Being Thrown to Infinity

If the mode of disagreement essentially encourages the dogmatic interlocutor to provide support for one side of the dispute, the mode ad infinitum makes it clear that the skeptic intends to keep pushing the question of support back further. Here is how Sextus describes the second mode:

And the mode from infinite regress is that in which we say that what is brought for assurance of the proposed matter is in need of something else, and that is in need of another, and so on until infinity, so that, since we have no where from which to begin the establishment [of the case], suspension follows. (PH I 166)²⁴⁸ Here Sextus uses the first person plural – the skeptics are the ones who say that the current evidence needs its own support and that support needs something else. So I take it that the mode of infinite regress is simply the dialectical move of repeatedly questioning the grounds for a position.²⁴⁹ One might think of this as the toddler's mode: One can always ask “why?” of any claim at all. While this is an over-simplification, it is not far

“Well, Melissus says motion does not exist.” But, notice what has happened. The two arguments are not parallel insofar as they appeal to different grounds, one to the appearances and the other to an authority.

According to Morison, each mode provides a mechanism to generate equally opposing arguments. But it is difficult to see why these arguments are equal given that they appeal to different kinds of putative evidence.

248ὁ δὲ ἀπὸ τῆς εἰς ἄπειρον ἐκπτώσεως ἐστὶν ἐν ᾧ τὸ φερόμενον εἰς πίστιν τοῦ προτεθέντος πράγματος πίστεως ἑτέρας χρῄζειν λέγομεν, κἀκεῖνο ἄλλης, καὶ μέχρις ἀπείρου, ὡς μὴ ἐχόντων ἡμῶν πόθεν ἀρξόμεθα τῆς κατασκευῆς τὴν ἐποχὴν ἀκολουθεῖν. (PH I 166)

249Diogenes Laertius, perhaps, makes this clearer. He says, “The mode of throwing out to infinity does not allow the matter being investigated to be secured because one thing receives credence from another and in this way [it continues] to infinity” (DL IX 88). The idea seems to be that one can always ask of the current claim being investigated why we should believe it to be the case. As long as the dogmatist continues to offer new grounds as the answer, that too can be questioned. Of course, the dogmatist might stamp his foot, insisting that no other grounds are needed. At that point, the skeptic will use a different mode.

off. This mode is not simply about asking for reason after reason; rather, it involves asking for the means to decide the earlier dispute.²⁵⁰ This explains why it is the second mode: Once the skeptic has pointed out a dispute, the dogmatist's first move it to try to support his side. The skeptic then asks for further grounds for the initial support. The dogmatist might offer them. The skeptic repeats the move, and the discussion could potentially continue in this way indefinitely.²⁵¹ Some interpretors might suggest that Sextus demands justification of the dogmatist or that the dogmatic norms of rationality require a reason be given for every belief. But on my view, the regressive mode does not demand that the dogmatist justify a belief (even though the dogmatist by his own norms might feel a demand). Rather the mode simply invites the dogmatist to support the view recognizing that, at some point, the dogmatist might very well simply assert that the current grounds in question are inexplicable or foundational. At that point, the skeptic must try a new tack and another mode will be introduced.

Sextus says that epochē follows the regressive mode, and it is important to be clear with respect to what the skeptic suspends judgment: The suspension is regarding the

250Thorsurd (2009) denies that this is the substance of the mode. He says, “Unlike the persistent child who keeps asking why, the sceptic's challenge arises from the dogmatist's own conception of justification and rational agency: the sceptic only reflects the dogmatist's epistemic ambitions” (149). As I

mentioned before, I think that this view of the modes creates a problem because, if the modes arise only from the the dogmatic view of justification and rationality, then the modes cannot work to produce epochē in the skeptic who has suspended judgment regarding justification and rationality. Obviously the skeptic had better suspend judgment about the adequate criteria for rational belief, but she will think that a given opposition seems equally weighted, and she will presumably look for what can be said in support of each opposition which thereby allows her to use the ad infinitum mode on herself.

