2. HUME'S ENQUIRY AND THE SKEPTICAL ARGUMENT THIS PAPER ADDRESSES

Our topic is enumerative inductive reasoning. For example, I've been to Tony's Pizzeria nineteen times over the past four years, and each time the pizza was good; I infer that Tony's will serve good pizza next Friday. (Psychologists tend to study ‘category-based induction’, in which one generalizes from a claim about tigers to a claim about lions, for example. Hayes et al. (Reference Hayes, Heit and Swendsen2010) survey this literature.)

Let's look at what Hume (Reference Hume and Beauchamp2000) says in the Enquiry section IV part II. I'll focus on extracting an interesting argument for skepticism, rather than subtle Hume scholarship. I reconstruct Hume's reasoning as (i)–(iv). Hume doesn't assert (v) or infer (vi), but as I explain below, it's hard to resist the skeptical conclusion if we grant (i) and (iv).

1. i. Whenever one reasons inductively, one thereby presupposes that the future will resemble the past. (premise)

2. ii. One cannot establish that the future will resemble the past by reasoning inductively, as one would thereby presuppose the very thing one attempts to establish. (inferred from i)

3. iii. There is no good argument of any other kind that the future will resemble the past. (premise)

4. iv. There is no good argument that the future will resemble the past. (inferred from ii and iii)

5. v. There is no non-inferential way to rationally judge that the future will resemble the past. (premise)

6. vi. It is irrational to reason inductively. (inferred from i, iv and v)

Hume reasons from (i) to (ii) as follows. (Drawing an ‘experimental conclusion’ is the same thing as reasoning inductively, as is making a ‘probable argument’ or an ‘argument regarding existence’.)

Hume defends (iii) as follows:

That is: arguments that are not inductive (‘moral’) are demonstrative. Demonstrative arguments only establish conclusions it would be contradictory to deny. But it is not a contradiction to deny that the future will resemble the past.

Hume doesn't infer (vi), but it is hard to resist given (i), (iv), and the plausible extra premise, (v). From (iv) and (v) it follows that there is no way (inferential or non-inferential) to rationally judge that the future will resemble the past. But it is irrational to believe a conclusion that rests on a presupposition one cannot rationally judge to be true. And so, given (i), the skeptical conclusion follows.

The rest of this paper does not focus on (i)–(vi), but on a variant that escapes the following objection to (i). The future may resemble the past in some respects and not others. Inductive inferences had better not presuppose that the future will resemble the past in all respects, for that supposition is contradictory. Let T₀ be the present moment. Define: an object x is ‘ribble’ at t iff: either t ≤ T₀ and x is red at t, or t > T₀ and x is not red at t. In the past, raspberries have been red, and they have been ribble. The future cannot resemble the past in both respects, as that would require future raspberries to be red and not red.Footnote ²

When we reason inductively, we do not presuppose that the future will resemble the past in all respects, including which things are ribble. So we need to replace Hume's (i) with a claim that inductive inferences presuppose that the future will resemble the past in certain respects. But which respects? When I reason inductively about the behavior of electrons, I don't presuppose that Tony's Pizzeria will continue to serve good pizza. The least demanding and hence most plausible premise is that: an inductive inference presupposes that the future will resemble the past with respect to the very feature one is projecting into the future. For example, when I infer inductively that the pizza at Tony's will be good next Friday, I thereby presuppose that if Tony's served good pizza in the past, it will do so in the future too.

One might suspect that some more general principle underlines my inductive inference. When I infer inductively that the pizza at Tony's will be good next Friday, do I thereby presuppose that if any given restaurant served good food in the past, it will do so in the future too? I don't think so. I take restaurants in my small city to be more stable and predictable than those in New York. I take chain restaurants to be more stable and predictable than independent ones. And so on (in ways I can't introspect). I doubt there is a neat general principle my inductive inference presupposes. So the skeptical argument is most plausible if it alleges that: my inductive inference presupposes that if Tony's served good pizza in the past, it will do so in the future too.

But this replacement for (i) still faces a problem. When I infer that the pizza at Tony's will be good next Friday, I am not presupposing that the future will continue forever to resemble the past in the relevant respect. After all, I am not willing to infer that Tony's will be serving good pizza in 100 years. The most plausible view is that when I infer that the pizza will be good at Tony's next Friday, I presuppose that the future will resemble the past in the relevant respect at least until next Friday.

