1. PERMISSIVISM AND UNIQUENESS

You're a permissivist if you reject the following thesis; you're an impermissivist if you accept it:

Notice that the discussion is framed in terms of ideally rational agents.Footnote ⁴ The question is not about how people as a matter of fact respond to a body of evidence E. It's about how they would respond if they were fully rational in their evaluation of E. How much divergence of opinion does ideal rationality allow? How much latitude is there in the evidence? That's where permissivists and impermissivists differ.

Looser formulations are possible:

Or maybe:

Uniqueness can be usefully discussed on a tripartite division of doxastic attitudes – belief, disbelief and suspension of judgement – but also in connection with credences, where permissivists allow, and impermissivists disallow, varying degrees of confidence in a proposition P. Thus we get two versions of permissivism:

The objection, the counter and the parry will go through on either version, so I'll stress one or the other as aids comprehension.

Two more preliminaries and we'll be set. First, there's a convenient term from White:

The extreme position, accordingly, is impermissivism: There are no permissive cases. Open the door to one, and you're permissive on matters of evidence.

Finally, there are two ways of specifying the domain in which permissiveness does or doesn't occur. You can hold that evidence is permissive or impermissive within the person, or you can hold that evidence is permissive or impermissive within the community of knowers. Thomas Kelly makes this sharp, distinguishing between permissivists who allow intrapersonal slack and permissivists who allow interpersonal slack (Kelly Reference Kelly, Steup, Turri and Sosa2014: 304).Footnote ⁷ The former hold that an individual could find herself in a situation such that more than one doxastic attitude (or credence) towards some proposition P is rationally permissible given her evidence. The latter hold that “different individuals possessing the same evidence might believe differently, and each be reasonable in believing as they do” (Kelly Reference Kelly, Steup, Turri and Sosa2014: 304). A taxonomy of permissiveness emerges, depending on which type of slack is allowed and disallowed: intrapersonal permissivism and impermissivism; interpersonal permissivism and impermissivism.Footnote ⁸ These distinctions will help us later.

Uniqueness seems very intuitive to me – almost obviously right. So what am I missing? Why would anyone deny Uniqueness? It loses some of its luster when you start thinking in terms of fine distinctions. Kelly's Alpha Centaurian thought experiment, which veers away from the “maximally coarse-grained” conception of belief – the tripartite conception – towards an increasingly fine-grained model of credences, is persuasive:

That really does sound strange. So there's definitely something going for permissivism, especially the moderate form.Footnote ⁹ But the arbitrariness objection is indifferent to this coarse-grained–fine-grained distinction. That's the real headache for permissivists: Arbitrariness infects their view at any degree of resolution.

2. THE ARBITRARINESS OF BEING PERMISSIVE

The arbitrariness objection to permissivism starts from the assumption that responsible enquiry is guided by evidence. It then proceeds: If there are permissive cases, there is no reason to let evidence guide enquiry. So there are no permissive cases. The key, conditional claim is supported by a thought experiment. It can be framed in terms of doxastic attitudes or credences. To avoid distracting complications (White Reference White2005: 457, note 3), White focuses on doxastic attitudes:

If the case is strongly permissive, more than one attitude gets a pass: I can believe that the defendant is guilty or disbelieve it. I'm free to take my pick. But then I must view the means by which I arrived at my favoured attitude “to be no better than arbitrarily popping a belief-inducing pill” (White Reference White2005: 451). So why bother with evidence? Seeing as there is reason to let enquiry be guided by evidence, permissivism must be rejected.

Here's another angle: An agent who takes herself to be in a permissive case with respect to some proposition P, and at the same time privileges her own attitude or credence towards P, adopts what Simpson helpfully calls a “quasi-akratic stance” (Simpson Reference Simpson2017: 523). A fully akratic stance is one in which an agent believes some proposition P but also holds that P is unsupported by her evidence (Horowitz Reference Horowitz2014: 718). Simpson's meaning, I think, is this: Suppose an agent believes P on E with a credence of 0.8. In doing so, she is in effect denying that any other credence is rationally permissible. Suppose she's also permissive. In opening herself to slack, she betrays her preference for 0.8. It's sort of like believing something and admitting that the belief has no support – it's sort of akratic – since she's simultaneously saying that the evidence justifies a credence of 0.8 and that it also justifies a credence of 0.3. If 0.3 is what the evidence makes reasonable, then stepping it up to 0.8 is to go 0.5 beyond what's reasonable. It's believing that much more without support. And that's downright arbitrary.

