Plurals and Deferred Ostension

I was trying to use some other examples of deferred ostension in order to put some constraints on what might be happening with the ‘we’ in “We won 4-2 last night”. The canonical example is (1)

(1) The ham sandwich is getting impatient.

This manages to communicate that the person who ordered the ham sandwich is getting impatient. That is, “the ham sandwich” somehow manages to pick out the person who ordered the ham sandwich.

Both the explicit term “the ham sandwich” and the intended referent, its orderer, are singular. I was wondering what happened when we made either plural. First, imagine that the person ordering hadn’t ordered a ham sandwich, but had instead ordered the olives. Then I think (2a) would be more or less appropriate, but (2b) would be infelicitous.

(2a) ?The olives are getting impatient.
(2b) #The olives is getting impatient.

Second, imagine that the intended referent is plural, but the phrase used is singular. So a table of people ordered the paella, and they are getting impatient. I think (3a) is a little better than (3b).

(3a) ?The paella are getting impatient.
(3b) ??The paella is getting impatient.

Do others agree with those judgments? If they’re right, they suggest that plurality ‘trumps’. That is, if either the noun phrase used, or the intended referent, is plural, then the verb should be plural as well.

Ishani and I have been talking about an odd usage of “we” that seems to raise interesting philosophical issues. I’ll just set up the puzzle today, and hopefully over the week there will be some attempts to solve the issue.

It’s common to say that “we” is a first-person plural pronoun. It’s also common to use “we” when referring to the activities of a group that, strictly speaking, you’re not part of. So, when asked about Geelong’s latest game, I might say something like “We were three goals down at half time, but we played well in the second half and won by ten points.” Now there’s a group of 22 guys who, in the example, played well in the second half. But I’m not one of them. I’m too old, too unfit, too useless and, crucially, not a registered player for the club. What’s going on in cases like this?

The easiest thing to say is that this is simply a mistaken use of language. But I don’t think that will do. For one thing, it’s simply too widespread a mistake to be written off so easily. In some sense, a usage that widespread can’t be simply mistaken. For another, the usage shows some degree of systematicity, the kind of systematicity that we as philosophers/semanticists should be in the business of explaining. We’ll see some of the respects of systematicity as we go along, but for now let me note just two of them. The first is that it’s very hard to have this kind of usage for first-person pronouns. (There are exceptions, but this is the rule.) So (1) is fine, but (2) is marked.

(1) We played well in the second half.
(2) *I played well in the second half.

The other is that there aren’t that many cases where we can say _We did X_ to mean that some group of which you’re particularly fond did X. So it is possible to say it about (most) liked sporting teams, but not about, say, your favourite restaurant. No matter how much you like _Le Rat_, if you’re simply a fan (rather than an employee) you can’t say

(3) *We got three stars from Bruni in the _Times_.

Similarly, it is possible to say _We did X_ to mean that a political group you affiliate with did X, but not a rock band you are a fan of. So if you’re a fan and supporter of Peter Garrett both as a rock star and a politician, and Garrett has a number 1 single and an 8 point lead in the polls, then (4) could be permissible, but (5) seems considerably more marked.

(4) We have an 8 point lead in the polls.
(5) *We have a number 1 single.

So it looks like there is something interesting to explain about the pattern of usage here. In fact, there seem to be two distinct questions to ask.

The first of these we might call the *truthmaker* question. That is, what relation must hold between the speaker and the group whose actions constituted X happening for _We did X_ to be true? (Or, if you don’t think these utterances are generally true, for it to be appropriate.)

The second of these we might call the *semantic* question. Say that we settle the truthmaker question by saying that the speaker S has to stand in some distinctive relation R to the group G that did X for _We did X_ to be true. There remains a question about how _We did X_ comes to have those truth conditions.

It could be that _we_ picks out the group G. That would be an odd way for _we_ to behave, since the speaker isn’t among the G. Call this result a kind of _deferred ostension_.

