Evidence Neutrality and Rules of Inference

In chapter 7 of The Philosophy of Philosophy, Timothy Williamson argues against the idea that intuitions are a key part of philosophical evidence. Part of his argument is indirect. He thinks the motivation for taking intuitions to be central comes from accepting a principle he calls Evidence Neutrality, and that that principle is false. I rather suspect that isn’t the best reason to take intuitions to be philosophical evidence, but we’ll set that aside here. What we’ll focus on here is whether Evidence Neutrality is true. Here is the initial statement of Evidence Neutrality.

Although the complete elimination of accidental mistakes and confusions is virtually impossible, we might hope that whether a proposition constitutes evidence is in principle uncontentiously decidable, in the sense that a community of inquirers can always in principle achieve common knowledge as to whether any given proposition constitutes evidence for the inquiry.

It seems to me that this is ambiguous between two readings.

  • The weaker reading is that it is decidable, by consensus, which propositions are, in principle, evidentially relevant to an inquiry as to whether p.
  • The stronger reading is that that is true, and it is also decidable, by consensus, in which epistemic direction each piece of evidence points .

I’m going to argue that one of the arguments against Evidence Neutrality, what we might call the argument from extremists, does not tell against the weaker version. I think (though this claim will eventually need defending) that if either version of Evidence Neutrality is metaphilosophically interesting, then the weaker version is interesting. So perhaps that’s all that we need to defend.

Evidence Neutrality (hereafter, EN) is a kind of dialectical conception of evidence (hereafter, DCE). What our evidence is just is what our interlocutors will allow as evidence. On the stronger reading, it is what our interlocutors will take to be evidence for our conclusions. On the weaker reading, it is what they’ll allow as evidence, though they may say one particular piece of evidence, a piece we take to be crucial, is not very strong. And the big question here is whether we should think of evidence dialectically.

It’s certainly true that evidence that is accepted by our interlocutors will be more persuasive in convincing interlocutors. But that’s no argument, at least no immediate argument, for a DCE. It might be that we have quite a lot of evidence that tells whether p, and our interlocutors are just mistaken about this. (Everyone makes mistakes.) Relatedly, some people may simply fail to be persuaded by arguments that are rationally persuasive. So we shouldn’t simply confuse which evidence is dialectically effective with which evidence is genuinely good. If we want to defend a DCE, we’ll have to argue for it more carefully than that.

The key point of the last paragraph is that some people will fail to be persuaded by genuinely good arguments. That suggests a problem; couldn’t we have evidence against a position, but just not evidence accepted by the partisans of that position? The simplest examples of this will be positions whose partisans are hostile to the very idea that evidence can tell in favour of anything at all. Here is how Wililamson converts such examples to arguments against EN.

Some scepticism, like scepticism about reason, is so radical that it leaves too little unchallenged for what remains as shared evidence to be an appropriate basis for evaluating the claims under challenge.

The point here is not a new one. David Lewis makes a similar observation in Logic for Equivocators.

The radical case for relevance [i.e. dialethism] should be dismissed just because the hypothesis it requires us to entertain is inconsistent. That may seem dogmatic. And it is: I am affirming the very thesis that Routley and Priest have called into question and – contrary to the rules of debate – I decline to defend it. Further, I concede that it is indefensible against their challenge. They have called so much into question that I have no foothold on undisputed ground. So much the worse for the demand that philosophers always must be ready to defend their theses under the rules of debate.

The point Williamson and Lewis make is clear enough. There are certain radical views that (a) we know to be mistaken, but (b) the nature of the position is such that it has, by its own lights, defences against the actual grounds for our knowledge that it is mistaken. Of course its lights are bad lights; our reasons are good reasons. But such positions have partisans. (This is clearer in Lewis’s case than in Williamson’s.) If our only evidence is the evidence they’ll let us share, we won’t have evidence against these positions. And that might suggest we don’t really know the positions are mistaken, contrary to assumption. (There is a fairly strong evidentialist assumption being made here, namely that if we don’t have evidence against such positions, we don’t know they are mistaken. It’s worth thinking through whether that assumption is right, but I won’t do it here.)

