According to White, the position is plausible because following evidence “is a fairly reliable guide to the truth.” Further to that, others have proposed different motivations for accepting an evidentialist position, e.g., according to Feldman and Conee (1985), as epistemic agents we have a role responsibility to follow our evidence.

But according to White, once we make it possible for arbitrary factors to override the result of evidential support, like in S's case above, it would be very hard to account for why we want to pose this sort of evidentialist requirement upon S, or any cognitive subject at all, in the first place. In short, White is pushing the idea that if we do judge cognitive subjects with S's line of reasoning to be rational, then the traditionally assumed evidentialist positions are heavily undermined.

Therefore, once she acknowledges being in a permissive situation, S should immediately question the rationality of her own doxastic commitment because she should be able to tell from the above line of reasoning that her attitude is no better justified than in hypothetical.

All of the above is to motivate three ideas: (i) It is never rational to knowingly form one's belief on an arbitrary basis. An explicit case would be hypothetical, for which we have strong intuition against calling that a rational way of belief-forming. (ii) Acknowledging being in a permissive situation is just like being in hypothetical; it is to knowingly form one's attitude on an arbitrary basis, because there is in effect no difference between pure and partial arbitrariness. (iii) Since we find what happened in hypothetical irrational, the same should apply to S's permissive case as well. That is, under our supposition that S acknowledges that she is in a permissive situation, we reach the result that she is aware that her current belief that Sam is guilty is arbitrarily formed, therefore, it is not a rational attitude.

However, by the definition of extreme intra-personal permissivism, if this is a permissive situation, then for S, both believing p and believing not-p, based on the current evidence, are rational. This means that acknowledging being in a permissive situation implies that it is rational for S to form her attitude, i.e., believing p, on an arbitrary basis.

We reach a contradiction here – under the supposition that S acknowledges that she is in a permissive situation, S is both rational and irrational in believing p. By reductio, we should deny that S acknowledges that she is in a permissive situation.

According to White, the above conclusion does not immediately make it impossible for S's current epistemic situation to be permissive. What it leads to is that even if this is indeed a permissive case, S can never acknowledge that fact – once she realizes she is in a permissive case, either she drops her current attitude (so the situation will not even qualify as a candidate for permissive situations); or, she is no longer in a permissive situation because she knowingly holds an arbitrarily formed attitude, hence is irrational.

With some generalization, it follows that extreme intra-personal permissivism is an unstable position – once a cognitive subject realizes that she is in a permissive situation, she can no longer be in one. According to White, this undermines permissivism radically, because the only position left for permissive views is that one can only be in a permissive situation if one is not aware of being in one.

White's target is not just intra-personal extreme permissivism. Instead, he considers the above line of reductio to threaten all of the permissive views I introduced in section 1. The reason is that allegedly, the arbitrariness problem is embedded in the purported defective structure of permissivism.

If that is the fundamental thought, then the attempt to generalize the reductio to other permissive structures should not be surprising. My reading is that White provides a multidimensional strengthening:

Dimension 1: from extreme permissivism to moderate permissivism: in the aforementioned legal scenario, the two rational available attitudes to S are believing Sam is guilty and believing Sam is not guilty. This, according to the terminology introduced in section 2.2, falls within the category of what White calls extreme permissivism. In abstract terms, this is a permissive case over believing not-p and believing p. However, it seems the same problem persists, even if the permissive commitment is more moderate, in a sense that one of the proposed rational doxastic attitudes is a neutral position, such as suspending one's judgment. A parallel argument as above would involve suggesting that if the current set of evidence indicates that S should suspend judgment while S acknowledges that both disbelieving Sam's purported guilt and withholding judgment are both rational. Then, S's withholding judgment is not rational as it wrongfully involves arbitrariness, so S can no longer be in a permissive case.