Putting these points together, I suggest that the most plausible claim in the ballpark of (i) is (1):

1. 1. Whenever one reasons inductively from E to H, one thereby presupposes that E→H.

I write “E→H” for the ordinary indicative conditional “if E then H”.Footnote ³ To illustrate, suppose I reason that since in my ten experiments electrons always repelled each other, electrons always repel each other. According to (1), I thereby presuppose that: if in my ten experiments electrons always repelled each other, then electrons always repel each other. When I infer that Tony's will serve good pizza next Friday, I thereby presuppose that if they've served good pizza each of the nineteen times I've been there over the past four years, then they will serve good pizza next Friday. That's a lot more plausible than what (i) says.

E→H is the claim most plausibly presupposed, as commitment to E→H goes hand in hand with reasoning from E to a full belief that H. If one doubts that E→H, then the inference from E to H is undermined. If one is convinced that E→H, then the inference from E to H won't be undermined by doubts about some other claim. Now the inference may also presuppose some logically weaker claims, entailed by E→H. But it won't be more plausible that the inference makes some weaker presupposition than that it presupposes E→H. Moreover, it would be harder to derive a skeptical conclusion from an unnecessarily weakened premise. So the best skeptical argument in the neighborhood takes (1) as a premise.Footnote ⁴

If we replace (i) with (1), then the rest of the skeptical argument needs to be reformulated. From now on, we will be concerned with the argument (1)–(5):

1. 1. Whenever one reasons inductively from E to H, one thereby presupposes that E→H. (premise)

2. 2. One cannot use the inductive inference from E to H as part of a conditional proof and thereby rationally conclude that E→H. (inferred from 1)

3. 3. There is no other way to rationally judge that E→H. (premise)

4. 4. There is no way to rationally judge that E→H. (inferred from 2 and 3)

5. 5. It is irrational to reason inductively. (inferred from 1 and 4)

In a conditional proof that E→H, one supposes that E, infers that H under the scope of that supposition, and then discharges the supposition to conclude that E→H. One reasons from E to H while leaving it open at that stage of inquiry whether E→H. Note that (2) only rules out the use of one particular inductive inference to establish that E→H, namely the inference from E to H. The use of other inductive arguments to establish that E→H is ruled out by (3).

One should want to hear more about the notion of presupposing which appears in (1). However, it wouldn't help present my rebuttal of the skeptical argument to start with a theory of presupposing. For now, let's just consider another example of the phenomenon, to suggest that we are not dealing with an isolated case.Footnote ⁵ Suppose one judges, in the normal kind of way, that one will be at the office at 9am tomorrow. Plausibly, one thereby presupposes that one won't be permanently abducted by purple aliens tonight. That explains why it is rationally impermissible to reason that since one will be at the office tomorrow at 9am, one won't be permanently abducted by purple aliens tonight.Footnote ⁶ The skeptical argument alleges that the same thing is wrong with a conditional proof that E→H: such reasoning presupposes the very thing it is meant to establish. Note that presupposing does not entail occurrently believing. For example, people anticipating another day at the office do not typically consider alternatives involving purple aliens. So the skeptical premise, (1), does not imply that people occurrently believe that E→H whenever they reason inductively from E to H. So (1) does imply that inductive reasoning is really deductive reasoning by modus ponens (as one reader has objected).

Some philosophers have thought that the problem of induction is generated by a mistaken assumption that inductive reasoning is a matter of following general rules. (For example, Okasha Reference Okasha2001, though Okasha Reference Okasha2005 is more circumspect; Norton Reference Norton2003, Reference Norton2014.) The argument (1)–(5) shows that this is not the case. Now I agree that we don't typically follow inductive rules. I argued above against several general suggested rules, starting with Hume's premise (i). Furthermore, the psychologists tell us that a variety of non-introspectible mechanisms are responsible for our inductive reasoning (Sloman and Lagnado Reference Sloman, Lagnado, Holyoak and Morrison2005: 111–13; Hayes et al. Reference Hayes, Heit and Swendsen2010). Because the mechanisms are not introspectible, it is not plausible that one ‘follows’ the general rules that they implictly encode. Similarly, it is not plausible that one ‘presupposes’ the general claims one can't tell are implicitly encoded by one's belief-forming mechanisms. But it remains plausible that reasoning from E to H presupposes that the world is a certain way: E→H, and thus that ¬(E&¬H). (1)–(5) is still a potent skeptical argument. So it does not solve the problem of induction to note that we don't follow general inductive rules. Okasha (Reference Okasha2001) is aware that (1)–(5) still needs addressing. In reply, he appeals to the Personalist Bayesian framework to argue that it isn't irrational to ‘presuppose’ that E→H. Let's now turn to this class of response. (Footnote 10 discusses the specifics of Okasha's position.)