Or it could be that _did X_ picks out a property that can be applied to a larger group than those that directly did X. So even if 22 guys on a field in Geelong won the game, _won_ in _We won_ could pick out a property that’s instantiated by a larger group, perhaps the group of all Geelong’s supporters. Call this result a kind of _deferred predication_.

The semantic question then is whether examples like (1) and (4) involve deferred predication or deferred ostension.

The truthmaker and semantic questions are related, we think, and hopefully by the end of the week we’ll have answers to them.

Asssume we have a radioactive particle with a half-life of 1. Then there is a countably additive probability function, whose domain includes all open intervals (x, y) and is closed under union and complementation, such that Pr(S) is the probability that the particle’s decay time is in S.

In cases where Pr(T) is non-zero, we can define Pr(S|T) in the usual way as Pr(S&T)/Pr(T). But even in cases where Pr(T) is zero, we might like to be able to have Pr(S|T) as defined.

Let T then be the set of rational numbers. (Note that if the domain of Pr is closed under countable union and complementation, then T will be in the domain.) Now we might wonder what Pr( |T) looks like. That is, we might wonder what Pr looks like when we conditionalise on T.

I think, and if I’m wrong here I’d welcome having this pointed out, that these conditional probabilities are not defined. And not because Pr(T)=0. In lots of cases probability conditional on a zero-probability event can be sensibly defined. But in this case, if there were such a thing as Pr( |T), then for any rational number _x_, Pr({x)|T) would be 0. And that would lead to a failure of countable additivity.

I imagine all of this is well known, but I hadn’t realised the consequences of this. Let D be the smallest set of sets of positive reals that includes all open intervals (x, y) and is closed under countable union and complementation with respect to the reals. Then there is no _conditional_ probability function from D x D\{} -> [0, 1] such that for any open interval (x, y), Pr((x, y)|R) is the chance that the particle will decay in (x, y). (By R here I mean the set of all reals.) If there is any function that has this last property, it must be defined over a narrower domain than D x D\{} -> [0, 1].

An interesting technical question came up in my probability lectures at St Andrews the other day, and it took me until now to realise the correct answer to it.

The question was whether there’s any good reason to think that credences can be irrational numbers. Why, went the question, couldn’t we hold the structure of credences to have the topology of the rationals rather than the reals?

Now one possible answer is that we want to preserve the Principal Principle and since physical theory gives us irrational chances, we might allow irrational credences. But I think this puts the cart before the horse. If we didn’t think that credences and chances had the right kind of topology to support the Principal Principle, I don’t think the Principal Principle would look that plausible.

A better answer involves countable additivity. The rationals are closed under finite addition, multiplication and non-zero division. But they’re not closed under countable additivity. (For examples, think of the expansions of _e_ or _pi_ as infinite series of rationals.) Since, I hold, we should think countable additivity is a coherence constraint on credences, we should think that credences have a structure that is closed under countable addition. And that means they should be (or at least include) the reals, not that they should be confined to the rationals.

For a long time I thought it was established that (given a standard axiomatisation of the probability calculus) countable additivity and countable conglomerability were equivalent. But I’ve lost confidence in my belief. So I’m wondering if anyone can tell me exactly what the answers are to a few questions below.

Just to make sure we’re clear, I’m taking countable additivity to be the principle that if each of the E_i in {E₁, …, E_n, …} are disjoint, then Pr(E₁ v … v E_n v …) = Pr(E₁) + … + Pr(E_n) + ….

And I’m taking countable conglomerability to be the following. Again, if each of the E_i in {E₁, …, E_n, …} are disjoint, then there is some E_i such that Pr(E | E_i) <= Pr(E).

_Question One_: Does a failure of countable additivity entail a failure of countable conglomerability?

I'm pretty sure that, as stated, the answer to that is *no*. Consider a standard finitely additive probability function. So there's some random variable X, and for all natural x, Pr(X=x)=0, while the Pr(X is a natural number)=1. Now insist that Pr is only defined over propositions of the form _X is in S_, where S is a finite or cofinite set of natural numbers. (By a cofinite set, I mean a set whose complement, relative to the naturals, is finite.) I'm reasonably sure that there's no way to generate a failure of countable conglomerability.