Dimension 2: from permissivism over doxastic attitudes to permissivism over epistemic standards: in White's terminology, permissivism over epistemic standards is named subtle permissivism. I would imagine that such a position is considered subtle because the permissive result on the attitude level is merely a product of treating alternative epistemic standards rationally as acceptable. All the above discussions so far treat evidence as if it alone can give us a unique answer (except for cases of dilemma, if any). But a permissivist might respond that instead of arbitrarily forming my attitude, I reached my conclusion through a reliable means, i.e., my epistemic standard; I would only reach the other conclusion through a different epistemic standard. White's general thought is that this sort of response merely makes the arbitrariness worry retreat to the level of epistemic standards. Once the cognitive subject is aware that there are multiple acceptable standards, she should question “why this over that?” if they are genuinely equally truth-conducive. There must have been some arbitrary factor that has determined my choice of one standard over the other. Hence, a contradiction – by supposition, both standards are rational; but in fact, given there is acknowledged arbitrariness involved in my picking my standard, it is in fact irrational. Therefore, I could not possibly acknowledge being in a permissive situation over epistemic standards.

Dimension 3: from intrapersonal permissivism to interpersonal permissivism: as introduced in section 2.2, White himself does not make the intrapersonal/interpersonal distinction explicitly. Once we make the dichotomy explicit, all arguments I introduced so far seem only to be about intra-personal cases. However, in multiple places in his paper (esp. section 5), he suggests that even if it is a permissive case across cognitive subjects, the same worry applies – why my attitude or standard over yours? Arbitrariness. By supposition, both are rational. In fact, mine is arbitrary and therefore rationally undermined. By reductio, give up the supposition.

In sum, for White, all of the aforementioned positions are subject to the same structured worry:

White's argument from arbitrariness (AfA henceforth)

Assumption: suppose for reductio that S rationally acknowledges that she is in a permissive situation.

Premise 1: if one rationally acknowledges that she is in a permissive situation of any kind, then by the definition of permissivism, it implies that it is rational for her to consciously form her doxastic attitude on an arbitrary basis.

Lemma 1: (by assumption) it is rational for S to consciously form her doxastic attitude on an arbitrary basis.

Premise 2: it is never rational to consciously form one's doxastic attitude arbitrarily.

Conclusion: it is impossible for S to rationally acknowledge that she is in a permissive situation.

The conclusion does not directly falsify permissivism. However, it implies that permissivism is an unstable position – even if permissivism is true, it is impossible for S to rationally believe that she is in a permissive situation – once the cognitive subject comes to a realization of her being in a permissive situation, she can no longer be in one.

4.2. Analyzing the AfA: my diagnosis and evaluation

I hope my reconstruction above has charitably captured how intuitive and sophisticated White's argument is. In this section, I aim to point out the weak spot in AfA. I argue that given the most charitable interpretation of the key notion of arbitrariness, P1 is not as impeccable as it initially appears.

Let me start with a review of our initial source of plausibility for each premise, with a focus on how we have interpreted arbitrariness so far. Our initial acceptance of P2 is because we intuitively recoil at what happened in hypothetical – knowingly forming one's doxastic attitude on a coin-flipping-like mechanism. Accordingly, we denied the rationality of the subject in hypothetical. Further to that, for any acknowledged belief-forming that inherits the same kind of arbitrariness as a decisive factor, we find a denial of rationality equally necessary. In general, for P2 to work, we expect that whenever we talk about arbitrariness and its cognates, we mean a coin-flipping-like mechanism.

The key to our acceptance of P1, given White's narrative, is that there is some sort of equivalence in S's permissive reasoning and the thought of reasoning in the hypothetical. As I have pointed out, there is a pure/partial difference there. But ultimately, we find P1 convincing because we think the two lines of reasoning are alike to a large extent – they are both dominated by arbitrariness. Here again, we took the sort of arbitrariness to have the same effect in permissive cases as in the hypothetical. That was how we reached P1.