You can't have it both ways, according to arbitrariness. You can't favour your own credence or attitude towards P and recognize the legitimacy of rival credences or attitudes. You might as well settle on a credence by spinning a wheel or picking values from a hat.

3. SLACK IN COGNITIVE DIVERSITY

Simpson sets two tasks for the permissivist in responding to arbitrariness:

Miriam Schoenfield makes a promising suggestion. She defines ‘epistemic standards’ like this:

And proposes meeting arbitrariness like this:

This satisfies Task 1, because a non-arbitrary reason for adopting DA₁ (or credence 0.8) has been identified. It is imposed by ES₁, which you regard as most truth-conducive. And it satisfies Task 2 because DA₂ (or credence 0.3) is enjoined by the (rationally acceptable) epistemic standards (ES₂) that the other person regards as most truth-conducive. You needn't regard DA₂ (or credence 0.3) as impermissible since “the rational status of any doxastic attitude is assessed relative to the agent's epistemic standards” (Simpson Reference Simpson2017: 528).

Simpson rejects this proposal: “Where before our problem was arbitrarily favoring one among two rationally permissible doxastic attitudes, now our problem is arbitrarily favoring one among two rationally permissible sets of epistemic standards. The problems … recur for Schoenfield at the level of epistemic standards” (Simpson Reference Simpson2017: 529). Unfortunately, the reference point for any epistemic evaluation is one's own set of epistemic standards. If your standards are ES₁, then you see ES₂ as less accurate, less truth-conducive than ES₁. You should give no weight to ES₂’s recommendation of DA₂ (or credence 0.3). How to play favourites with your own epistemic standards without in the process discrediting your peer's?Footnote ¹² It's not obvious that you can.

But Schoenfield is onto something with her appeals to epistemic standards, according to Simpson, and the core idea can be preserved without falling into arbitrariness. His ingenious move is to tie epistemic standards to cognitive ability:

To put it very simply, my epistemic standards might be most truth-conducive for me given my cognitive abilities and yours might be most truth-conducive for you given your cognitive abilities. We should thus follow the recommendations of our own standards. That's where evidential slack creeps in.

Simpson brings this thought to life with an example he calls detectives (Simpson Reference Simpson2017: 531–33). Veronica Mars and Nancy Drew are investigating a crime. They share a body of evidence. Their beliefs differ as to who committed the crime. Mars believes ‘X is the culprit’ with a credence of 0.8; Drew gives it a 0.3. (I'm simplifying the example and making it about credences.) Can they be permissive? Can they regard the other's credence as rationally permissible while standing firm on their own? Apparently so, since they bring different epistemic standards to bear on the evidence and – here we move beyond Schoenfield – the standards are well-suited to their respective cognitive abilities:

By relativizing standards to the agent's cognitive abilities and making each aware of the other's situation, Simpson has found a novel way of allowing them to non-arbitrarily prioritize their own preferred credences while acknowledging the rationality of their rival's. This solution is highly attractive. Let's put it through the wringer.Footnote ¹³

4. NO EXCUSE IN COGNITIVE DIVERSITY

I'm going to argue that the appeal to differing epistemic standards tied to differing cognitive abilities does not block the arbitrariness objection, since it does not accomplish Task 2 – it does not provide a non-arbitrary reason for privileging one's own credences (or doxastic attitudes) in a way that still recognizes the legitimacy, or rational permissibility, of rival credences (or doxastic attitudes) on the same body of evidence. Rival credences get no validation, in other words, by filtering through epistemic standards that are customized to an agent's cognitive quirks. I'll try to make this clear with a few examples. They are intentionally farfetched – pushing Simpson's brand of permissivism to the breaking point so that its problems become apparent. We can ease our way into the examples with a simple analogy concerning vision.

