1. INFINITISM

According to the familiar “regress of reasons argument” for foundationalism, a subject, S, can be justified in a proposition, p, by having a good reason – say, proposition q – for it. S had better be justified in q, if q is to serve to justify p. So S might need to have a reason, r, for q. And another reason again for r, and so on. The infinitist rejects the foundationalists’ claim that this chain of reasons comes to an end with foundational propositions. And justification cannot be circular, so the chain of reasons cannot loop back on itself. Instead, the infinitist says, the chain can, and does, go on indefinitely. So, for the infinitist, justification of a proposition for any person requires that the person have, or have available to them, an endless, non-repeating chain of reasons. (Reasons here are understood as being propositions. In this context, a sensory experience, for example, is not a reason.)

Two points require expansion. One is the distinction between propositional and doxastic justification, and the second is the idea of evidence being available to a subject.

Propositional and doxastic justification. I will follow Klein in treating infinitism as being a theory essentially about propositional justification.Footnote ³ As Klein puts it,

The usual way of drawing the distinction between propositional and doxastic (belief) justification is illustrated nicely by the following case (due to Turri Reference Turri2010).Footnote ⁴ Two jurors in the same trial hear the same evidence, which is such as to justify a guilty verdict. Juror A concludes from the evidence that the defendant is guilty. Juror B also says that the defendant is guilty, but reaches this belief not from a consideration of the evidence presented, but because, as he says, the defendant “looks suspicious”. The proposition that the defendant is guilty is justified for both jurors, but Juror A's belief that p is justified, while Juror B's belief is not. Or: the claim that the defendant is guilty is propositionally justified for both of them, but only Juror A is doxastically justified.

Klein's generic account of doxastic justification suggests that it is close to the common-sense notion of a reasonable or sensible belief. He writes: “A belief that h is doxastically justified for S when and only when S is acting in an epistemically responsible manner in believing that h” (Klein Reference Klein2007a: 6). In a later discussion “epistemically responsible” is replaced by the notion of being “entitled” to hold a belief (Klein Reference Klein and Neta2014a: 96).

Klein's understanding of propositional justification is in line with the common (though not universal) conception, according to which being propositionally justified is a matter of having, or having available to one, good evidence for the truth of the proposition. Klein also shares the generally accepted view that one can be propositionally justified in proposition p without actually believing that p. We can have reasons available to us without believing them, and indeed without even being aware that they exist (see Klein Reference Klein2007a: 6). Thus, it is possible for someone to be propositionally justified in a chain of reasons, each supporting the next, without actually believing the propositions in the chain. Infinitism, though committed to there being infinite chains of propositions, is not committed to the implausible claim that we hold infinite sets of beliefs arranged in such chains.

The corresponding common understanding of what is required for doxastic justification is that one is doxastically justified in a belief if one has propositional justification for the propositional content of one's belief state, and one's belief is based on the evidence providing the propositional justification. So, one may be propositionally justified in p while not being doxastically justified, but being doxastically justified requires that one be propositionally justified. In a crude but self-explanatory symbolism, we may represent this as follows: DJp → PJp, but ~(PJp → DJp). Klein at one point endorses this view (Klein Reference Klein2005a: 156–7).Footnote ⁵

The availability of evidence. S being propositionally justified in p requires adequate evidence, and, for an infinitist, adequate evidence is a matter of an infinite chain of propositions, each providing a reason for its successor. But, as noted, it does not require that S believe all these propositions. S may believe a finite number of the propositions in a chain, but it is sufficient if all the rest (of which there are an infinite number) are available to him. So an account of availability is clearly vital for the infinitist. However, according to Klein in his recent writings, infinitists may differ among themselves on this matter, and may pick and choose among stringent or relaxed requirements for what is to be counted as available to S. An example of a stringent reading of availability could be that proposition q would be available to S as a reason for p if, after thinking for a short time about how p might be supported, S would come to believe q, recognising it as a reason for p. (One imagines someone thinking: “I think it's obviously the case that such and such, but hold on, what reasons are there for that? Ah, yes of course, there's so and so …”.) On a much more relaxed account, q will be available to S if S would (or, perhaps, could) come to believe that q “after considerable effort, for example locating, gathering and examining new evidence”.Footnote ⁶

The lack of specificity about availability is unsatisfactory, since any assessment of infinitism requires that we know what sort of availability there is supposed to be. Clearly enough, on some moderately stringent accounts of availability, it would follow quickly that infinitism was simply false. Take any proposition in which you believe yourself to be justified. Formulate your (non-repeating) chain of reasons that provide your evidence for it, giving yourself five minutes, (say), for the formulation of each reason. Sooner or later, and probably sooner, you will fail. You will have run out of available reasons, and you will have to conclude that your chain of reasons is finite. You will then need to conclude that either (a) you were not after all justified in the proposition concerned, or (b) infinitism is wrong, or (c) that account of available evidence is wrong. For the purposes of the discussion to follow I propose to pick (c), and simply assume that there is some more relaxed account of available evidence that we can accept.