Throughout the argument, the notion of arbitrariness must be interpreted in this natural and non-technical way, to preserve our intuition for both premises as well as a recognition of the consistency over AfA as a whole. This is why I consider the coin-flipping reading as charitable.

But I think when we take a look at White's premise 1 alone, we would sense a problem with this coin-flipping interpretation of arbitrariness. As I have explained, White intends to suggest that partial and pure arbitrariness is in effect the same – they both override the result of evidential support. But even if we grant that the non-evidential factors do have an overturning potential against the result of evidential support, it is unclear why they have to function in a coin-flipping-like manner. In other words, even when we accept that the additional non-evidential factor in permissivism is indeed the decisive factor, just like coin-flipping decides the result in hypothetical, there is actually a lack of explanation on why it has to be of the same category, namely, to perform in a random, coin-flipping-like manner.

Even if this can be proven true ultimately, as White might insist, I find the lack of explanation in his current formulation of AfA to be a weakness. One potential route around this is to insist that no explanation is required here – non-evidential factors are always arbitrary per se because that is what we mean by arbitrary.

Here is my response: if you embed this stipulated sense of arbitrary into P2, P2 would be question-begging – it would almost be a direct denial of permissivism being acknowledgeable. In a way, this is just like packaging whatever extra-evidential factors that are deemed admissible in rational belief-forming by permissive views, labeling them as arbitrary, and calling it irrational to knowingly form attitudes based on them.

Therefore, the most charitable way of interpreting the notion of arbitrariness in AfA is in terms of a coin-flipping-like random mechanism, because that preserves our intuition that motivated our initial acceptance of the argument as well as prevents the argument from begging the question against permissivism. However, even under this charitable reading of AfA, both premises of the argument can still be dubious.

Before responding to White's argument, let me clarify the dialectics so far. White's intended scope for AfA is universal in a two-fold sense. He targets all epistemologies with any of the permissive structures mentioned in section 2.2, and argues that any permissive case entailed by any of these permissive accounts is a victim of his conclusion. Therefore, a counterexample to White's conclusion simply needs to be a permissive case where one of the premises does not apply.

In the last two sections, I will pursue my current diagnosis in a more vivid and concrete way. Most of my argument intends to go against P1: in a nutshell, the idea is that quite a few candidates suggested by alternative theories of epistemic rationality actually function in a perfectly systematic and non-arbitrary way. In addition to that, once we establish this new framework, it is unclear why the coin-flipping type of arbitrariness in belief-forming has to be unacceptable all the time.

5. The impurist responses

In section 3.3, I gave an argument that shows all impurist views are permissive by definition. In this section, I show how exactly individual impurist views are permissive and why they are all resistant to White's argument. I start with pragmatic encroachment views in sections 5.1 to 5.3 and then I move on to pragmatism in section 5.4.

5.1. Pragmatic encroachment as impurism

The first impurist theory we shall be looking into is the earliest and most prominent pragmatic encroachment attempt raised by Jeremy Fantl and Matthew McGrath (2002):

Fantl and McGrath's Pragmatic Encrochment (PE) thesis: S is justified in believing that p only if S is rational to act as if p.

As it stands, the thesis poses a necessary condition on justified or rational belief. To explain, the amount of justification needed for the belief that p to be justified varies depending on how significant the action related to p is. The more that is at stake regarding this action, the more evidence one needs in order to be justified or rational in believing p.

Fantl and McGrath especially emphasize that their support for the above thesis is not an appeal to our intuitions for particular cases, but “a theoretical argument for a condition on justification.” However, they do later apply their thesis to a pair of cases, in which the subjects' evidential statuses are the same while practical stakes differ, to show the predictions their theory entails. In addition, broadly construed, their theory starts with a condition on knowledge, but later targets justification. Generally speaking, they appeal to a decision-theoretic framework as the methodological justification for their account (see Hawthorne & Stanley (2008) for discussions).¹²