Suppose that my mother and I are standing on a bridge looking down at a cruise ship going past. And suppose that we have the same relevant background beliefs. How many lounge chairs are there on the deck by the pool, we're wondering? Looks like three to me – plain as day. So I form the belief that there are three lounge chairs by the pool with a credence of 0.8. My mother should form the same belief with the same credence since we have the same body of evidence, right? Wrong. My mother has bad vision. All she sees are three blurry red patches against a bluish background. Maybe there are some blue chairs that she can't make out. Maybe someone redistributed or stacked several red cushions from any number of different chairs. A lower credence, therefore – say, 0.3 – might be more reasonable for my mother, but not on the same body of evidence. Her evidence is different than mine precisely because her perceptual abilities are different.

The lounge chair analogy homes in on the obvious: Differing perceptual abilities afford different bodies of evidence.Footnote ¹⁴ Is it the same with other mental abilities, the kind more relevant for Simpson? Let's weigh that in connection with his main example – detectives. Mars is good at interpreting signs of insincere testimony in isolation and Drew is not. Say they're hearing testimony regarding the murder of the College Dean. Is it any good? When Mars sees the witness scratching his face, covering his mouth, or smiling without squinting, she takes these as signs of deception. But it's all lost on Nancy Drew. Why is that? If she has difficulty paying attention and simply doesn't notice these things – if the actions don't even register – then her evidence is clearly not the same as the evidence available to Mars. If that's what's going on, then Drew is something like my mother on the bridge: Her perceptual input is comparatively impoverished. So her doxastic output will naturally differ. She'll assume that the witness is credible. Mars will be suspicious. But that won't implicate Uniqueness.

If she does notice them, on the other hand, her inability to grasp their meaning is more plausibly construed as a lack of knowledge. What appears to be a difference in cognitive competence is in fact a difference in background beliefs. Mars must have some additional information. Either she is expressly aware that these actions are characteristic signs of deception, or else she's built up some implicit knowledge of their significance. So once again the evidence is different. Once again Uniqueness is safe.Footnote ¹⁵

Simpson's detectives example, therefore – the backbone of his argument – provides ambiguous support for his thesis. The readings I'm suggesting may be more natural. It's certainly hard for me to see this as a permissive case, since I just don't find it credible that Mars and Drew are working with the same materials. Perhaps some additional details could be tacked on to give the permissive reading a boost. But there's nothing in the description given to make it necessary.Footnote ¹⁶

I don't want to push too hard on this point, however, since Simpson might be able to establish evidential parity by expanding the story, and – here's the main thing – I'd still be sceptical that the case is permissive. I'd like to try a different strategy: going to extremes. Sometimes it's easier to sort out the subtler, less obvious cases, by looking at extreme examples and using them as a guide to the harder ones. This will work so long as the extreme and the central cases are relevantly similar. The examples I have in mind are designed to illustrate, and make plausible, the following idea: We shouldn't (and probably don't) regard differences in cognitive abilities as licensing rival doxastic attitudes towards the same proposition on the same body of evidence, since we shouldn't (and probably don't) regard a difference in cognitive abilities as an epistemically valid excuse for not believing what, by our lights, the evidence supports. Alternatively, if differences in cognitive ability can make a body of evidence permissive, then differences in cognitive ability can make (epistemic) irrationality epistemically acceptable. But that's a mistake, I hope you'll agree. Let the extremes pump your intuitions.Footnote ¹⁷

My first case makes use of a much discussed mathematical problem devised by Shane Frederick: “A bat and ball cost $1.10. The bat costs one dollar more than the ball. How much does the ball cost?” (Kahneman Reference Kahneman2011: 44). The quick and tempting answer – the System 1 answer, in Kahneman's terms – is 10¢. The correct answer is 5¢. Most college students get this wrong (Kahneman Reference Kahneman2011: 44–45). Now suppose that Victoria and Elizabeth are working with the same body of evidence E, and that E includes these two propositions (or the corresponding beliefs),Footnote ¹⁸ no defeaters, and nothing else that's relevant:

Victoria, we'll suppose, answered correctly: 5¢. Elizabeth answered incorrectly: 10¢. Let's suppose further that Elizabeth is cognitively incapable of focusing on math problems – cognitively incapable of engaging slow, System 2 thinking – and so is unable to perform even simple calculations.