_Question Two_: Assume there is a random variable X such that Pr(X is in S1 | X is in S2) is defined for every S1, S2 that are non-empty subsets of the naturals. And assume that whenever S2 is infinite, and the intersection of S1 with S2 is finite, then Pr(X is in S1 | X is in S2) is 0. (So Pr violates countable additivity.) Does Pr fail to respect countable conglomerability?

I'm even more confident that the answer to this is *yes*. Here's the proof. Any positive integer _x_ can be uniquely represented in the form 2ⁿ(2m+1), with _n_ and _m_ non-negative integers. For short, let a statement of the form _n=x_ mean that X is one of the numbers such that when represented this way, _n=x_, and similarly for _m_. Then for any non-negative integer, Pr(X is odd | _m=x_) = 0, since for any given _m_ there is one way to be odd, and infinitely many ways to be even. By conglomerability, that implies Pr(X is odd) = 0. But an exactly parallel argument can be used to argue that Pr(X+1 is odd) = 0. And this leads to a contradiction.

_Question Three_: Assume there is a random variable X such that for any x, Pr(X=x)=0, while Pr(X is a natural number)=1, and that Pr(X is in S1 | X is in S2) is defined for every S1, S2 that are non-empty subsets of the naturals. Does Pr fail to respect countable conglomerability?

This is what I don’t know the answer to. I think the answer is *yes*, but I can’t see any obvious proof. Nor can I come up with a counterexample. Does anyone know (a) what the answer to this question is, and (b) where I might find a nice proof of the answer?

Much thanks in advance for helpful replies!

There is one other argument that Williamson deploys against Evidence Neutrality: it is unattainable. EN requires that the community be able to decide what its evidence is. But an individual can’t, in all cases, even decide what her own evidence is. In hard cases, EN doesn’t just fail as a theory of group evidence, it fails as a theory of individual evidence.

This isn’t something special about evidence. Williamson thinks there is almost nothing that we can, in all cases, tell whether it obtains. Evidence is undecidable because, he argues, practically everything is undecidable in hard cases. The latter conclusion has constraints for norms. If there are norms, then they can’t be things that we know to obtain. Williamson gives a nice example. When one is speaking to a group, the rule _Adjust the volume of your voice to the size of the room_ is a good rule, an ideal to aim for, even if we don’t know, and can’t in principle know, the exact size of the room. Such a norm is a regulative ideal; we aim for it, even if we can’t always tell how close we are to hitting it.

So there can be norms that we can’t always obtain, or perhaps can at best obtain by luck. EN might, for all Williamson has said, have such a position. We should use evidence that all the members of our community recognise as evidence. The benefits of such a rule can be seen by looking at the relative success, over the course of human history, of individual and group research projects. The great majority of our knowledge of the world is the outcome of research by large, and often widely dispersed, communities of researchers. Even in cases where a great individual advances knowledge, such as Darwin in his theorising about evolution, the individual’s work is typically improved by holding themselves to EN as a norm. In Darwin’s case, the reason for this is relatively clear, and I think instructive. Darwin collected so much evidence over such a long period of time, that the only way his younger self could convince his later self that it was all part of his evidence was by the same methods that his younger self could convince the community of biologists that it was part of his evidence. It was holding to EN that allowed him to engage in a fruitful long-term research project.

In many ways, EN is quite a weak norm. In earlier posts I discussed what amount to two major exceptions to it. First, EN doesn’t require rule neutrality. So the maverick scientist can hold EN while coming to quite bizarre conclusions by adopting various odd rules. As we saw above, we can put some constraints on what makes a good rule, but those constraints won’t individuate the good rules. Second, EN, as I’m interpreting it, allows one to choose one’s own community. One of the ways we uphold EN in science is by excluding from the community those who doubt the relevant evidence collecting methods. That means we exclude the odd crank and sceptic, but it also means we exclude, from this particular community for the while, those scientists who carefully study the evidence collection methods that we use. In the latter case at least, there is a very real risk that our community’s work will be wasted because we are using bad methods. But the alternative, waiting until there is a rigorous defence of a method before we start using it, threatens a collapse into Cartesian scepticism.