However, as is evident from the passage quoted from Klein in the introductory paragraphs above, Klein at one point gave serious consideration to option (a). Another infinitist, Scott Aikin, also expresses this sanguine attitude to possible sceptical consequences. While not committing himself to the view that infinitism actually does have sceptical consequences, Aikin nonetheless takes this possibility seriously.

As I will argue in the next section, it is a mistake to say that this may be the case. It clearly is the case.

2. NO JUSTIFIED BELIEFS FOR THE INFINITIST

On a very stringent account of availability, then, a subject S may prove not to be justified in any proposition. On the other hand, given a very relaxed account of availability, where there is a limit neither on the time for finding a reason, nor on the amount of help S may have in finding reasons from other sources, it may never be possible to conclude that any proposition is not justified for S. Given an account of availability of some intermediate degree of stringency, it will doubtless turn out that we can establish that some propositions are not justified for S but there will be other propositions for which this cannot be established.

The different accounts of availability differ in their consequences for our ability to establish that any particular proposition is not justified for S. However, none of them give us any help in establishing that a given proposition is justified for S. In the cases where it is not established that the proposition is not justified for S, all that can be said is that the chain of available reasons may go on indefinitely from whatever point we have taken it to, or it may not. We can never conclude that S does have available to her an infinite chain of reasons. No matter how satisfactory our production of reasons has been up to a certain point, there is always the possibility that after that point the reasons are going to run out, no more being available. The chain of available reasons might be infinite, but it might be finite. (Presumably there are lots of propositions that are not justified for a given subject, so there will be lots of finite chains.) And we cannot tell which is the case.

This matters because not knowing that one is propositionally justified in p amounts to not knowing whether one has (or has available) good evidence for the truth of p. If, as I have argued, infinitism forces us to the conclusion that we have no idea of whether we have good evidence for any of the propositions that we believe true, then that in itself could well be regarded as a serious reductio of the theory. Doubtless people believe that they have good evidence, but if infinitism is right, they cannot be (propositionally, and consequently, doxastically) justified in this. No one ever has propositional justification that they have propositional justification for any belief. For any subject and any proposition p, the infinitist is committed to ~(PJ(PJp)). It is worth noting that the failure to be propositionally justified in PJp is not a matter of not having enough evidence to be justified. It is a matter of not having any evidence at all.

There has been some sort of acknowledgement of this problem for long time, not only in the writings of Klein and Aikin already cited, but also in the work of various critics of infinitism. For example, Jay Harker writes: “… a theory of epistemic justification that countenances the existence of infinite justificatory chains is a theory according to which there may be justified beliefs such that we could never show or even know that they are justified. And while such a predicament is not logically impossible, it is certainly less than ideal” (Harker Reference Harker1984: 264). But “less than ideal” seems something of an understatement. The situation is much worse, because recognition that one has no evidence as to whether or not there is any evidence for a proposition leaves one in the following position: one is not justified in believing that proposition.

And this is the situation faced by an infinitist, for any proposition.

Forgetting infinitism for the moment, consider Simon, who makes the claim that proposition p is true. Asked for his evidence, he provides reasons, including the proposition q. Pressed further, Simon cites r as a reason for q. Asked for evidence for r, it turns out that he cannot provide it, despite having made sustained efforts to find such evidence. We (and he) might well hope that there are such further reasons that he will, at some future point, be able to uncover, but it may be the case that we, and he, have to recognise that we lack any reason to think either that he will or that he will not. Would we then consider Simon's belief that p to be justified? I suggest not. He may or may not have propositional justification – we don't know one way or the other – but Simon surely does not have doxastic justification.