Since Elizabeth's cognitive abilities differ from Victoria's, she makes use of different epistemic standards – standards more suited to her distinctive capacities. We can specify the operative principle for each of the agents (the programme instruction for solving math problems) like this:

We'll concentrate on Elizabeth's answer (10¢). The output of ES1-CURSORY MATH on E is belief in P3; the output of ES2-CAREFUL MATH is disbelief:

Given these assumptions, should we conclude that belief in P3 was epistemically permissible for Elizabeth on E but not permissible for Victoria? Should we call the case permissive? No way: Elizabeth's inability to understand what her evidence implies doesn't alter its implications. The fact that she has different epistemic standards does not affect the evidential relations themselves, in other words, and does not affect what propositions a body of evidence supports, or makes reasonable.Footnote ²⁰ ES1-CURSORY MATH might be a good rule of thumb for Elizabeth: A pre-reflective intuition could be better in a mathematical context than nothing. Who knows? But it doesn't help Elizabeth here: She doesn't end up believing the proposition that her evidence supports on the basis of the evidence that supports it. That's the bottom line: P1 and P2 do not provide evidential support for P3, and so do not make belief in P3 reasonable. Though people might employ different epistemic standards suited to their differing cognitive abilities, E just doesn't make belief in P3 rationally permissible. A fully rational agent whose body of evidence included P1 and P2 (and no defeaters) would disbelieve P3. No good at math? Can't concentrate? Sorry, it's still irrational for you to believe P3 on the basis of E. Your evidence is squarely against it.

My second case is radical. Albert has a neurological peculiarity that makes him extremely prone to error in drawing out the logical implications of his beliefs. Accordingly, his epistemic standards include a rule along the lines of:

Albert justifiably believes P4 (has no non-defeated defeaters, etc.):

Since his epistemic standards include no inference licence from ‘P ∧ Q’ to ‘Q’, he suspends on:

Without knowing anything else about Albert's epistemic circumstances, I think I can say that his suspension on P5 is at odds with his evidence. So I can say that it's irrational.Footnote ²¹ Whether or not Albert can believe P5 on the basis of P4, or can find his way from P4 to P5, he should. His cognitive distinctiveness and rogue epistemic standards do not justify suspending on a proposition that a fully rational agent with the same evidence would believe.Footnote ²² Unless Simpson can identify some relevant difference between this logic case and detectives, his argument is toast.

The final case is inductive. Suppose that Philip's hippocampus was damaged in a riding accident at a fairly young age resulting in severe anterograde amnesia: He can form no new long-term memories. And suppose he never saw a beetle before the accident but sees one now for the first time.Footnote ²³ So he believes:

Since Philip can form no new long-term memories, he can't perform an enumerative induction. But since he learned before the accident that regularity is common in nature, one of his epistemic principles – suited to his unusual condition – is ES4-QUICK INDUCTION:

So Philip believes P7:

While following ES4-QUICK INDUCTION might sometimes give Philip a true belief, it's not the case that a body of evidence including one observed x that is F supports the belief that all xs are F. An ideally rational agent would not infer that all xs are F from observation of a single Fx. An ideally rational agent would suspend on P7 given this evidence. So Albert should too. It's the only permissible attitude.