Mark Schroeder (2012) also provides a pragmatic encroachment account but both the motivation and underlying mechanism differ from the previous view. He adopts the following Jamesian line of thought to explain how pragmatic encroachment on knowledge or epistemic justification is possible – there are two kinds of epistemic goals: avoiding falsehood and attaining truth. Consequently, different cognitive strategies ought to be deployed for different purposes. Specially, one has a reason to withhold judgment about p when the goal of avoiding falsehood outweighs the goal of finding out the truth with regard to p. Crucial to our purpose, he argues that the reason to withhold cannot be evidential. Here is why: (P1) Evidence about p is either for or against p. (P2) Evidence for p is a reason to believe p; evidence against p is a reason to believe not-p. (C₁) Evidential reasons can only be reasons to believe p or believe not-p. (C₂) Reasons to withhold cannot be evidential, therefore, they have to be from something practical by nature. This is how practical considerations encroach upon the epistemic.

It is worth noting that Schroeder's view corresponds to Thomas Kelly's defense (2103) of permissivism against epistemic instrumentalism. While the two views differ in their exact formulations, they both commit to a fundamental Jamesian epistemology.¹³

5.2. How pragmatic encroachment views are permissive

Two things need to be flagged before we move on to case demonstration and arguments for why pragmatic encroachment views are permissive accounts. First, in order to have a unified picture, I shall appeal to probabilistic notions for the purpose of illustration. But a theorist of pragmatic encroachment does not necessarily have to commit to a probabilistic understanding of the strength of evidential support or think about epistemic standards in terms of probability parameters. As a matter of fact, aside from the general controversy I mentioned in section 2.2, there is a lack of consensus among theories of pragmatic encroachment of how coarse-grained attitudes and fine-grained attitudes ought to relate. (See Fantl and McGrath 2009; Ross and Schroeder 2014.)

Second, the cases I shall use are legal by nature. In this sense, they are different from the examples of both Fantl and McGrath (2009) and Schroeder (2012), in which the propositions of focus are not shaded with this extra layer of complication from the philosophy of law. However, I aim to provide an intuitive narrative that corresponds to White's jury case introduced in section 4 in order to better prepare for further arguments later. Therefore, I adapt the train case of Fantl and McGrath (2002) and the bank case of Schroeder (2012) into a parallel series of legal cases. However, admittedly, how the legal conception of evidence and standard of proof in criminal trials ought to be captured are in themselves complicated and significant issues. Therefore, the authors do not necessarily have to accept my results in applying their theory to the legal domain – though I do think appealing to legal cases offers us a nice way to utilize the current legal practices and theories as preliminarily justified intuition.

We can now move to the cases as there will be discussions afterward. In what follows, let P and E be variables that stand for some proposition and some set of evidence, and p stand for the proposition that Sam is guilty, and e for the evidence possessed by some subject S.

Low stake: Suppose Xinyan Zhu is a responsible citizen who is concerned with public security in the neighborhood. However, Xinyan is a busy equity analyst and the only occasion she could learn about public affairs (beyond her area of focus) is during her newspaper reading while having breakfast. It is then she reads about the People versus Sam trial. When it comes to crime-related news, due to both a concern for public justice and self-preservation, she has an epistemic standard of Pr(P|E) ≥ 0.7 for forming a belief that S is guilty of a certain crime. She therefore thoroughly examines the evidence that is legally permitted to be shown to the public in the newspaper, which bears a Pr(p|e_a) = 0.8. Given 0.8 > 0.7, she then comes to the belief that Sam is guilty.