Arguably, the Personalist Bayesian frameworkFootnote ⁷ doesn't allow the skeptical argument to be formulated. Personalist Bayesian views attribute degrees of belief to people, rather than full beliefs. They hold that people's degrees of belief at a time should be probabilistically coherent, with some versions placing further rational constraints. Some versions also hold that there are rational constraints on how one changes one's degrees of belief. The Personalist Bayesian framework makes it hard to ask a troubling question as to how one could rationally judge that E→H, or how one could rationally have a high degree of belief in H given E. If one's degrees of belief are in the approved class (probabilistically coherent and meeting any other requirement), and one hasn't changed one's degrees of belief in a forbidden fashion, then no worry can be raised in this framework about one's high degree of belief in H given E. So it seems that nothing in the vicinity of the skeptical argument can be formulated in this framework.Footnote ⁸ This would speak in favor of Personalist Bayesianism, if the skeptical problem stated above were insoluble.Footnote ⁹ On the other hand, the problem seems real. So if it can be straightforwardly solved, then that is reason to celebrate, and to take frameworks in which the problem cannot be stated to be expressively incomplete.Footnote ¹⁰

Many formal epistemologists and philosophers of science refer to a very different issue as “the problem of induction”. They are concerned to say what makes some non-deductive inferences rational and some irrational. (In the Personalist Bayesian framework, this forms part of “the problem of the priors”: are induction-friendly degrees of belief rationally required, and if so, why?) As we'll see, we can say where (1)–(5) goes wrong, without saying what distinguishes good inductive arguments. Conversely, I don't see why explaining what makes some non-deductive inferences rational would tell us where (1)–(5) goes wrong. Compare deductive inference. It is one thing to explain when P logically entails C; it is quite another to defuse the skeptical worry that one would, per impossibile, need to know first that P entails C before one can reason from P to C. Similarly, we must not run together the two issues sometimes called “the problem of induction”. (As I explain in the following footnote, I doubt the issues are equally worthy of the name.Footnote ¹¹)

3. HOW MIGHT WE RESPOND TO THE SKEPTICAL ARGUMENT?

The skeptical conclusion, (5), is obviously false. Our task is to find an account of where the skeptical argument goes wrong that satisfies us, we sensible philosophers who are sure that much inductive reasoning is rational. This task should not be confused with the pointless one of trying to change the mind of an inductive skeptic. One should not insist that we “avoid begging the question against the skeptic”, for we are not in conversation with such a lunatic, but with ourselves.Footnote ¹² For more on this, see for example Pryor (Reference Pryor2000: 517–8), Greco (Reference Greco2000: 22–3), or Jackson (Reference Jackson2015: §1). Astute readers may suspect that (1)–(5) generalizes naturally to an argument for skepticism about all inference, including deduction. I agree (see Haack Reference Haack1976; Boghossian Reference Boghossian2001, Reference Boghossian2003); but let's stick to the argument that's before us.

Let's quickly look over the possible objections to the skeptical argument, ending with my strategy and a plan for the rest of the paper. One cannot reject the inference from (2) and (3) to (4), and the inference from (1) to (2) seems solid. That leaves one inference and two premises to consider.

One might attack the inference from (1) and (4) to (5), but that's not where my money is. According to this approach, reasoning inductively presupposes that E→H, which one cannot rationally believe, but that's OK. For example, Crispin Wright (Reference Wright2004) distinguishes ‘trusting’ that p from judging or believing that p. In his view, it can be epistemically rational to trust that p, even when p is neither non-inferentially obvious nor supported by one's evidence. Wright explores sophisticated variants of the idea that it is epistemically rational to trust that a proposition is true, when doing so is needed for inquiry to take place at all. Maybe this idea could be parlayed into the claim that when one reasons inductively from E to H, it is epistemically rational to trust that E→H. On this proposal, it is rationally permissible to reason inductively, thereby presupposing that E→H, because one rationally trusts that E→H, even though one cannot rationally believe that E→H. I worry that rationally trusting that E→H is not enough. It seems that if we merely hope or hypothesize that the presupposition is true, then we should merely hope or hypothesize that our inductive predictions are true. Wright (Reference Wright2004: 207) calls this ‘the leaching problem’ for his proposal.Footnote ¹³ To my mind, he does not solve the problem, and the prospects for a solution are gloomy. Let's put this class of response aside (without pretending that I've presented a decisive case against it here).