If these wacky cases didn't shake your confidence in the cognitive abilities strategy for blocking arbitrariness, then try this: Take any proposition P and any body of evidence E about which you're feeling permissive. The particular values of the rival credences won't matter, so let's just say they're 0.3 for you and 0.8 for someone else. In your estimation, a credence of 0.3 in P is justified by your total evidence E. Now to implicate cognitive abilities, suppose the other person, Anoushka, has the same body of evidence E, is vastly more intelligent than you, and better at interpreting evidence. Her epistemic standards recommend a credence of 0.8 in P, so if you're permissive here, you judge that a credence of 0.8 is rationally permissible for her. But doesn't that give you a reason to think that 0.8 is the right credence? She's smarter than you and her epistemic standards are better. Your credence of 0.3 is suboptimal precisely because a credence of 0.8 is prescribed by better epistemic standards and a more perceptive interpretation of the evidence. The 0.3 only looks right because you misjudge E. And given your views about Anoushka and her epistemic superiority, you can see that. So it would be arbitrary and irrational for you to stick with 0.3. It's off the mark, according to you.

Probably the best thing for Simpson to say at this point is that it's not about better or worse standards and outputs. Different standards working on the same evidence yield different – and equally valid – doxastic outputs.Footnote ²⁴ It's the equal validity part that puzzles me: However you spin it, one of the credences is going to look better to you, so you'll see the standards and abilities that recommend rival credences as somehow worse and those credences as incorrect. So you can't be permissive. Perhaps this thought will make the impermissivist outlook less puzzling to those who agree with Simpson.

The main point of this section is that differences in cognitive ability produce no evidential slack. The math, logic and induction examples draw out the implications of being permissive in this way. Those implications are bizarre.Footnote ²⁵

5. FINE DISTINCTIONS AND SYSTEM OUTPUTS

A possible worry is that the exaggerated cases I put forward are too clean-cut and artificial to be persuasive. As the evidence gets messier, stubborn insistence on Uniqueness starts to feel somewhat dogmatic. My response, as above, is that easy, conspicuous cases like these can help us sort through harder, messier cases like detectives. I see no reason to think that they can't, and I see no contrast between them.Footnote ²⁶ But there's a particular kind of messiness that might spell disaster for impermissivists of any description: ineliminable vagueness. When evidential circumstances are highly complex, when defeaters and defeater-defeaters run in both directions, it could be objectively vague whether or not some body of evidence E supports a particular proposition P or its negation (Matheson Reference Matheson2011: 370). When it is objectively vague whether or not some relevant bit of information – a fading memory, say, or a barely discernible sensation – actually belongs to E, the total evidential force of E with respect to P could be indeterminate as well.Footnote ²⁷

Matheson, who identifies these two sources of vagueness, leaves us guessing what objective indeterminacy in the evidence really amounts to, so I'll make it intuitive with a lowly example from my childhood. It's an example of the second type – where the force and composition of a given body of evidence is indeterminate owing to vagueness regarding possession. As I mentioned above (footnote 18), I think evidence is fully mental. If I have no cognitive access to x, then x is not available evidence. The books on my desk contain plenty of information, but since I haven't read them, it's not information for me. Things that I have read and retained, by contrast, are a part of my evidence – as are current perceptions and memories. But sometimes it's unclear whether or not I'm actually in some particular mental state or can access some particular mental item. Now for the personal touch.

When I was about four we went to the circus. I'm quite certain of that. It was an indoor arena and we sat on bleachers. But then there's the question of a panther. It seems to me that one of two things happened: Either (1) they arranged to surprise the audience by letting the panther run up the stairs between the bleachers and do a lap behind us, or (2) I imagined how cool it would be if they did. This is a perfect example, since I can never pin down the evidence. Sometimes I remember it happening. Sometimes I'm convinced that it didn't. It's the sort of shtick that was common in the 70s, and it's just what a kid would make up. So my body of evidence is objectively indeterminate with respect to ‘The panther did a lap behind us.’ It all depends on that memory. But that's what I can't work out. So what am I supposed to believe? There doesn't seem to be a clear answer, since the boundaries of my evidence are hazy.

Vagueness poking holes in Uniqueness is music to permissivists’ ears: Where evidence is indeterminate, the temptation is to argue that “there can be distinct doxastic attitudes that are such that one would be justified in adopting either of them towards a proposition” (Matheson Reference Matheson2011: 370). If the evidence is vague regarding P, the permissivist might reasonably see this as a failure of Uniqueness: More than one doxastic attitude would be permitted. I could reasonably believe that the panther did a lap and I could reasonably believe that it didn't.

