Epistemological infinitism is an unorthodox view which is lately generating a lot of interest. Whereas foundationalism and coherentism have long ruled the roost when it comes to theories of justification, infinitism presents a long-neglected and often disparaged alternative. Ad Infinitum collects 14 essays on the topic by leading figures in contemporary epistemology, exploring arguments for and against the view and contrasting it with its rivals. Despite sometimes succumbing to the worst tendencies of contemporary analytic epistemology—the kind that invite criticisms of tediousness and scholasticism—the volume is a mostly engaging group of essays with several standouts. In what follows, I will briefly explain infinitism and then highlight what I take to be the high points of the collection.

Driving our theoretical options when it comes to theories of justification is the ancient Regress Argument—what Michael Williams (in this volume and elsewhere) calls “Agrippa’s Trilemma” (227). This is a sceptical argument which suggests that, in a dialectical or dialogical context, when you make an assertion or claim to knowledge, it is open to your interlocutor to ask how you know what you said is true. You can give reasons, but ultimately, the argument goes, one of three scenarios will occur:

1. i) You will cease giving reasons and rest dogmatically on an assumption.

2. ii) You will end up relying on a previous reason to justify a reason further down the chain, thus reasoning in a circle.

3. iii) The chain of reasons will go on ad infinitum.

In all of these cases, says the Agrippan sceptic, the claimant’s original assertion is not justified, because justification cannot come via brute assumption, circular reasoning, or infinite regress of reasons. Thus, our theoretical options take the form of trying to say that one of these outcomes is in fact not bad, but does confer proper justification after all. Option i) is foundationalism, option ii) is coherentism, and option iii) is infinitism.

Though discussion of infinitism has a long (and mostly negative) history, its best-known contemporary proponent is Peter Klein, one of the volume’s co-editors. Klein’s view rests on a crucial distinction: between propositional justification and doxastic justification (111). Simply put, propositional justification refers to a propositional content’s being in fact justified, whereas doxastic justification refers to an agent’s actual belief being justified (by, for example, being based on, or caused in the right way by, whatever it is that actually justifies the propositional content of the belief). In this way, one can see how a proposition could be justified by an infinite series of reasons, even if an agent’s particular belief is not justified by an infinite series of other beliefs, which seems absurd. Indeed, the infinitist holds that, in any given dialectical context, an agent’s reasons will come to an end at some contextually-appropriate stopping point. But that exhausts the agent’s doxastic justification; the proposition’s justification is still based on an infinite series.

Infinitists, then, can reject foundationalism and coherentism as solutions to the Regress Argument, but do not fall into scepticism because they can defend the infinitist option. (Indeed, infinitists argue that foundationalism and coherentism themselves cannot escape falling into a regress of reasons, and thus that either infinitism or scepticism is inevitable. ^{Footnote 1} )

So much for my sketch of infinitism. I will now survey some of the high points of the collection under consideration.

To begin, Turri and Klein’s introduction does a good job of setting infinitism in its historical and philosophical context, giving the main forms of argument for the view, and then outlining some of the most common objections to it. The editors do not take a big-picture view of the papers in the volume, however, preferring to let each paper speak for itself. Whatever the merits of that approach, I do think that readers would be better served by such a synoptic overview of the contributions and how they move the infinitism debate forward. Instead, in a preface, the editors provide a one-sentence synopsis of each essay, which, while perhaps helpful for reminding readers which paper is about what, does not fill the need I have identified.

I was particularly impressed by five papers in the collection: those by Klein, Ram Neta, Ernest Sosa, John Turri, and Michael Williams. Neta’s and Turri’s contributions are models of contemporary analytic epistemology which many would do well to imitate—they are creative, clear, and free of unnecessary technicality. Neta argues that the most common objections to Klein’s case for infinitism fail, but devises a new objection that he thinks may be fatal. Turri’s paper, while only tangentially related to infinitism, is a clever defense of “inferential creationism,” the idea that inference or reasoning “can create justification” (210). Turri argues that though traditionally infinitists have lined-up for creationism and infinitism’s opponents against it, in actuality “creationism can and should be a common ground of non-skeptical epistemology” (ibid.).

Sosa and Klein are keen to stress the continuities and relations between infinitism and foundationalism, with Sosa holding that he and Klein are both committed to a kind of infinitism as well as a kind of foundationalism (208f.), and Klein arguing that a partial rapprochement between infinitism and foundationalism is possible, namely that there are “contextually basic beliefs; but the context can shift and they are no longer basic” (123).

This view sounds quite a bit like Williams’ distinctive contextualist view, but Williams identifies a crucial difference that he thinks makes all the difference—namely, a difference which allows us to avoid the Regress Argument entirely. Williams argues that Agrippa’s Trilemma is undermined by recognizing that it is based on what he calls “Claimant-Querier Asymmetry” (CQA), the idea that “if I represent myself as knowing … that p, there is nothing you have to have done, no way that things have to be, or no special position you have to be in in order for it to be permissible … for you to enter an epistemic question” (231). In other words, the sceptic is “entitled to iterate his epistemic queries without end” (ibid.). But, Williams argues, CQA is false—doubts require grounds just as much as do claims to knowledge. In some contexts, doubts as to whether a claimant knows something have no motivation, and thus cannot be intelligibly entered. If that is the case, then the regress of reasons doesn’t even get off the ground.

I believe that Williams’ paper poses the biggest threat to the infinitist (and, for that matter, the foundationalist and coherentist). For if we can avoid Agrippa’s Trilemma entirely, and re-orient our epistemology away from CQA, infinitism ceases to be a relevant theoretical option. A Williams-style contextualism seems more representative of our actual epistemic practices, and helps us avoid the Regress Argument in the first place. Though Klein’s proposed rapprochement between infinitism and foundationalism in this volume comes close to Williams’ view, it still takes the Regress Argument seriously, which Williams, I think rightly, shows us we need not.

In the end, though infinitism may not be the correct theory of justification, exploring it as a possibility is worthwhile to illuminate neglected avenues of epistemological thought. This volume is a commendable, if somewhat flawed, contribution to that worthwhile endeavour.