So it seems the weakness in the skeptical argument lies in the premises, (1) and (3). In fact, my proposal denies both (1) and (3). But let me first explain the burden on rejecting them.

It is not easy to deny (1) with plausibility.Footnote ¹⁴ It is irrational to suspend judgment on whether E→H and yet reason from E to H. A natural diagnosis is that by reasoning from E to H, one presupposes that E→H.

Moreover, (2) is compelling; I think it would be unwise to deny (1) in order to deny (2). In fact, it is incoherent to deny (1) solely in order to deny (2). The key to the skeptical puzzle cannot be to endorse the conditional proof that E→H. If (2) is false and the conditional proof is legitimate, then one can reason from E to H while leaving it open at that point in inquiry whether E→H. If that's right (which it isn't), we can reason inductively without worrying about whether E→H. Whether one can establish that E→H, by conditional proof or any other means, is then irrelevant to the rationality of inductive reasoning.

One might object that (2) must be wrong, else all conditional proofs would be illegitimate. But (2) does not have such a wide-reaching consequence. While it's initially plausible that reasoning directly from P to C presupposes that P→C, it is not compelling that one presupposes that P→C when one reasons from P to L and then from L to C. That is, one need not first settle that P→C, before reasoning from P to L to C. So (2) only threatens the shortest conditional proofs, in which one reasons in one step from P to C, and concludes that P→C. Such conditional proofs do seem to violate the proper order of settling questions, even in the case of deductive inference from P to C (that's why there's a skeptical problem about deduction of the same form as our problem about induction). Moreover, (2) is compatible with endorsing conditional proof as a rule of deductive logic. One can hold that all instances of conditional proof are logically valid, though some presuppose the very thing they are meant to establish. Compare: modus ponens is a logically valid rule, but it presupposes the very thing one tries to establish to reason by modus ponens from the premises that I will be at the office at 9am tomorrow, and that if I will be in the office at 9am tomorrow then I won't be permanently abducted by purple aliens tonight. In Crispin Wright's terminology (Reference Wright2002), one's warrant for the premises ‘fails to transmit’ to the conclusion, though the inference is logically valid. Similarly, (2) does not imply that conditional proof is not a rule of logic.

To satisfactorily resolve the skeptical puzzle by denying (3), one must give a plausible account of how one can rationally judge that E→H.Footnote ¹⁵ I don't find it plausible that one must establish that E→H independently of reasoning from E to H. Surely the appeal of reasoning from E to H needn't be recreated using other intellectual resources.Footnote ¹⁶ However, it isn't obvious how one can respect this point without endorsing a conditional proof of E→H, i.e. denying (2). (My proposal finds a way to do so.)

Let me add a Humean problem for denying (3).Footnote ¹⁷ It would be worrying if one could only know that E→H by means of a clever philosophical argument. Most people are not in possession of a clever argument that E→H. That would raise the spectre that, given (1), most people are being irrational when they reason inductively: they thereby presuppose that E→H without having in hand a justification for doing so. To my mind, the rational way to judge that E→H must be in everyone's grasp.

My strategy is as follows. When people reason from E to H, and consider the question of whether E→H, they typically judge that E→H. For example, I'm sure you believe that if electrons repelled each other in the past, then they will continue to do so next week. (If you don't, then you need a doctor, and not a doctor of philosophy.) My core idea is that people judge that E→H in exactly the right way, a way that is rational and typically produces knowledge of the conditional. I will sketch a psychological theory of how people actually come to judge that E→H. On this account, people do not settle that E→H by conditional proof. Nor do they establish that E→H independently of reasoning from E to H. Roughly: one recognizes that the inference stands or falls together with judging that E→H, and the high degree to which the inference seems right causes one both to judge that E→H and to reason from E to H. When it is rational to reason from E to H, it is also rational to judge that E→H in the way my proposal describes. So when the question comes up, people usually judge that E→H in a rational way.