Even if EN is a norm of evidence, a regulative ideal, rather than a constitutive principle of evidence, we might still be pushed hard towards taking intuitions to be evidence. Or at least we might be so pushed some of the time. It doesn’t violate EN to take what nutritionists tell us about a healthy diet at face value; the reports of nutrition science are common ground among the community of ethicists. But we can hardly take facts about disputed examples, for instance, as given, even if they are quite intuitive to some of us. And even if, as it turns out, we know the answer. If there are people who are, by any decent standard, part of our community of philosophers, who disagree about the cases, we should be able to give our grounds for disagreement. Not because this is necessary for knowledge, but because the policy of subjecting our evidence to the community’s judgment is a better policy than any known alternative.

To be sure, some work needs to be done to show that that taking intuitions as basic does conform to this idea. As Williamson notes, one thing that might (even in somewhat realistic cases) be in dispute is the strength of an intuition. So taking EN as normative might require some modification to intuition-driven philosophical practice. But I don’t think it will require as big a diversion as Williamson’s preferred anti-psychologistic approach.

If Evidence Neutrality (EN) is true, it is presumably true everywhere. One way to argue against it then is to argue that it doesn’t hold in other subjects. And that’s what Williamson does. He argues that it doesn’t hold in particular in science.

bq. If Evidence Neutrality psychologises evidence in philosophy, it psychologises evidence in the natural sciences too. But it is fanciful to regard evidence in the natural sciences as consisting of psychological facts rather than, for example, facts about the results of experiments and measurements. When scientists state their evidence in their publications, they state mainly non-psychological facts (unless they are psychologists); are they not best placed to know what their evidence is?

If this were a true description of the position of evidence in science, it would be a problem for EN. But it isn’t. EN doesn’t psychologise evidence in science, it _institutionalises_ it. Let’s recall the original statement of EN.

bq. [W]hether 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. (Emphasis added)

Here’s one way to preserve EN in a field. Adopt some standards for something being evidence in that field, standards that are in practice (if not always in theory) decidable. Then take questions about whether those standards are good standards to belong to another field. That is, take it that people who are questioning the standards, questioning whether these standards genuinely generate evidence, to be outside the community in the sense relevant to EN. They might of course be part of another intellectual community, but they aren’t part of this community. That way we can preserve EN within every given community.

Compare a principle we might call Foul Neutrality (FN) governing a sport. It’s pretty important for playing football that we have a quick method for deciding what’s a foul and what isn’t. And this must be decidable independent of one’s interest in the game. We don’t get FN by psychologising fouls; we get it by having referees. The referees could be wrong, and indeed we could have interesting projects about improving the quality of referees. But when we engage in that project we’ve stopped playing football. The community of footballers (as such) satisfies FN because it’s part of being in that community that we take the referee’s word as final.

Science isn’t like football in that it requires absolute respect of the referees judgment. But it is frequently true that the project of using methods or devices to produce evidence is quite distinct from the project of evaluating whether those methods or devices are good. And we can sensibly individuate communities by looking at which methods they take as given. The short version of my response to this argument is that that’s really how science works; i.e. that science consists of communities so individuated. Each community has a refereeing institution. Or, at least, it is how it works in the vast majority of cases. In cases where the refereeing institutions break down, where there isn’t some other community to serve in effect as referee for your community, then we might have to fall back on psychological states. But EN doesn’t systematically psychologise evidence in science.

