Mellor’s account of the warrant of induction in his inaugural lecture of that name turns on a comparison with observation. The idea is to get clear on the warrant of observation and then use that to motivate an account of induction. For one thing, he argues, the traditional problem stems, in part, from assuming that induction should have a warrant which even observation cannot have. Since a well grounded observation trumps a well grounded induction, that must be wrong. But his account of observation is revisionary. He says that it isn’t factive. Seeing something is so does not imply that it is so.
But observations are... fallible, a fact we obscure when we use words like ‘observe’ so that by mere definition we can’t observe what isn’t there. So I will not use ‘observe’, ‘see’, ‘hear’, etc. in that misleading way. When my looking to see if there are sparrows makes me believe that there are, I shall say that I see that there are, whether there are or not. For there might not be: our senses always can give us false beliefs and sometimes do. Observation no more entails the truth of the beliefs it gives us than induction does. How then can it warrant them? [Mellor 1988]
The question here is how observation warrants the truth of the beliefs it motivates. Mellor’s answer is that causal links enable observations to warrant beliefs because, he claims, the fact that makes a belief true is what causes the belief to be held. (Given that this is supposed to be the warrant observation provides, the causal connection must (I assume) be via a suitable sensory path.)
The claim that observation isn’t factive can now be accommodated via the further – independently plausible – claim that causation isn’t deterministic. If causation merely raises the chances of its effects (ie if it doesn’t have to make the chances of its effects = 1) then thinking that one sees a sparrow can warrant a belief in sparrows by suitably raising the chances of their being sparrows, though not to 1 and other things can also cause a belief in sparrows.
This then serves as a point of departure for thinking about the warrant of the truth of beliefs produced by induction. In this case, it cannot be that the facts that cause the beliefs are the same facts that make those beliefs true because induction isn’t a kind of direct perception of the future, for example. Rather, the facts that cause the inductive belief are the inductive base: the premises not the conclusion of the inductive inference. So what warrants the truth of the resultant belief in the conclusion?
Mellor’s answer is that the warrant is the lawlike connection between the truth of the premises and the truth of the conclusion. Providing that the world is suitably lawlike, induction is warranted. Hence a quotation at the start of the lecture from Frank Ramsey ‘we are all convinced by inductive arguments, and our conviction is reasonable because the world is so constituted that inductive arguments lead on the whole to true opinions’. But the laws need not be deterministic to provide a warrant. They just need to raise the chances of effects sufficiently.
Suppose, to simplify the discussion (it’s not essential), that your inferential habits are deterministic, like your mass: this habit would always make you infer that a lecture was terse, never that it wasn’t. And suppose that every lecture has some chance of being terse. Then whenever your premise (‘this is a lecture’) is true, your conclusion (‘this is terse’) has some chance of being true. And if this chance is high enough, your prediction is warranted. [Mellor 1988]
Being warranted depends on what the laws of nature are. But providing there is a sufficient natural uniformity, induction is warranted. Now putting it like this (Mellow does not) invites a comparison with versions of the problem of induction going back to Hume in which defences of induction that invoke the uniformity of nature face a problem. Since a claim about uniformity is not a ‘relation of ideas’ it must be a matter of fact. But it isn’t a directly perceivable matter of fact and thus must be the result of an inference from what can be observed. What inference? Well induction. So if the defence of induction requires appeal to the uniformity of nature, it looks to be circular. Here’s Mellor’s summary of that worry.
So far so good - provided these warrants needn’t be self-intimating. I say the law that all tree frogs are green warrants my inferring that something is green from the fact that it’s a tree frog. But suppose I must know that I have this warrant. Then I must know this law. So I must believe it, and this belief must be warranted. But the law entails the very inference which it’s meant to warrant: tree frogs can’t all be green unless this one is. So unless my inference is warranted already, my belief in the law won’t be warranted. Thus to claim that the law is what warrants this particular application of it simply begs the question of whether it’s warranted at all. [Mellor 1988]
The solution is to part company with an assumption built into Hume’s version: that justification is self-intimating or that to be justified, one must know the justification. Mellor’s solution is an externalist denial of that. One can be warranted without knowing the warrant.
This is the stock objection to contingent solutions to the problem of induction: they beg the question. And so they would if belief-warrants had to be self-intimating. But … they don’t. The law that all tree frogs are green can warrant the habit of inference which induction will then give me, just because I needn’t know that it does. I can know by induction that a frog is green without knowing that law, just as I can know that it’s green by looking at it without knowing I’m not colour-blind. I may know the law, just as I may know that I’m not colour-blind; but I needn’t. So my saying that the law is what warrants this induction doesn’t beg the question. [Mellor 1988]
The lecture conducts some further business. Because of the nature of the appeal to indeterministic or probabilistic laws in this epistemological context, Mellor reminds us that these can be thought of as objective chances with mind-independent causes and effects. He also explains the advantage of larger sample sizes in the premises of inductions and why counter-induction is generally a less good strategy than induction in a lawlike world but that no strategy triumphs in a lawless world. But the general idea is that a possibly probabilistic but generally lawlike universe warrants a form of inference which moves between nomologically related properties.
One question this prompts is the relation of warrant and truth. In the case of observation, there is a potential for a gap which isn’t there in a disjunctive account. Since ‘seeing’ a sparrow does not entail that there is a sparrow, a warranting but merely probabilistic relation between sparrows and beliefs in sparrows can coincide with the falsity of a belief. So Mellor accepts the idea that two subjects can be equally warranted in their beliefs, one can be false and the other true but the latter subject nevertheless have knowledge. That seems odd as it seems that the fact that their belief is true is, relative to their counterpart, a matter of some luck (likely though they are to be right).