I think, however, that this point goes by too fast. Remember that EN and DCE are claims about evidence. They aren’t claims about what we can do with evidence. To see the importance of this distinction, it’s worth recalling Lewis Carroll’s fable of Achilles and the Tortoise. (The points to follow are perhaps familiar from recent work of Paul Boghossian and Crispin Wright. And I’m indebted here to discussions with Crispin. But note that I’m expressly not committing myself to Boghossian’s views about the meanings of the logical connectives.)

Achilles knows p, and p -> q. He wants to infer q. The tortoise says, wait a second, are you sure that’s a good inference? Achilles says he is sure. He’s sure, he says, that (p & (p -> q)) -> q. The tortoise thinks for a second, and then says that that does sound right. Let’s have that as another premise he says. Achilles happily agrees, and then proceeds to infer q. The tortoise is still not sure. He wants to know how Achilles is drawing that conclusion. Achilles says he’s sure that if (p & (p -> q)) & (p & (p -> q)) -> q then q. The tortoise agrees that looks true, and says it seems like a pretty good premise to have. Achilles tries again to infer q, and the tortoise is again worried about why he’s drawing that conclusion. The story continues for a surprising while, with Achilles adding more and more premises, and seemingly getting no closer to overcoming the Tortoise’s worries.

There’s a mundane lesson to be drawn from that, and an exciting lesson. The mundane lesson is that there is a distinction between premises and rules. Indeed, in every axiomatic formal system, we are given both axioms and rules to generate theorems from old axioms/theorems. In some simple systems the only rule might be modus ponens, the rule that Achilles was looking for. In other systems we might need a rule like necessitation, or universal-introduction. But we always need something more than just axioms.

The exciting lesson is that rules aren’t the kind of things that stand in need of rational justification. They are, to put it perhaps in Wittgensteinian terms, things that justify, rather than things that are justified. Here is how we might draw that conclusion. We can imagine the tortoise not as an unhelpful interlocutor, but as our own nagging doubts. Our own inner Descartes, if you like. If the rules have justifications, then we should be able to give them. And if we give them, we can add them as extra premises from which we reason. But this is the key mistake Achilles makes. At some point we need to stop adding premises, and start doing something with the premises. And that can’t always be supported by reasons. For imagine it could. That is, imagine the rule that let us go from A to B could be supported by evidence E. Then we can still ask, what’s the rule that lets us go from A and E to B? Still we’ll need a rule, and perhaps now we’ll be out of evidence. At some point a jump needs to be made without evidence.

So I conclude rules don’t need evidential justification. That’s not to say that all rules are created equally. There are normative standards governing rules, even though they are not supported by evidence. This makes their status quite delicate. As I read him, Gilbert Ryle introduced the idea of knowledge how directly to address this problem. Following rules can’t be simply propositional knowledge, because that leads to a regress. On the other hand, following rules is normatively, even rationally, evaluable. Ryle thought that if we recognise a category of know how, we can steer between these rocks; we can have something that’s a kind of knowledge, the exercise of which can be rational or irrational, but which doesn’t require evidence.

If it isn’t required that we be able to justify our use of rules to ourselves, it doesn’t seem like it should be required that we be able to justify them to our friends. And that in turn suggests that a dialectical conception of rules would be inappropriate. Who cares if our (rational) friends don’t like the rules we’re using? The only way we could make them like them is by offering reasons that our rules are good rules, and by hypothesis we don’t even need to be able to articulate such reasons to ourselves. Perhaps we don’t even need to have such reasons. So a dialectical conception of rules is bad, and more specifically, Rule Neutrality (understood along the same lines as Evidence Neutrality) is bad.

But note that once we ditch Rule Neutrality, we can respond to the extremists that Lewis and Williamson are worried about without sacrificing Evidence Neutrality. Here’s my evidence that dialethism is false. If dialethism is true, some contradiction is true. Taking that to be evidence doesn’t violate Evidence Neutrality, because it’s agreed on all sides. From that it follows, by a rule that I properly accept (i.e. reductio) that dialethism is false. Of course, the dialethists don’t buy that rule. But that’s not my problem, since I’m only committed to sharing evidence with them, not sharing rules. If I accepted the strong form of Evidence Neutrality, that might be a problem, because of course the dialethists don’t think this is evidence against dialethism. On the weak form of Evidence Neutrality, that isn’t a problem either.