We might think that evidence must consist of facts measured rather than something about their measurement, because those are the kinds of things we can submit to statistical testing. But that argument, if it works, proves too much. Williamson’s initial description of scientific evidence was that it consisted of “the results of experiments and measurements”. But that’s ambiguous between two readings. On the first, scientists just state the outcomes of their measurements. That is the kind of thing that you can do statistical analysis on. On the second, they state the results of the measurement, and describe what kind of measurement it is. And that’s, I think, the true reading. At least for results of any interest, you have to describe how you got them, as well as what you got. But you can’t do statistical analysis on a description of a kind of measurement. So it isn’t true that all scientific evidence consists of things you can plug into mathematical equations.

On the other hand, this picture of scientific practice does seem to support the institutional picture of evidence. Why is it that we report the methods as well as the result? One simple answer is that it is settled (relative to the kind of science we’re engaged with) that using that method produces scientific evidence. That’s not to say that the method is beyond dispute. It might be that some other science studies the workings of the very machines that a particular science takes for granted in their operations. It’s merely to say that this science has approved the method in question.

We can see this even more clearly if we look at engineering settings rather than science settings. Imagine we’re working on a bridge construction project, and we need to know the density of some concrete. We’ve got a machine that measures concrete density, so we use it and, assuming the answers are plausible, we’ll take those answers as given. Evidence Neutrality will be ssatisfied because we’ll agree to use the machine. Of course, the only reason we trust the machine is that there is someone, typically someone else, whose job it is to test the machine on a regular basis, and service it, or have it serviced, if it isn’t, and although we might not know the details of how this process works, we’ll have a nice certificate saying the machine is in good condition to use. Now the folks who calibrate machines like this aren’t perfect, so there are other people whose job it is to audit them on a regular basis. And auditors aren’t perfect either, so there will be some body, perhaps a certification body, that oversees them. A positive mark from an auditor only licences a calibrator to approve a machine if the auditor is in turn certified. The board itself may need to be checked, so maybe it will have a board, perhaps including representatives of people like bridge builders who use the machines that we’re all interested in.

The crucial point about this story is that at every stage in the process, EN is satisfied. It is similar, I think, in sciences, though the structure is more fluid. Just which sciences will validate the use of the measurement techniques in other sciences is not as straightforward as in engineering. And the precise boundary between questions that are internal to a given science and questions external to it will change over time. When many questions central to the science start to turn on a particular kind of question about measurement, then those measurement questions may become part of the science. (For instance, if experimental philosophy really takes off, perhaps questions about survey design will be regarded as philosophical questions in the future. More prominently, in recent years questions about the behaviour of satellites have become part of climate science because of the importance of satellites to climate measurement.) But still the broad structure is fairly similar.

The big difference between science and engineering is what happens at the end of the process. The way I described the bridge building case was that eventually, the people responsible for checking the activities of others were the very people (or at least the representatives of them) who were being watched over to start with. That obviously isn’t what happens in science. We don’t check the activities of (say) particle physicists by putting together a board of psychiatrists, nutritionists, economists etc. How might we satisfy EN in basic physics?

Two obvious answers spring to mind. One, either common sense or philosophy tells us that we can take perceptual evidence as given. So even in fundamental physics we can individuate the community in such a way that those who are raising sceptical doubts are doing something else, namely philosophy.

The other answer is that we might take scientific evidence, at the most fundamental level, to be psychological states. Certainly it isn’t uncommon for _philosophers_ of physics to take the role of physical theory to explain our observings. That’s part of why we’ve ended up with such psychologically flavoured interpretations of quantum mechanics, from the Copenhagen interpretation to the many minds interpretation. Perhaps that’s just philosophers bringing in bad philosophical prejudices, but it seems like we _can_ do science respecting EN. That’s because EN mostly is satisfied by the institutional structure of science, and when it isn’t, it doesn’t seem to destroy science to take some evidence to be psychological. So there isn’t an argument from science against EN.

In the previous post we argued that as well as evidence, we need a notion of an unjustified rule that takes us from evidence to conclusion. Some may think that this notion is too obscure, or at least philosophically disreputable to do the work it’s put to. This section is then a discussion of rules that aims to increase their respectability. The idea is obviously not new; it traces back as least as far as Wittgenstein on rule-following, if not back to Carroll himself. And it has links to contemporary epistemology, wherever someone says that there are things we are entitled to assume without argument. But since it is doing so much work here, and since in conversation it has often been the most puzzling aspect of the argument to others, it may be worth saying just a little about what I’m taking rules to be here.