I spell out the psychological story in two stages. §4 explains how some psychologists working on metacognition understand the idea that some inferences seem right to a high degree. §5 extends that story to say how one judges that E→H. §6 then layers the epistemological claims on top of the psychological account. I explain why the proposal satisfyingly resolves the skeptical puzzle. In particular, the account of how we judge that E→H explains why we normally overlook the view that we did so in exactly the right way. That leads us to worry that there is no way to rationally judge that E→H, and thus to be ensnared by the skeptical argument.

The psychological theory described below is speculative. I hope you will forgive me for adopting the tone of assertion as I explain the proposal, leaving out the hedges that are no doubt necessary. The proposal is plausible, however, and illustrative. I hope it is already clear that we want a psychological explanation for why people judge that E→H without naturally thinking that they thereby settled the matter rationally. Any such psychological account allows us to solve the skeptical puzzle along the lines suggested in §6.

4. FEELINGS OF RIGHTNESS

People do not always judge things to be the way they seem. Psychologists classify this as a kind of metacognition (their name for the monitoring and control of one's mental processes). Asher Koriat and Valerie Thompson's work suggests a unified account of how we regulate belief-formation, whether the source is memory, reasoning, or something else. On this approach, a seeming that p is a representation that p with a Feeling Of Rightness (FOR) attached. A strong FOR typically causes the subject to judge that p, inquiring no further into the matter. A weak FOR (which might be better called a Feeling Of Doubt) typically causes the subject to withhold judgment, sometimes prompting further inquiry. The differing strengths of the relevant FORs explains why we often unreflectively judge things to be as they seem, but sometimes do not. (Beliefs about one's competence and the circumstances, and other feelings, can also play a part.) Subjects typically have no introspective access to why certain contents Feel Right to particular degrees. In fact, the strength of the attached FOR is determined by the character of the processing that yields the content of the seeming.

Koriat (Reference Koriat, Zelazo, Moscovitch and Thompson2007) presents this picture for memory, and surveys the empirical work motivating it. Thompson (Reference Thompson, Evans and Frankish2009) argues that the same framework should be applied to reasoning. She introduces the terminology of ‘FORs’, whereas Koriat talks of subjective feelings of confidence. Thompson et al. (Reference Thompson, Prowse Turner and Pennycook2011, Reference Thompson, Prowse Turner, Pennycook, Ball, Brack, Ophir and Ackerman2013a, b) argue directly that we must posit FORs in the case of reasoning to make sense of certain experimental data. In particular, FORs must be distinguished from global feelings of fluency, to which they are assimilated in the literature surveyed by Alter and Oppenheimer (Reference Alter and Oppenheimer2009).Footnote ¹⁸ Thompson's experiments concern syllogistic and mathematical reasoning, not inductive reasoning. But it seems generally plausible to understand seemings as representations with FORs attached. Evans and Stanovich make FORs central to their general model of judgment and decision-making (Reference Evans and Stanovich2013a: 223, 236; Reference Evans and Stanovich2013b: 265, 267). Joelle Proust (Reference Proust2013) seems to have a similar picture in mind. In recent work, Koriat goes further, arguing that a common kind of mechanism determines the FORs in a variety of judgments and decisions (Koriat Reference Koriat2011, Reference Koriat2012, Reference Koriat2013; Koriat and Adiv Reference Koriat and Adiv2011). So because the general account of seemings and self-confidence is plausible, it is plausible that inductive reasoning results in a representation of the conclusion, with an attached FOR.Footnote ¹⁹

(I've proposed that seemings are representations with FORs attached. This counts as an ‘experience view’ of seemings according to the recent philosophical literature, surveyed by Tucker (Reference Tucker and Tucker2013b: §1) and Moretti (Reference Moretti2015: §2). That is, my proposal holds that seemings have representational content, the distinctive phenomenology of Feelings of Rightness, and that they aren't simply beliefs or inclinations to believe. This last point is assumed by the next part of my treatment of inductive skepticism. §5 argues that one typically judges that E→H without it seeming to one that E→H. So its seeming to one that P is not the same thing as being inclined to judge that P.)