High stake: Suppose Belinda Chen was appointed as a jury member for the murder trial People versus Sam. She was a conscientious citizen who was determined to find out the truth of whether Sam was guilty, because she found it an obligation to convict Sam if and only if Sam's guilt is beyond a reasonable doubt (BARD). In legal theory, the BARD standard, when cashed out in probabilistic terms, is usually considered to be a standard of Pr(P|E) ≥ 0.9 or 0.95 (Laudan 2011). Moreover, Belinda found it a significant matter to put someone in jail with governmental coercive power, and she did not want to falsely convict an innocent man. Therefore, BARD as 0.9 is where Belinda's current epistemic standard lies. The trial began, and she was presented with a fair amount of evidence for a starter. Although she recognized that the evidence pointed to Sam's being guilty to a large extent, yielding a Pr(p|e_b) = 0.8, she was still withholding her judgment about whether Sam was guilty due to her 0.9 standard.

Low stake′: Unfortunately, Belinda overheard a conversation between the prosecutors discussing the murder trial when she was in the bathroom. She did not hear any details about the murder, especially not anything that can be counted as evidence regarding Sam's guilt, so her evidential status is still at Pr(p|e) = 0.8. However, given the court instructions, she still found it necessary to recuse herself and so she did. After her recusal, as a caring and diligent member of the community (just like Xinyan), she still paid her attention to the result of the trial, but she also found it a relief that she no longer participated in a life-or-death decision anymore. Therefore, her current epistemic standard for believing that Sam is guilty is at Pr(P|E) ≥ 0.7. Consequently, she formed a belief that Sam is indeed guilty of murder.

We can see that e_a and e_b confer the same evidential probability when it comes to supporting the proposition p. Let us apply the theories of Fantl and McGrath (2009) and Schroeder (2012) theory to the cases above to see their potential predictions about the above cases.

According to Fantl and McGrath, a subject S is rational to believe p only if she is rational to act as if p. In high stake, Belinda would be irrational to believe that Sam is guilty, due to the high stake attached to her belief of whether Sam is guilty of murder – a guilty conviction can be made against Sam if Belinda does form the belief. Given the current 0.8 evidential probability does not surpass her 0.9 standard, she is rationally permitted to stay neutral – her withholding judgment and waiting for further evidence in support of p before forming a belief that p ensures that she does not convict an innocent man.

On the contrary, in low stake and low stake′, the respective subjects, Xinyan and Belinda, are rational to act as if Sam is in fact guilty of murder, provided the setup. To explain, a 0.7 standard serves their own inclination for fair treatment to other citizens while ensuring their own safety. And because the current evidential status at 0.8 is already higher than 0.7, there is no need to spend the cost for further inquiry, both Xinyan's and Belinda's beliefs are therefore rationally permissible. In short, the necessary condition from action constraint is satisfied, and the overall picture shows the subjects are rational in believing p.

Similarly, for Schroeder's account, high stake should be read as a situation where the goal of avoiding falsehood about p outweighs the goal of attaining truth about p to a large extent. Potentially, for such a situation, a 0.9 standard is proper. Belinda therefore has a reason to withhold judgment; however, according to our setting, low stake and low stake′ are still situations in which avoiding falsehood outweighs missing out on true belief, but to a smaller extent. A 0.7 standard reflects this well. Accordingly, provided the current evidential probability in supporting p is at 0.8, both subjects are permitted to believe p.

In sum, all subjects mentioned are rationally permitted to hold their current doxastic attitudes according to both Fantl and McGrath (2009) and Schroeder (2012).

We see from the definitions in section 2.2, permissivist theses are existential claims. They simply claim there are possible cases in which based on the same evidence, different doxastic attitudes toward the same propositions are epistemically permissible. That is, once we found theory X entails a permissive case, X is a version of permissivism. Therefore, comparing the results above and with the definitions provided in section 2.2, we would reach the summary that both PE views entail the permissive views as follows:

Moderate interpersonal permissivism: under the supposition that both subjects, S and S′, have the same set of evidence, in low stake, S (Xinyan) is rationally permitted to believe p, whereas in high stake, S′ (Belinda) is rationally permitted¹⁴ to suspend judgment about p.

Moderate (diachronic) intra-personal permissivism: Under the supposition that the subject S (Belinda) has the same set of evidence over time, in high stake, S (Belinda) is rationally permitted to suspend judgment. In contrast, S (Belinda) is rationally permitted to believe p in low stake′.