Matheson pulls the plug on this reasoning: If it is indeterminate whether believing, disbelieving or suspending on P fits E, then E enjoins no doxastic attitude (Matheson Reference Matheson2011: 371).Footnote ²⁸ We're simply at a loss for what to do when the evidence is vague, but that hardly implies that we can take our pick of attitudes or credences. Vague evidence permits nothing and enjoins nothing. So Uniqueness can live with indeterminacy.Footnote ²⁹

This is a crucial point for impermissivists, but our interest is the clue it provides for dealing with fine distinctions. Recall Thomas Kelly's Alpha Centaurian thought experiment. Kelly isn't suggesting that we are like the Alpha Centaurians, of course, but let's consider the possibility. Are we like them, epistemically speaking? There are actually two questions here. First, does evidence really parse this finely? Does it ever happen that the probability of P given one body of evidence is .83527 while the probability of P given another body of evidence is .83528? Maybe sometimes (in controlled experiments and card games), but I doubt if it happens very often when it comes to everyday events and the bodies of evidence that people typically possess. Did the dog eat my shoe again? It's doubtful that my evidence on this matter would discriminate between its being .83527 likely that the dog ate my shoe and its being .83528 likely.Footnote ³⁰ Secondly, do our credences really parse this finely? Is there any psychological difference – any difference at all – between believing that the dog ate my shoe with a credence of .83527 and believing it with a credence of .83528? I'm oblivious to any such fine tuning of my beliefs. But it doesn't matter, actually. Dividing the question this way makes it easier to see that Uniqueness gets it right whether our epistemic circumstances are Alpha Centaurian or not. Let's see what Uniqueness has to say – what it should say – about various pairings between degree of evidential resolution (that was the first question) and degree of credential resolution (that was the second).

To simplify the problem, we'll assume that there are only two scales (this is an idealization): The evidence scale is either finely parsed, which means that it's capable of supporting a proposition to such precise degrees as .83527 and .83528, or else it is coarsely parsed and can support a proposition to such coarse degrees as …0.7, 0.8, 0.9…, but nothing in between. The credence scales will be the same: finely parsed means that our credences can taper to a .83527 degree of confidence and a .83528 degree of confidence (etc.); coarsely parsed means they get as sharp as …0.7, 0.8, 09…, but nothing in between.Footnote ³¹

Now consider the possible pairings: evidence and credences each parse finely or coarsely – so four combinations.

If the evidence supports ‘The dog ate my shoe’ to degree .83527, but our credences can only get as precise as …0.7, 0.8, 0.9…, then the rational thing to do is to believe that the dog ate my shoe with a credence of 0.8. In other words, if, as a matter of psychological fact, there's no such thing as a credence of .83527, then the evidence doesn't require any such thing. Given the evidence I have, and given the type of system I am, the uniquely rational credence towards ‘The dog ate my shoe’ is 0.8. An ideally rational agent whose credences parse coarsely, would shift her confidence up or down to the next closest evidential value. If the only possible credential outputs for a system are coarse, then a 0.8 degree of confidence in P is the only fitting response to evidence that makes P .83527 likely. To extend Simpson's computational metaphor, this is a system limitation that shunts outputs along ‘circuits’ that are hardwired into it.

But what if the finely parsing evidence scale makes it 0.85 likely that the dog ate my shoe? Wouldn't it be okay for me to take the ‘high end’ credence of 0.9 or the ‘low end’ credence of 0.8, since E hits the midpoint exactly? One could argue that such a case is permissive.Footnote ³² But one shouldn't. If I went with a credence of 0.8, I would in effect be saying (arbitrarily) that the evidence makes a credence of 0.8 more reasonable than a credence of 0.9. But it doesn't. There is no ‘closest credence’ to degree 0.85 for a creature on the coarse credence scale we're imagining. So neither credence is prescribed.Footnote ³³ (It's something like Buridan's ass for belief.)