5. TWO-ALTERNATIVE FORCED CHOICES

I propose that one judges that E→H as part of a Two-Alternative Forced Choice (TAFC). TAFCs are a well-studied kind of decision-task. Choosing between two possible free gifts is an example of a ‘value-based’ Two-Alternative Forced Choice. The choice is ‘forced’ because one conceives of the decision-task in a way that rules out rejecting both gifts. The two options are ‘alternatives’ because one takes them to be mutually exclusive. Psychologists also classify certain belief-forming tasks as Two-Alternative Forced Choices. For example, Koriat (Reference Koriat2012: 87) investigates how confident people are in their answers to general knowledge TAFCs like: “What actress played Dorothy in the original version of the movie The Wizard of Oz? [a] Judy Garland, [b] Greta Garbo.” Bogacz et al. (Reference Bogacz, Brown, Moehlis, Holmes and Cohen2006) review and compare models of the mechanism by which people perform perceptual TAFCs, such as whether the tendency of the dots on a screen is to move to the right or to the left.

These psychologists think that TAFCs form a unified psychological kind. They think similar mechanisms produce one's answer, and one's level of confidence in it, in perceptual TAFCs, general knowledge tasks, and value-based choices. Bogacz et al. (Reference Bogacz, Usher, Zhang and McClelland2007: §5) extend a model of perceptual choice to value-based choice. They assert that perceptual and value-based choices “involve a common selection mechanism” (Reference Bogacz, Usher, Zhang and McClelland2007: 1664), though that kind of mechanism is implemented in different regions of the brain in the two cases (Reference Bogacz, Usher, Zhang and McClelland2007: 1669). Koriat gives a unified treatment of degrees of confidence in perceptually based answers (Reference Koriat2011), answers to TAFC general knowledge questions (Reference Koriat2012), answers to moral questions (Koriat and Aviv Reference Koriat and Adiv2011), and in matters of personal preference (Koriat Reference Koriat2013). Koriat (Reference Koriat2011) rebuts arguments that different mechanisms are employed in perceptual and general knowledge TAFCs.

Plausibly, some TAFCs have as outputs two mental states. Value-based decision-making is a matter of choosing between options, and at least some of the time, one picks one option and rejects the other in one go. Suppose one has difficulty picking between two job offers (an example junior philosophers may find fanciful). Eventually one comes to prefer the first job to the second. It would be strange to think the preference can only directly cause one to intend to accept the first job, which then causes one to intend to reject the second. Rather, the output of the decision-task can be both the intention to accept the first job and the intention to reject the second. The two intentions are outputted in one go.Footnote ²⁰

I suggest that when one is tempted to reason from E to H, wondering whether E→H presents one with a Two-Alternative Forced Choice. The alternatives are: inferring that H, versus refusing to judge that E→H. One takes the two alternatives to be mutually exclusive, and rightly so. One thereby recognizes that it would be irrational to reason from E to H, but yet refuse to judge that E→H. The choice is forced, because one takes the two alternatives to be exhaustive. That is: it wouldn't make sense to refuse to reason from E to H, and yet judge that E→H. Let's call this TAFC “Hume's Choice”.

Usually, formulating such a TAFC does not undermine appeal of the inference from E to H. We stick with the inference, and as that requires, we judge that E→H. For example, I might draw the relevant inductive inference and also judge that if it has snowed in NYC every December in the last 100 years, then it will snow in NYC next December.Footnote ²¹

Let me suggest a mechanism by which people resolve Hume's Choice anti-skeptically. The only thing that affects the decision is the strong FOR attached to the representation of H, the conclusion. That FOR tilts the scales decisively towards inferring that H, and away from not judging that E→H. The output of the decision task is both the picking of the former option and the rejection of the latter. That is, the output is both a judgment that H and a judgment that E→H. Crucially for what follows, no FOR is generated that attaches to the judgment that E→H. The FOR attaching to the judgment that H does all the work of resolving the decision task. Call this psychological procedure: judging that E→H as an accompaniment to inferring that H.Footnote ²²

6. THE EPISTEMOLOGICAL CLAIMS

I want to make two epistemic claims about judging that E→H as an accompaniment to inferring that H: it can be rational to do so, and one can thereby come to know that E→H. Suppose that the inductive argument from E to H is a good one. (The doctor is on standby for anyone who doubts there are good inductive arguments.) That is, suppose that conditions are such that if S does not consider whether E→H, then it is rational for S to reason from E to H. Then in virtue of the same factors, it is also rational for S to judge that E→H as an accompaniment to inferring that H. If, on the other hand, one reasons irrationally from E to H, then one judges that E→H irrationally. This account does not say what makes it rational to reason from E to H. Instead, it says that whatever makes the inference rational also makes it rational to judge that E→H in the designated way.