A few clarifications need to be made here. First, we can now see to what extent the exact numbers for the evidential probability that I stipulated just now matter in deriving the permissive results: in order to have a permissive case over believing p and withholding judgment about p, we simply need two epistemic standards (across subjects for interpersonal cases, and within a subject for intra-personal ones) that are (1) both greater than 0.5, and (2) differ from each other in their level of stringency. The second condition then allows there to be a “permissive zone” for which when the evidential probability for p is in it, subjects with different stakes are permitted to have different attitudes. In our cases above, it is in between 0.7 ≥ Pr(P|E) ≥ 0.9 or 0.95. But the exact numbers can vary.

Second, relatedly, even if we give up the probabilistic notions entirely, so long as there is a “permissive zone” in between two different requirements about the strength of evidential support for p, the same permissive views can still be deduced.

5.3. Why pragmatic encroachment views are resistant to the AfA

Recall our reconstruction and analysis of AfA. One way to constitute a counterexample to P1 is to describe a permissive situation in which the S's attitude is indeed determined by some non-evidential factor, but such a factor does not generate doxastic results randomly. Instead, the factor works in a systematic and regulated way, and consequently departs in its nature from coin-flipping. Then, acknowledging that one is in such a permissive situation does not imply it is rational to knowingly form one's attitude arbitrarily.

In my opinion, it is obvious by this point that permissive cases entailed by PE, as spelled out in section 5.2, are precisely such counterexamples. To be explicit, let me abstract and rearrange these cases in an “evidence + potential arbitrary factor X” form to examine whether X is indeed arbitrary. In both of the moderate interpersonal and intrapersonal cases, the subjects' current attitudes are indeed determined by a non-evidential factor, i.e., stakes, in addition to evidential considerations.

However, the stakes do not generate results arbitrarily. We have seen from section 5.2, not only do stakes regulate the deployment of epistemic standards in a way that promotes their overall epistemic and practical goals, detailed justification has been provided to show why that has to be the case. Further, as far as the PE theses are concerned, there is no further source of slackness in the processes to allow any coin-flipping-like arbitrariness.

Whether these PE accounts are ultimately true is beyond our consideration here – what matters is that according to these PE permissive views, rational doxastic attitudes are not even partially formed on any arbitrary basis. Consequently, cognitive subjects, such as Xinyan and Belinda, can stably stay in a permissive situation when they come to a realization that they are in a PE permissive case.

5.4. Pragmatism as a more radical impurist permissivist view

We have seen how PE theories entail permissive situations that do not exhibit the coin-flipping, or I-just-want-to-believe-as-so arbitrariness. However, I think the problem goes deeper and certain impurists can take us a step further. In this section, I bring a more radical form of impurism into consideration and show you why this P2 of AfA may also be challenged by impurist accounts.

The view was raised by Susanna Rinard (2017) and is named equal treatment for belief. Fundamentally, Rinard's (2019) idea is that doxastic states should be normatively regulated and evaluated in the same way as action states. In other words, she rejects the widely endorsed distinction between “epistemic rationality” and “practical rationality.” Instead, she proposes a unified normative system that governs all states.

Now, for our purposes, let us first see why this view is an impurism: for two subjects (or two time-slices of the same subject), let us assume that they are on a par regarding all their truth-relevant standings about p, but differ greatly in their p-related practical environment. For S, believing p will significantly promote her overall happiness, whereas having the doxastic attitude would make S′ miserable. Everything else is equal. Now according to Rinard's equal treatment, S ought to believe p but S′ ought not to, so long as we'd make the parallel judgments in the case of actions. This entails that S is permitted to believe p and S′ is permitted to not to believe p.

Therefore, it is clear how this is also a permissive view. The big discovery for us, however, is that since acknowledged arbitrariness in decision-making is allowed in many scenarios – “Flip a coin if you can't choose between strawberry and chocolate ice-cream” – as far as Rinard is concerned, the same should apply to belief-forming as well.