For another illustration, consider this variant of the jury case. Juror D hears all the evidence, and soundly infers from it the proposition p – that the defendant is guilty. So Juror D is propositionally justified in p. However, the inference from the evidence to p is complex and involves a series of steps, and Juror D recognises that he has evidence that his reasoning capacity in such complex matters is not completely reliable, as he has caught himself making errors on some occasions in the past. This further evidence is not evidence against p, but is evidence against the proposition that he has propositional justification for p. Juror D is not justified in the proposition that he is propositionally justified in p. In such a case I submit that Juror D is obviously not doxastically justified in believing that p. He might become justified in believing that p, but only after, for instance, he makes a careful check over his complex inference, or he has other people check and confirm it, so that he became propositionally justified in his own propositional justification for p.

What is the principle operating here? It looks as though Juror D is not justified in believing the defendant guilty because he is not justified in believing that he has propositional justification for p. So the immediate temptation is to say that the principle is this: that a necessary condition for being doxastically justified in p is that the subject be doxastically justified in the metabelief that she has propositional justification for p; in our symbolism, DJp → DJ(PJp). The temptation is to be resisted. This principle clearly generates an unacceptable regress of meta-beliefs, and in addition implausibly precludes children and others who hold no meta-beliefs of this sort from ever holding justified beliefs. It must be rejected.

I suggest instead that what lies behind the Juror D case is not that Juror D lacks doxastic justification in a meta-belief (or even that he lacks propositional justification in a meta-proposition). The problem with Juror D is a belief that he has, and not a belief that he lacks. We might say, as a first approximation, that the belief that he has that prevents him from being justified in believing p (the guilty verdict) is the belief that he may not have propositional justification for p. However, describing the situation in this way suggests the possibility that he could believe that he probably has such propositional justification, but he is not sure. This may be appropriate enough in the Juror D case, but the infinitist's position is different. An infinitist convinced by my argument will justifiedly believe himself to have no good evidence at all that he has (or does not have) propositional justification for p. A preferable, and more precise, formulation is that he is justified in believing that he has no evidence for the proposition that p is propositionally justified. Such a belief is a defeater for doxastic justification.

The principle I propose, then, is:

Call this “Principle A”.

In the Juror D case, there is some indeterminacy, I expect, about what degree of doubt there must be about one's propositional justification before doxastic justification is lost. We will probably not say that the belief: “There is a ten per cent chance that I do not have propositional justification for p” defeats doxastic justification for the belief that p. We doubtless will say that we have a defeater when the chance is ninety per cent. And if it is fifty per cent, I submit that we have a defeater as well. If S believes that there is an even chance that he lacks propositional evidence for p, then he is not justified in believing p. If the best he can say is something like “I may or may not have adequate evidence for p”, we simply do not think him justified if he continues to hold that p. We do not think him epistemically responsible, or epistemically entitled to the belief.

The infinitist cannot even say that there is a fifty per cent chance that he has propositional justification. He has to admit he has no idea whether or not he has propositional justification for p, because he can have no idea whether any chain of available reasons supporting p is infinite or not. And it is not just that he is not fully justified or justified to the degree that would be required for knowledge (whatever these may amount to). He is not justified at all in believing p. He is not even a little bit epistemically responsible if he believes p. He is in this position with all of his beliefs, and so an alert infinitist cannot be justified in any of his beliefs.

We do not have here an argument to the effect that a consequence of infinitism is general scepticism. Someone who is not an infinitist will of course not hold the belief that is a defeater. His beliefs may or may not be justified, but those that are not will be unjustified for more mundane reasons – lack of evidence, bad reasoning and so forth. Some infinitists will not hold the defeating belief either, simply because they have failed to see that it follows directly from their theory. The reductio argument against infinitism that I have put forward is then a limited one: infinitists, once they fully appreciate the implications of their theory, are precluded from any doxastic justification whatever. We turn in Section 4 to the question of whether this limited sceptical outcome is a sufficient reductio of their theory. But first, there is an objection that must be considered.

3. AN OBJECTION BASED ON AN ALTERNATIVE ACCOUNT OF DOXASTIC JUSTIFICATION

It was noted in footnote 5 that, while Klein in 2005 accepted the conventional view that doxastic justification required propositional justification, in 2007 he gave an account of doxastic justification such that propositional justification was not required. Call this account K.

This account of doxastic justification could be elaborated in various ways and would require a more detailed appraisal than there is space for here. I will restrict my discussion to what I take to be Klein's understanding of satisfying “contextually determined requirements”. This is that the requirements are satisfied when reasons for p have been traced as far as a set of reasons, q1 … qn, that are such that no one in that context feels a need to provide further reasons for q1 … qn. That is, p has been shown to be supported by propositions that are not, in that context, in question. In fact, what is or is not in question largely defines the context. If someone decides to question either the truth or justifiedness of one of q1 … qn, then the context has changed, and support for the questioned proposition is needed. It in turn is taken to be doxastically justified for the person who believes it if reasons for it can be traced back to further propositions that in this new context are not in question.