Suppose that conditions are such that if S does not consider whether E→H, then S can come to know that H by inferring it from E. Then S can come to know that E→H by judging it as an accompaniment to inferring that H. Call this knowledge by accompaniment that E→H.Footnote ²³

Judging that E→H as an accompaniment to inferring that H is not a case of reasoning by conditional proof. In a conditional proof, one reasons from E to H while leaving it open at that stage of inquiry whether E→H (one settles that E→H at the following stage). When one judges that E→H as an accompaniment to judging that H, one does not reason from E to H while leaving it open whether E→H. So the current proposal does not deny statement (2) of the skeptical argument, which prohibits a conditional proof. The proposal rejects premise (3) instead, describing some other way of rationally judging that E→H. It also rejects (1), as I will now explain.

Statement (1) says that an inductive inference from E to H presupposes that E→H. The spirit of my proposal is that the inductive inference does not pre-suppose that E→H, but rather co-supposes it. In other words: (1) claims that one must settle that E→H epistemically prior to reasoning from E to H. The present proposal says that it is rationally permissible to judge that E→H as an accompaniment to inferring that H. Plausibly, doing so counts as: reasoning from E to H and settling that E→H at the same point epistemically speaking. So on this view, one need not settle that E→H epistemically prior to reasoning from E to H; (1) is false.

In my view, notions like epistemic priority are ways of talking about a distinctive kind of epistemic rationality constraint on one's thinking (Jackson Reference JacksonForthcoming: §1). For example, it is rationally forbidden to: reason from E to H while suspending judgment on whether E→H. Performing a conditional proof that E→H violates this prohibition. It is not forbidden to: infer that H while ignoring the question of whether E→H. The important thing is that it is rationally permissible to judge that E→H as an accompaniment to inferring that H. We can say that doing so counts as ‘inferring that H and settling that E→H at the same point epistemically speaking’.

It is not a strange or isolated claim that one can, indeed must, settle that E→H at the same point epistemically speaking as one reasons from E to H. It is independently plausible that one must settle that P and settle that one knows that P at the same point epistemically speaking. It seems impermissible to settle one matter epistemically prior to settling the other. One cannot reason, “P, but I wonder whether I know it. Well, I believe that P, and justifiedly so, and surely I am not in a weird Gettier case. So I know that P.” Nor can one reason, “I know that P, but I wonder whether P. Well, knowledge is factive. So P.”Footnote ²⁴

I've suggested that one must settle that E→H and infer H from E at the same point epistemically speaking. With this view articulated, I feel no residual intuition that (1) is true. (1) initially seems right because we see that it is impermissible to settle that E→H epistemically posterior to reasoning from E to H (say by conditional proof); we fail to see that there is a way to settle the two matters at the same point epistemically speaking; and so we erroneously conclude one must settle that E→H epistemically prior to drawing the inductive inference.

(It is permissible to infer that H under the scope of a mere supposition that E, and judge that E→H as an accompaniment to drawing that inductive inference. One thereby settles that E→H at the same point epistemically speaking as one inductively infers that H from the supposition that E. Suppose that one then learns that E, and infers that H by modus ponens (not inductively). One thereby settled that E→H epistemically prior to settling that H (by MP), and permissibly so. This casts no doubt on the claim that E→H must be settled at the same point epistemically speaking as one draws the inductive inference, be it from a belief or a supposition that E.)Footnote ²⁵