The argument in that section relied on Lewis Carroll’s example involving modus ponens, and that might suggest that modus ponens is the kind of rule that we need. Indeed, it often seems that some philosophers think that it’s the _only_ rule we need. (Many philosophers have said that conditionalisation, which is really just a probabilistic form of modus ponens, is the only rule we need.) I think this example is misleading for four related reasons.

First, modus ponens is a rule of *implication* and what we’re really looking for here are rules of *inference*. We’re looking for rules that tell you what to do with evidence. And what you do with evidence is draw inferences from it. These may not, in any interesting sense, be implications of the evidence.

Second, modus ponens is necessarily truth preserving, and this might be thought to be related to its acceptability. This seems like a mistake twice over to me. It’s arguable (indeed I’ll briefly argue for it presently) that we need some ampliative rules to explain the rationality of induction. And there are necessarily truth preserving rules that we cannot employ without justification. The rule that lets us infer _p and oxygen has atomic number 8_ from _p_ is necessarily truth preserving, but not a rule we could freely employ without independent justification.

Third, modus ponens can be used in suppositional reasoning just as well as in regular reasoning. It would take us way too far afield to investigate this properly, but I suspect some of the rules we’ll look at can’t be properly be used in all suppositions. (Of course some rules of _implication_, at least in some formulations, also have restrictions on when they can be used; think of the restrictions on necessessitation or universal-introduction.)

Fourth, modus ponens might (although this is controversial) be constitutively related to the meaning of the conditional. Perhaps, as some inferentialists believe, the meaning is determined by the acceptability of the rule. Perhaps the meaning directly implies that it is an acceptable rule. If either of those things are true, they aren’t I think things we’d want to generalise to, say, rules for rational inductive inference. (There is obviously a lot to be said here, such as considering what might justify inferences related to logic if not meaning. Many recent papers by Boghossian, Williamson, Wright and others are relevant here. But I’m just going to avoid that issue for today, in large part because I do find it mysterious how to generalise much of that debate from issues about modus ponens to issues about, say, enumerative induction.)

Now all that is just to say what rules are not. Can we say what they are? As noted above, in some ways rules are very familiar. Any time any philosopher claims that we are warranted, or entitled, to, without justification, rely on the deliverances of some source, it seems they are proposing that the inference from _The source says p_ to _p_ is a good rule. So we can take dogmatists about perception (e.g. Pryor’s “The Sceptic and the Dogmatist”) as endorsing a rule that lets us move from _Appears that p_ to _p_ without antecedent justification. And some anti-reductionists about testimony seem to hold that the rule which licences the inference from _I’m told that p_ to _p_ is a good one. So in some ways this isn’t a new idea, it’s just a way of framing an old idea. There are, however, two reasons we might think that this is a good framing. First, it lets us ask some relatively precise questions about the statement of the rules. Second, by thinking about rules as a class, we can formulate restrictions on what could be a rule.

It is harder than one might like to actually state rules that we can or do use. Clearly it isn’t a rule that we can, in every case, infer from _Appears that p_ to _p_; there are illusions, some of which we know about. Nor is it a rule that we can, in every case, infer from _I have observed many Fs in widespread conditions, and they have all been Gs_ to _The next F I observe will be G_; there are gruesome predicates. We could try to incorporate the exceptions into the rule, but a quick glance at how one might do this reveals that it isn’t too attractive, at least as long as we want to have non-trivial rules. Probably we need something different.

In the case of appearance, there is a natural move to make. Instead of a single rule with all sorts of qualifications, we might try to defend the following two unqualified rules.

(A) If it appears to you that _p_, then you have a reason to believe that _p_.