An example illustrates what is intended by this account, and also shows how temptingly it seems to fit with our ordinary ascriptions of doxastic justification. We take someone to be justified in believing that a traffic accident took place at a certain intersection a day ago if they give as reasons for their belief the claims that they were told this by a friend, who was present at the time and witnessed the accident. In normal circumstances the context will usually be such that these latter claims are not felt to require further backing. No further reasons need to be given in support of the friend's truthfulness or competence. If for some reason a question is raised about the friend's truthfulness or competence, this counts as changing the context, and reasons are then sought to back up propositions about truthfulness and competence. But until such questions are raised, we count the original belief as justified.

Now, at first sight K appears incompatible with Principle A. K proposes a sufficient condition for doxastic justification, but A is an additional necessary condition. If the condition stated in A needs to be met, then meeting the condition in K is not sufficient. This assumes, of course, that A and K are independent. The incompatibility depends on it not being the case that the non-fulfilment of A entails the non-fulfilment of K. Let us consider this point.

Suppose that we have a situation where reasons for p have been traced to propositions q1 … qn, and those in the context – including S, of course – believe it unnecessary to seek or provide further reasons in support of q1 … qn. (Using the traffic accident example, p might be the belief about the traffic accident, and q1 … qn would be beliefs to the effect that one had been told this by one's friend, and that the friend was present at the time.) Presumably, this would be because they take q1 … qn to be true. Presumably, also, they assume that q1 … qn are all propositionally justified for them. Perhaps the issue of whether they have evidence for q1 … qn has never entered their minds, but were the question put to them, they would answer yes. In the dispositional sense of “believe”, they believe that q1 … qn are justified.

Now suppose that one person in the context – let it be S himself – comes to believe that for all he knows, he has no evidence for q1 … qn. Or, more precisely, he is justified in believing that he has no justification for the proposition that he has any propositional justification for q1 … qn. Call that belief B. If one is an epistemically responsible agent, it seems reasonable to suppose that one's coming to justifiedly hold B would raise a question about those beliefs previously simply assumed. One would no longer be able to simply assume that q1 … qn are propositionally justified. Indeed, it seems one should no longer simply assume their truth. If it is pointed out to you that there is some doubt about whether you have any reason or evidence for something you have been assuming true, is not the natural reaction of a reasonable person going to be to try to find or assemble some evidence?

If this way of thinking about the matter is correct, then in the case where S believes justifiedly that he has no reason to think that he has any evidence for q1 … qn, he is in the position of not having traced back the reasons of p to propositions for which, in the context, he feels no need to provide further reasons. If Principle A is not fulfilled in the situation, then he ought, as an epistemically responsible agent, to recognise the need for further reasons. In other words, Principles A and K are not, as they seemed prima facie, incompatible. Non-fulfilment of A involves non-fulfilment of K.

Someone who disagrees with this conclusion is taking a different view to that proposed above of what it is to change a context. They are taking the view that, where reasons for p have been traced to q1 … qn, and in the context q1 … qn are assumed true and justified by the relevant participants, adding that one such participant, S, comes justifiedly to believe that he lacks justification for the proposition that he has evidence for p does not change the context. And because the context has not changed, it remains that, by K, S remains justified in p.

The most reasonable response to such a reading of K is simply: so much the worse for K. Suppose S says to himself: “I might have further evidence for q1 … qn, but I might not. And I have no idea at all whether or not I do. And I certainly have no evidence for the proposition that I do have evidence for p.” In other words, A is not fulfilled. In any such case, I submit that it is appropriate to say that S is not justified in believing p, where we think of doxastic justification in terms of what it is epistemically responsible to believe, or what one is epistemically entitled to believe. Where there is a challenge to our default presumption that a belief we have accepted is well-evidenced, the epistemically responsible thing to do is to pursue the matter until one is reassured that the evidence for it is in fact there. To neglect to do so is epistemically irresponsible.