It’s a little trickier to respond to the reasons sceptic, but I think it can be done, especially if we think about induction. So imagine that I see a lot of Fs that are all Gs, and I see them in a lot of different places etc. I conclude that I have good reason to believe the next F I see will be G. This is a direct inference; there is no mediating premise. If you don’t think so, try to imagine (a) what such a premise could be, and (b) how it could be justified? I think there aren’t good answers to this question, or at least that any answer is less certain than I am in the conclusion. So my frequent observation of green emeralds is sufficient evidence to conclude that I have a reason to believe something, and hence that reasons scepticism is false.

Summing up, I think that Williamson here has run together two similar, but importantly distinct, principles: Evidence Neutrality and Rule Neutrality. I think he’s right that if you accept both, you’ll have thrown away all hope of a good response to certain positions to which there are good responses. So we shouldn’t accept both of those principles. But if we accept that evidence is knowledge, as Williamson does, then we should think that all our evidence requires justification. And we shouldn’t think that our rules do. Since the acceptability of our evidence/rules to our (rational) interlocutors is grounded in this need for justification, it seems that our reason to accept Evidence Neutrality is not a reason to accept Rule Neutrality. So Rule Neutrality must go. And when it does, the argument from extremism against Evidence Neutrality goes too.

There’s a lot to say about rules, and I’ll say a very little about it tomorrow.

4 Replies to “Evidence Neutrality and Rules of Inference”

  1. This is interesting, Brian. I’m not sure whether I completely understand or not. Is this an objection?

    You say that, once we reject Rule Neutrality, we can hold onto Evidence Neutrality. The dialethists accept that if dialethism is true, then a contradiction is true; all parties admit this to be evidence. So this proposition satisfies the requirement of evidence neutrality. But Evidence Neutrality is a claim about ALL evidence. Even once we’ve quarantined the failures of Rule Neutrality, won’t there still be some evidence that violates Evidence Neutrality? Like, for example, the fact that if a view implies a contradiction, then it is false?

    I agree with you that we NEEDN’T cite this evidence in order to conclude that dialethism is false; the inference you spell out looks good to me. But I still think it’s evidence we have. And won’t it violate evidence neutrality?

  2. You’re right, that would violate Evidence Neutrality if it was part of our evidence that anything which implied a contradiction was false. And I guess it is somewhat intuitive that this is part of our evidence.

    Two thoughts in reply.

    One, since we have the reductio rule, it hardly matters for us epistemically whether we have that evidence or not.

    Two, there’s a weaker form of Evidence Neutrality that I think this response doesn’t touch, but which still does the work Evidence Neutrality needs to do. We can take Evidence Neutrality as (what I’m going to call in a forthcoming post) a regulative ideal.

    That is, we should waive our rights to any evidence not shared by our interlocutors, or more broadly by the research community we’re part of. The justification for this is going to be (a) fairly hand-wavy and (b) rule consequentialist. I think practice shows that deep commitment to being part of a research community leads to better epistemic outcomes, and part of that commitment is to take communal standards of evidence seriously.

    The stuff about rules is still important. If being part of the community of philosophers meant you didn’t have enough evidence to use reductio, that would be awful. But I don’t think it has that consequence.

    So short version of reply: I think you’re right that there is an intuitive problem for EN here. It’s not quite the problem TW thought it was, but a problem. But I hope it’s not a problem for the version of EN I want to end up defending.

  3. I’m not sure what to make of the “it hardly matters whether we have the evidence or not” line. My objection was based on what I took to be the clear fact that we do have it, not that we need it for some important reason.

  4. I was being unclear.

    I was taking TW to make an objection that it would be terrible if we didn’t have this evidence. I replied that it wouldn’t be so terrible.

    Now you’re making a different, and perhaps better, objection, namely that intuitively we do have this evidence. I agree. But I think we should agree in doing philosophy not to appeal to this evidence. There’s a positive reason for this and a negative reason.

    The positive reason is that restricting our evidence to those things our friends will agree with is, on the whole, a beneficial policy. Sometimes it means we’ll waive perfectly good evidence. But sometimes it means we’ll be kept from walking down dead ends. The latter is really bad, and acting as if EN is true is one good way to minimise the chance of it.

    The negative reason is that restricting ourselves to shared evidence doesn’t stop us from having lots of important knowledge. One reason for that is that we can, to an extent, pick our friends. Another reason is that we can keep to rules.

    But I agree, I think, that acting as if EN was true will mean we act as if we don’t have some evidence that we do actually have.

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