(ND) If you have a reason to believe that _p_, and this reason isn’t defeated, believe that _p_

The conjunction of (A) and (ND) entails Pryor’s dogmatism, although that conjunction is considerably stronger than dogmatism. For example, it entails that appearances that you have reason to believe are deceptive provide some reasons; dogmatism as such is silent on such appearances. But both rules seem at least defensible, even given the existence of illusions. (Of course, if they are good rules, they don’t need a defence. But we can reasonably expect that a good rule won’t be such that we can have good reason to believe it is bad, and (A) and (ND) pass that rule.)

The case of induction is a little trickier, because as soon as we think about the rule a hard question arises. We can only project non-gruesome predicates. Does that mean (a) that the non-gruesomeness of the projected predicates should be an input to inferences licenced by the rule, or (b) that the rule requires no such input, but it only licences inferences when the predicates are in fact non-grue? The latter sounds more plausible; otherwise no one who lacked the concept of a gruesome predicate could rationally make inductive inferences. But it raises tricky questions about using that rule in suppositional reasoning. What if (assuming this is possible) different predicates would be gruesome if _p_ were true, and we are inferring under the supposition that _p_? It isn’t obvious just what restrictions should be put on the use of this rule in a suppositional context. Perhaps those restrictions are quite tight. This has important consquences for arguments for the contingent a priori that assume that we can make inductive inferences in suppositional contexts, such as John Hawthorne’s “Deeply Contingent A Priori Knowledge” and my “Scepticism, Rationalism and Externalism”.

That was all about the nature of rules; we might wonder whether there is anything that we can say about which rules there are. Different ways of thinking about Carroll’s example suggest two different constraints on rules, one more liberal and the other more conservative.

The more liberal constraint is a kind of transcendental consideration. In many cases it seems, at least prima facie, that we can get knowledge from a certain source, but we couldn’t antecedently justify the use of that source. A classic example of this kind of reasoning is C.A.J. Coady’s arguments for against reductionism in testimony. The thought there is that so much of the time the only way we have of checking one person’s testimony is through the testimony of another, that if we weren’t able to take some testimony as basic knowledge, we’d be led to a debilitating scepticism. That seems unacceptable, so we might take such a rule as given.

The more conservative constraint takes more seriously the particular way in which we need a rule to sidestep Carroll’s tortoise. The core problem isn’t just that when we add another premise, one that justifies a particular use of the rule, we need yet more to get to the conclusion. Rather, the core problem is that when we add the kind of premise that could justify the rule, we need another step of the very same rule. Justifying this particular use of the rule doesn’t seem to get us any closer to where we need to be. Perhaps those cases, where justifying a particular use of the rule still requires the rule, are the only cases where there are unjustified rules.

This seems to be a more conservative principle because whenever it obtains, we’ll be able to give a transcendental argument for the existence of a rule. But the converse doesn’t seem to hold. We might justify taking someone’s testimony about being true because we believe them to be generally reliable. We still need a rule saying that it’s good to believe those who are generally reliable, but that doesn’t seem like the same rule. Similarly, we might accept (A) as a derived, and hence justified, rule because the best explanation of our experiences is that they are generally reliable. (Jonathan Vogel has argued for this at length over the years.) We still need a rule saying that we should believe the best explanation of a phenomena, but that doesn’t look like rule (A) again. On the other hand, Hume’s arguments about induction arguably do show that a justification of induction will need to use induction. And a justification of (ND) will, I imagine, still use something equivalent to it. So even on the more conservative conception of rules, they may still be rules.

These are enormous questions, to say the least, so I don’t think this goes close to settling anything. But I hope it’s enough to suggest that we haven’t given up on systematic epistemology once we admit the notion of unjustified rules that justify inferences. And admitting that, which Carroll’s example suggests we must, is enough to sidestep Williamson’s argument against EN.

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.

bq. 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.

bq. 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_.

bq. 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.