You may disagree with Rinard, especially if you are a purist. But let us recap the dialectics. The question, essentially, is not whether it is never rational to consciously form one's doxastic attitude arbitrarily, but if White can assume that it is never rational to consciously form one's doxastic attitude arbitrarily.

Recall that White did not really justify this premise, except for the appeal to our intuition in the legal cases. But as you may also recall, based on the conceptual resources generated from the impurist discourse, that was a high-stake situation. So several questions arise: what if it is a low-stake situation – believing either the strawberry ice-cream would be better than the chocolate one, or the other way around? Or regardless of the stake, what if it is a forced decision-making scenario but the evidence is so neutral that it does not point in either direction?

White also rhetorically asks why it would be necessary to impose an evidentialist constraint on rationality in the first place if it would then be subsumed by arbitrariness anyway, to undermine the permissive accounts. However, a radical impurist's answer might as well be a rhetorical “Why indeed.”

Rinard further provides an argument that explains this impurist stance – she suggests that the connection between rationality and truth is contingent. She considers that while acquiring true beliefs is normally the rational move because cognitive subjects tend to be better off with truth beliefs than false ones in most scenarios, this is not necessarily the case (see Rinard (2017) for examples). Rinard notes that in this sense, her view allows a higher level of flexibility in accommodating our intuition, as compared to evidentialism.

But once we grant this, it naturally undermines the common support for evidentialism as suggested by White: even if we all agree that evidence is highly truth-conducive, there are still circumstances in which truth is not what we are seeking for in the first place. As a result, evidentialism, uniqueness, and White's P2 would all lose their grounds in this regard.

I am sympathetic to her ideas. But more crucially, for the current dialectics, I think her view at least leads us to question why we should assume acknowledged coin-flipping type of arbitrariness is nothing but unacceptable, and hence leads us to see another way of how impurism can be resistant to White's attack.

6. Conclusion: impurist permissivism and epistemic conflicts

As promised, this paper laid out a defense of impurist permissivism. I argued how impurist accounts are all permissivism by definitions, and demonstrated to you how prominent impurist accounts deliver permissivist results. Specifically, the less radical¹⁵ impurist views such as pragmatic encroachment deliver their permissive results in a systematic, non-arbitrary way; while the more radical versions of impurism, such as pragmatism, do accept acknowledged arbitrariness. But whether such coin-flipping like arbitrariness is allowed is precisely the point of the debate and cannot be dismissed without further justification as in White's argument. Overall, this shows that all impurist views are resilient to White's alleged attack on all permissive epistemologies.¹⁶

Moreover, in more elaborate terms, the paper is also a defense for impurism as permissivism. It is worth noting how perceiving impurist views as permissive accounts also advances our understanding of these theories themselves. We see an aspect of pragmatic encroachment that we previously neglected: we now recognize how certain kinds of disagreement can be explained through how much is on the line for different stake-holders, and we see how, inversely, the plausibility of these pair-cases supports encroachment theses. There are cases in which filling in small details can help us explain away the superficial conflicts, like in the bookstore case we encountered in section 2.1 – presumably, your friend needs the book for an important test tomorrow, but you only want to read it out of sheer short-term curiosity due to her recent sharings. So, surely awareness of this rational disagreement should not undermine the rationality of your current attitude, because you can be assured that both of your and your friend's current attitudes are each governed by your own practical considerations in a non-arbitrary way. In addition, we also see that pragmatist views help us explain cases where conflictual doxastic commitments may indeed be due to acknowledged arbitrary factors, but even that, may not necessarily undermine that rationality of either party.

It is these dynamic and flexible perspectives impurist accounts offer that make them able to explain significant parts of our complex epistemic life as well as providing us with the theoretical assets required in undertaking how major discourses in the contemporary debates may converge.¹⁷