As a result, we can say that Principle A stands. One may adopt K, Klein's (Reference Klein2007a) account of doxastic justification on the interpretation which makes it compatible with A, but if it interpreted as incompatible with A, then K is to be rejected.Footnote ⁸

4. IS A SCEPTICAL RESULT A REDUCTIO?

It has been noted that both Klein and Aikin allow that infinitism is a theory that may lead to the sceptical conclusions. But their view seemed to be merely that infinitism involved the possibility of scepticism. The argument here has been that it involves the actuality of scepticism, at least for an infinitist who recognises the implications of his theory. It remains unclear to me whether these proponents of infinitism consider that a sceptical consequence, if realised, would be a knockdown argument against infinitism. “That infinitism makes skepticism more likely can be a reason against it, but again, it's no reductio” (Aikin Reference Aikin2011: 49). But what if the situation is that infinitism makes a sceptical consequence certain? Can Aikin “live with that”?

I suggest that whether a sceptical consequence is a reductio of infinitism depends on just how one construes infinitism. There is a little-noticed difference between two conceptions of the infinitist enterprise. Indeed this difference applies equally to the theories of foundationalism and coherentism. For present purposes, let us call foundationalism, coherentism and infinitism “structure theories”, understanding that this is merely a useful name, and is not intended to reveal anything about the nature of the theories.

A first way to understand structure theories is to see them as accounts of the propositional justifications that we take ourselves to have, and explanations of how we come to have them. Such theories assume that there indeed are some propositions that are justified for us, and offer views about how they depend on each other, how the system of justified propositions is structured, and so forth. I dub these “explanatory structure theories”.

An alternative view of structure theories is that they are setting up criteria for what is to be counted as propositionally justified and what is not. They are giving us formulae like “Proposition p is justified for subject S iff …” where what follows may make reference to foundational propositions, or to infinite chains of propositions, or to something else again. I dub these “criterial structure theories”.

Explanatory structure theories are incompatible with scepticism. Scepticism renders them empty, since there are no justified propositions to explain, or to fit into any sort of structure. Criterial structure theories on the other hand purport to tell us only what is to be counted as a justified proposition, and are silent on whether anything actually meets the criterion and is to be so counted. They are sometimes referred to as meta-epistemological theories, to distinguish them from applied, or normative theories that are about what propositions are or are not actually justified (e.g., Fumerton Reference Fumerton2006: 5–6).

Which sort of infinitism – explanatory or criterial – has Klein been putting before us? There are times when his infinitism has looked like an explanatory theory. He at some points presents scepticism as another possible theory, a rival alongside foundationalism, infinitism and coherentism, suggesting that he saw scepticism as incompatible with infinitism (Klein Reference Klein and Neta2014a: 113; Reference Klein, Turri and Klein2014b: 107). Similarly, in setting up the issues for a presentation of his infinitism, he often makes reference to the ancient sceptics, who were clearly putting forward explanatory structure theories, and who equally clearly thought scepticism incompatible with the three structure theories (see Klein Reference Klein1999, Reference Klein2005a, Reference Klein2007a, Reference Klein and Greco2008, Reference Klein, Bernecker and Pritchard2011). However, there are also indications that he is thinking of the structure theories as criterial, as when he sets out three alternative “concepts of propositional justification” (Klein Reference Klein2007a: 6–8). In any case, it seems reasonable in the circumstances, and given Klein's own apparent tolerance of the possibility of sceptical consequences flowing from infinitism, to treat his infinitism as criterial.

The same is true, but more clearly so, in the case of Aikin, who explicitly refers to his theory as meta-epistemological infinitism, and writes: “The correctness of a meta-epistemology and its skeptical consequences are separate questions” (Aikin Reference Aikin2011: 48).

If the argument of Section 2 is sound, then, infinitism conceived as an explanatory structural theory can be dismissed. That the sceptical result concerns beliefs and not propositions does not affect this result. Neither is it affected by the fact that we do not have a wholesale scepticism claiming that no belief is justified, but a more limited scepticism, leaving the infinitist herself with no justified beliefs.

What of the infinitist who is a criterial theorist? If, as such an infinitist will argue, it is reasonable to adopt the infinitist concept of propositional justification, then it is reasonable to adopt whatever consequences follow, so it is reasonable to come to a sceptical assessment of one's own beliefs. The criterial infinitist is going to have to decide whether to accept that conclusion, or revise her infinitist criterion for propositional justification. The first course will gain her the fellowship of other sceptics, who have arrived at their position by other routes, but will involve facing up to, and dealing somehow with, the difficult consequences of adopting scepticism.Footnote ⁹ The second, alternative, course will amount to admission that the sceptical conclusion has constituted a fatal objection to infinitism, even when it is considered as a criterial structural theory. While the first course permits continued commitment to infinitism, the sceptical consequence will seem to most theorists a sufficient reason for abandonment of the view.Footnote ¹⁰