On my proposal, it is rational to judge that E→H as an accompaniment to inductively inferring that H. The proposal tells us where to object to the skeptical argument: we should reject premises (1) and (3). I think the proposal also fulfils the final requirement on a satisfying solution to the skeptical puzzle: it explains why people typically overlook the proposed solution. In my view, people regularly judge that E→H as an accompaniment to inferring that H. However, they overlook that they thereby judged that E→H in a rational way. Why do people overlook that they judged E→H in exactly the right way?—because no FOR attaches to the judgment that E→H. That judgment is the result of the relevant TAFC being resolved by the strong FOR attaching to the judgment that H. Most judgments come with FORs attached; but judging by accompaniment is an exception. When a judgment that P Feels Right, the FOR will also cause one to judge that one knows that P,Footnote ²⁶ and thus that whatever one did was sufficient to know it. For example, a judgment that nothing could be red all over and blue all over Feels Right, and so one will be satisfied that one knows, even if one can't tell much of a story about how one knows. But when one judges that E→H, the normal cause of a judgment that one has done enough to know is missing. In the absence of a FOR, one falls back on one's beliefs about one's knowledge-forming capacities to say whether one knows that E→H. But one doesn't already believe that there is knowledge by accompaniment. Knowledge by accompaniment never got added to the list of ways one believes one can come to know things, for the same reason one doesn't add it now: there were no FORs attached that would cause one to judge that one is forming knowledge. The ways of coming to know things that are on a typical person's list fail to explain how one could know that E→H. So it seems that there is no way for one to know that E→H, and for similar reasons, no way to rationally judge that E→H. It is irrational to combine judging that one can't know that E→H with judging that E→H. One falls into skeptical puzzlement, as one sees that it is irrational to reason inductively while suspending judgment on the relevant conditionals. Adding knowledge by accompaniment to one's list of ways one takes oneself to know things removes the source of skeptical puzzlement.

How does my treatment of the skeptical problem differ from one grounded in Phenomenal Conservatism? Phenomenal conservatism says that its seeming to one that P makes one justified in believing that P, given that one has no defeating beliefs.Footnote ²⁷ On the view we'll compare to mine, it seems to you that E→H, and so you form a justified belief that E→H. Thus the skeptical problem is easily dealt with. I think my proposal is superior for two reasons. Firstly, the phenomenal conservative story makes it mystifying how the skeptical problem gets any traction in the first place. If it just seems true that E→H, why do we get worried that there's no way for us to know it? By contrast, my view is that it does not seem true that E→H. No FOR attaches to the representation that E→H. That's why people don't judge that they simply know that E→H, but instead wonder how they could know such a thing.Footnote ²⁸ Secondly, phenomenal conservatism makes it too easy to get justified beliefs. If President Trump's past behavior seems to you to establish that the America is about to be Made Great Again, then you are justified in believing it, according to phenomenal conservatism. By contrast, I did not specify a view about when an inductive inference is rational. I just said: if the inductive inference is rational then it is rational to judge that E→H as an accompaniment (and only then). My proposal lets you say whatever you like about which inductive inferences are rational.Footnote ²⁹

7. MORAL UPLIFT

You might be underwhelmed by my resolution of the skeptical puzzle. Other putative resolutions say exciting, deep things about the human condition. (Problems aren't deep per se, solutions are.) For example, one might reject the inference from (1) and (4) to (5), and assert the exciting moral that scientific knowledge is based on blind faith in the relevant conditionals. This would cast religious faith in a different light – heady stuff. According to the solution I've proposed, the skeptical puzzle gets its bite from a blind spot in our psychology. We overlook the possibility of knowledge by accompaniment because the relevant judgments do not have a FOR attached. But a judgment that E→H is neither a punt in the dark, nor something that you can give an argument for. You just need to stick with your inclination to reason from E to H, and in the appropriately related way, judge that E→H. Maybe the moral is that sometimes, you just need to stick to your guns. Unfortunately, people who stick to their guns are often being stupid. Sometimes doing your best is enough, sometimes it isn't. Hardly a conclusion that elevates the soul.

Let me suggest some reasons to value an unflashy solution to the skeptical problem. Firstly, philosophy can stand for reasoned inquiry, full-throated and unembarrassed. Surveying 250 years' worth of implausible responses to the skeptical argument, naïve thinkers might be tempted to conclude that there really is something fishy about inductive inference. Even if they don't fall into that trap, they might be tempted to draw another pernicious moral: thinking about anything too much leads to absurdity and quagmire. We wouldn't want those to be the take-home morals of Philosophy 101. Resolving the skeptical puzzle removes the support for such intellectual pessimism. Philosophy is thus better-placed to help spread respect for accumulating relevant evidence and drawing proper conclusions. Whether or not abstruse epistemology can better society, there is value in standing for what is right and against quackery in health-care, cynical denial of climate change, and bone-headed economic and social policies. A resolution to the skeptical puzzle also has intrinsic aesthetic-cum-intellectual value. The skeptical puzzle confused us. Confusion is ugly. A satisfying resolution replaces intellectual ugliness with serene clarity. That is our aim. One may fall short and still say something stimulating and plausible. Such an essay, I hope, would not be entirely contemptible.Footnote ³⁰