A disjunctivist like McDowell can attempt to account for the fallibility of observation by conceding that whilst that faculty as a whole is fallible, its exercise on particular occasions falls into two sub-groups: actually seeing the sparrow or merely thinking one sees the sparrow. In the good disjunct, no probability is in play: the sparrow is simply there in view. So the warrant in the good disjunct is of a quite different kind to that in the bad disjunct. (The worry now is whatever is surprising about the idea that warrant and truth cannot come apart symmetrically.)
Returning to Mellor, in one kind of case of failed induction, there seems to be a similar possibility for a false but warranted induction: the unlucky case in which a probabilistic connection fails to yield the fact that fits the inductively supported conclusion. But I wonder about a case in which, for fully deterministic reasons, one causal regularity is trumped by another. The regular spinning of the Earth may be interrupted by a supernova, eg. In that case, the sun’s previous behaviour considered alone might be thought to warrant the inductive belief that it would rise the next day but the physical system as a whole suggests that such a belief is not, in fact, warranted. The former approach would require some principles of individuation of the physical system considered independently of the subject’s grasp which seems tricky. But the latter approach would undermine the possibility, in deterministic cases, of warranted but false beliefs. Whilst it might seem the exercise of epistemic responsibility, the inference isn’t in fact warranted. This seems odd.
The appeal to me, however, of Mellor’s approach is that it sidesteps the ‘internalist’ version of the problem of induction. Not requiring that one knows the principle of uniformity of nature more generally, or the local laws more specifically, blocks the circularity which Hume stresses. So is there a way of embracing that and which maps something like a disjunctivist ‘correction’ of the warrant of observation onto induction? Not quite, I think.
Note that there are opposing tensions in calling McDowell’s disjunctivist picture of seeing ‘internalist’ and ‘externalist’. It is externalist, or perhaps more precisely not internalist, insofar as the fact that one occupies the good or the bad disjunct depends on a worldly favour which is beyond what the subject can control (hence the rejection of the interiorization of the space of reasons). But it is internalist, or rather not externalist, insofar as, if one is in the good disjunct, the seen sparrow is simply there for the subject, in no sense external to their experience (contra the highest common factor approach).
At first sight, it doesn’t seem possible to play quite this game with the inductive base. One cannot simply see in the observed past behaviour of ‘sunrise’, for example, the next day’s rise, that very event. Recall that in setting up Hume's problem, the connection between past and future regularities is a matter of fact rather than a relation of ideas. But then, within the class of matters of fact, such a regularity is not directly observable and must be extracted or inferred from what is observable (past regularities). At that point, we realise that the principle needed to do this presupposes the very thing that was supposed to be the conclusion of the inference.
With Mellor in mind, we might suggest that the observed past sunrises physically necessitate the next day’s rise. But if so, it isn’t so clear what the difference is in what is available to the subject between observing past sunrises which necessitate a future sunrise and sunrises which do not. The subsequent necessitation seems to be something external to what is observed and thus external to the subject’s grasp. So the feature of the disjunctivist account of observation which merits the description 'internal or at least not external' does not apply to Mellor's view of the law that connects past to future sunrises. Such a law is not part of what the subject can take in.
In McDowell’s discussion of the testimonial transmission of knowledge, he suggests that we speak of hearing, in another’s words, that things are thus and so. There is also here a possible line of analogy in that, for one to hear that things are thus and so, the interlocutor must be reliable and that is not something one typically ensures oneself. So their reliability is not in their utterance but is a precondition for hearing in their utterance the facts.
There is, however, also a potential disanalogy to induction here. The ‘content’ that the sun will rise tomorrow – or the sun’s rise, tomorrow – is not there in the induction base to be embraced. It seems that it must be inferred from that. This might suggest that there isn’t an equivalent idea to the mix of internal and external that characterises observation in the good disjunct. The link from past to future seems, as it is with Mellor’s account, an external addition to is observed. But the problem of making the connection external is that were it ‘blankly external’, as McDowell sometimes says, then it is hard to see how it can contribute the subject’s epistemic standing.
To get something akin to the disjunctivist account of the good disjunct for observation for the case of induction, I think we need to think along these lines. The subject who bases a prediction for the future on experience of past events must not merely take the past facts as atomic.To have a bearing on the future, they see a kind pattern or ‘habit’ in the sun’s behaviour. They see in the past behaviour of the sun its ongoing, and hence future implicating, pattern. And if the pattern really is ongoing – by contrast with a kind of bad disjunct in which the seeming pattern is not really there – then the subject does have a justification which balances internal and external.
Hume’s problem of induction is generated not just from the fact that the inference from past to future is not a ‘relation of ideas’ and hence must be a matter of fact but also because it is not a matter for direct perception and hence must be an inference. But perhaps the latter distinction does not neatly divide two aspects of the inductive base: atomic facts and subsequent inference. One sees in the facts the ongoing pattern.
McDowell’s own comments on the problem of induction are aimed rather differently. He attempts to deconstruct the starting assumption which compares induction with observation unfavourably. But I wonder whether by denying the separation of observation and induction they also sustain something like a disjunctivist view of seeing the enduring pattern in the past events:
there cannot be a predicament in which one is receiving testimony from one’s senses but has not yet taken any inductive steps. To stay with the experience of colour... colour experience’s being testimony of the senses depends on the subject’s already knowing a good deal about, for instance, the effect of different sorts of illumination on colour appearances... [McDowell 1998: 411]
So the supposed predicament of the inductive sceptic is a fiction... Hume’s formulation can seem to describe a predicament only if one does not think through the idea that its subject already has the testimony of the senses and this means that scepticism about induction can seem gripping only in combination with a straightforwardly interiorizing epistemology for perception. [McDowell 1998: 412].