The second pairing inverts the first:

Just as a creature capable of both believing and disbelieving P should do neither when the evidence fails to discriminate between them, so a creature capable of having credences of .83527 and .83528 should do neither when the evidence fails to discriminate between them. Hairsplitting believers like us should form a credence of 0.8 when E makes P 0.8 likely, since a credence of .83527 goes beyond E.

The third pairing is an easy sell:

If the evidence supports ‘The dog ate my shoe’ with a probability of 0.8, and I believe it with a credence of 0.9, I've departed from ideal rationality. And I shouldn't. I should align my credences with the evidence, and the match here is perfect – no slack.

The final pairing smells like trouble, but it's not:

If both evidence and credences parse finely, then when the evidence makes it .83527 likely that the dog ate my shoe, I should form that credence. Why? Because I can and I ought to be rational. This is the right outcome. It only sounds funny to say that a .00001 misalignment constitutes a departure from ideal rationality because we naturally assume that neither evidence nor credences are that discriminating. (I'm sure they're not.) But if they both were, then clearly we should align our beliefs with the evidence as neatly as we can. Why not get that kind of precision in our beliefs if we're capable of it? Surely we epistemically ought to do what is epistemically best. Forget humans for a second: If two Alpha Centaurians, Binar and Proxima, had the same body of evidence E and E made it .83527 likely that the dog ate Binar's grav boot, then Proxima would think it's crazy that Binar's credence is .83528. Uniqueness gives the intuitively correct recommendation here too.

Now the permissivist may be ready with a response. Doesn't this view open the door to permissivism at another level? If the probability that the dog ate my shoe on E is .83527, then the uniquely rational doxastic response from an agent whose credences parse coarsely is 0.8. I doubt that our credences are even that fine-grained, but supposing that they are, E requires a credence of 0.8 from me and from any other agent with the same input. Is that right? Any agent? What about Proxima whose credences parse finely? Isn't the uniquely rational response from an Alpha Centaurian a credence of .83527? If so, then we may be facing permissivism at a higher level – permissivism between systems of different types. This mirrors the intrapersonal–interpersonal distinction one level up. The permissivist pushing this line might admit that intraspecies permissivism is ruled out, but that interspecies permissivism isn't.

This makes sense. The evidence is not going to enjoin outputs from us of a kind that systems like us don't produce. Consider Keplerites – aliens living on Kepler-442b (if that's possible). The doxastic outputs of Keplerites, we'll suppose, parse more coarsely than ours. Say they have a three-place control: belief, suspension, disbelief. Now suppose the probability of P on E is 0.8 and the probability of Q on E is 0.6. The uniquely rational response for us is a credence of 0.8 in P and 0.6 in Q. But for the Keplerite, whose outputs are limited to three, the uniquely rational doxastic responses are shunted up for P and down for Q – belief in P and suspension on Q. Sounds right to me. There's no arbitrariness in favouring the doxastic outputs that systems like us deliver and at the same time recognizing that other systems may be capable of issuing outputs that cleave more closely to the evidence. The same body of evidence E could enjoin a credence of 0.8 in P from me, a credence of .83527 from an Alpha Centaurian, and belief from a Keplerite (but never a credence of 0.8 from me, a credence of .51361 from the Alpha Centaurian, and disbelief from the Keplerite). Slack arises from a difference in doxastic resolution, but never from the weight of evidence.

Note that there is no tension here with my rejection of the cognitive abilities proposal for blocking arbitrariness. It is not a matter of allowing that differences in cognitive abilities change the character of evidential relations. They remain constant. It's simply a recognition that limitations on the resolving power of a belief-forming system not only can, but must, change the ‘programme instruction’ for producing a doxastic output. It's an unsupported empirical assumption I'm making that the resolving power of systems like us is constant, so that the rationally required output is constant.Footnote ³⁴ If that assumption turned out to be false – though I can't imagine a good test – then I'd happily admit a degree of interpersonal slack.Footnote ³⁵ But that would be perfectly consistent with my claim that differences in cognitive ability make no impact on the evidential relations themselves.Footnote ³⁶