In the previous post I mentioned that Williamson clearly opposes in chapter 7 a broadly psychological conception of philosophical evidence. But it isn’t exactly clear just what his target is. At times he seems to be arguing against psychological evidence _ever_ being philosophically worthwhile. For example, consider the following batch of quotes.

bq. “For now I face the challenge of arguing from a psychological premise, that I believe or we are inclined to believe the Gettier proposition, to an epistemological conclusion, the Gettier proposition itself. That gap is not easily bridged.”

bq. “Since psychological evidence has no obvious bearing on many philosophical issues, judgment scepticism is also encouraged in ways that do not depend on the consequence fallacy.”

bq. “In explaining why we have intuitions, analytic philosophy has a preference for explanations that make those intuitions true over explanations that make them untrue, but the justification for that preference remains unclear”

In those quotes his opponent seems to hold the relatively weak view that psychological evidence can (sometimes) be useful evidence for philosophical conclusion. But other times he seems to take his opponent to be the person who holds the much stronger view that only intuitions are evidence. For instance, he says

bq. “One result [of EN] is the uneasy conception many contemporary analytic philosophers have of their own methodology. They think that, in philosophy, ultimately our evidence consists only of intuitions.”

I think it’s hard to believe that’s really a widespread view in philosophy. Does Singer’s argument for vegetarianism rest (even ultimately) on intuitions about the nutritional value of a vegetarian diet? Does the well-known argument from special relativity against presentism rest on intuitions about whether special relativity is true? Nevertheless, Williamson does attribute it to many (unnamed) philosophers. And yet some of Williamson’s arguments seem directed particularly against this position. For instance, he says

bq. “Taken far enough, the psychologisation of philosophical method becomes self-defeating”

And he cites approvingly Joel Pust’s conclusion that it is self-defeating to hold that

bq. “Aside from propositions describing the occurrence of her judgements, S is justified in believing only those propositions which are part of the best explanation of S’s making the judgements that she makes”

Probably Pust and Williamson are right here, but it hardly tells against anything but a strawman version of the psychological view of evidence. Finally, Williamson objects to a version of Reflective Equilibrium that just attempts to get our intuitions into equilibrium with the following argument.

bq. “The reflective equilibrium account, as usually understood, already assigns a proto-evidential role to at least one kind of non-psychological fact. For it treats philosophers as relying on logical relations between theories and intuitions, in particular their consistency and inconsistency.”

The theme again is that we need some evidence other than intuitions, something that should be common ground. (For reasons I’ll suggest in the next post, I’m not sure this is a good argument for that conclusion though.)

We haven’t got very far by trying to characterise what Williamson’s opponent says. Perhaps it is better to look at his positive proposal for what is evidence in philosophy. We get one statement of what that positive conclusion.

bq. “Our evidence in philosophy consists of facts, most of them non-psychological, to which we have appropriate epistemic access.”

That, in conjunction with the quotes above, suggests he is defending the following three theses.

1. Not all philosophical evidence is psychological.
2. Having _p_ be part of your evidence requires appropriate epistemic access to _p_.
3. The intuition that _p_, or the fact that one has that intuition, is weak evidence, perhaps no evidence at all, that _p_.

A position that denied all three of those would clearly be among the targets of Williamson’s chapter. But that would be crazy, since (1) is obviously true. But a position like the one I sketched at the end of the last post, which was neutral on (2) and denied (3), would still seem to be at odds with the bulk of what Williamson says, and I think is meant to be among the positions ruled out by the considerations he raises.

Now such a position does not seem especially related to the sceptical positions that are the targets of sections 3 and 4 of Williamson’s chapter 7. But that’s as things should be. The question of what our evidence is doesn’t immediately settle the question of what knowledge we have. Taking perceptual evidence to be psychological might be a precursor to defending external world scepticism. But it might also be a precursor to adopting indirect realism. Of course Williamson, by accepting knowledge as evidence, has effectively ruled out classical forms of indirect realism, where we know about the world on the basis of purely phenomenal evidence. But that shouldn’t be presupposed here I think. A position that holds that psychological states, or facts about them, are often crucial evidence for us is opposed to the core doctrines of Williamson’s chapter, even if it is also opposed to some of his other opponents.