251Barnes (1990, 39) notes several places where Sextus appeals to regressions which do not involve some question of justification: PH II 40; III 44, 67, 68, 76, 162; M VII 312, IX 221, 261, 435; X 20, 76, 129, 256; M I 180, 242, 245; III 81. He suggests that these examples may help us understand the mode of regression. However, I take it that these are not examples of the use of the mode because the question of support is essential to the way the mode works. Rather, I think that Sextus used other appeals to infinity in addition to that which characterizes the Agrippan mode.

initial question. The reason he gives is that there is no where from which to begin the establishment of the question. But that is not because the skeptic has identified a fallacy that the dogmatist is using.²⁵² Rather, it is because the investigation of the question was itself suspended when discussion turned to the grounds for the support of one side in the question (and the grounds for that). In other words, the skeptic suspends judgment as long as the question is not decided, and one way for the skeptic to put off the decision is by investigating the grounds, and the grounds for the grounds, and so on, indefinitely. This also means that the suspension is conditional; epochē follows the regressive mode as long as the dogmatist continues to provide reasons for the previous reasons or support for the previous support. Once he stands his ground and asserts that he has reached the

foundations, then another mode must be used in order to continue the debate.

When Sextus actually appeals to this mode in his texts, of course, he does not ask

“Why?” interminably. Rather, when it becomes clear that the support for the support (of a particular question) follows a pattern, he indicates that this can go on ad infinitum. So, for example, when Sextus introduces the philosophical dispute regarding existence of the criterion of truth, he raises the question of whether we need a criterion by which to determine the correct criterion of truth. Regarding dogmatic attempts to establish such a criterion, he says, “...while, if they want to judge the criterion by a criterion, then we throw them to infinity” (PH II 20).²⁵³ It is immediately obvious that if you need a

criterion to judge the criterion of truth, then one can simply ask about the second criterion

252Barnes and Hankinson both suggest that this is how the regressive mode works. I discuss Barnes' account in some detail below, but see also Hankinson (1995a, 186, 188).

253ἡμῶν ..., ἐάν τε κριτηρίῳ τὸ κριτήριον κρίνειν ἐθέλωσιν, εἰς ἀπειρίαν αὐτοὺς ἐκβαλλόντων. (PH II 20).

how we should judge that, and this line of questioning could go on forever assuming a dogmatic appeal to another criterion in each case.²⁵⁴ So I take it that, while Sextus does not as a matter of fact run through an infinite regress, the force of the mode is that if the question of support can be pushed back, then the skeptic will do so.

Note that on my interpretation, this mode involves a dialectical move (potentially, a series of moves) rather than an argument. To appreciate the importance of this, consider the problem that arises for the gladiatorial interpretation: Barnes suggests that the

regressive mode is used when the dogmatist offers a regressive argument. For example, claim p is supported by the set of reasons R1. The R1 is in turn supported by R2 which is supported by R3, and so on, ad infinitum. So, in a sense, the entire, unending string of support is the argument offered by the dogmatist for claim p. Barnes rightly wonders why we should expect to suspend judgment on p just because the dogmatist has offered such an argument. After all, we should not suspend judgment on p simply because the

dogmatist has offered a bad argument for p, since there may be some other good

argument for p, one that does support p.²⁵⁵ But even if we grant that we should suspend judgment on claim p as far as this argument goes, we might still wonder what about this argument should cause us to suspend judgment. Here Barnes gets bogged down in questions of the justification of infinite sequences.²⁵⁶ He points out that while we cannot

254Sextus uses the regressive mode when he considers the possibility that the dogmatist justifies something – like the criterion – by means of the same type of epistemic entity – another criterion. So you end up with a series of justifications of like kind. For series of proofs, see PH I 122; II 85, 182, III 8, 36, 53; M VII 339; VIII 16, 21, 78, 347; M II 109, 112. For series of criteria, see PH II 20, 36, 78, 89, 90, 92, 93;

III 36, 241; M VII 340, 429, 441; VIII 19. For series of signs, see PH II 124, 128. For series of explanations, see PH I 186; III 24. For series of definitions, see PH II 207. These examples also illustrate the way in which the regressive mode does not simply generate regresses of reasons, but regresses of the means to adjudicate the issue.

255Barnes (1990, 42).

256Barnes (1990) develops this line of argument in some detail; see pp. 48-51.

go through an infinite series of arguments in a finite amount of time, that does not mean that we cannot see the pattern in an infinite sequence of arguments. Consider the

following series as an example:

n) ...

...

3) [(p & q1) & q2 ]& q3├ (p & q1) & q2

2) (p & q1) & q2 ├ p & q1

1) p & q1 ├ p

In the given example, each conclusion is the premise in the next sequent, and each premise implies its conclusion. Anyone can see the pattern and generate the nth previous sequent. Thus, Barnes argues that while Sextus may be right that we cannot go through an infinite number of arguments, it is false that one cannot state the support for any given claim in an infinite series. Barnes suggests that these sorts of considerations should lead us to reject Sextus' apparent claim that we cannot establish something on the basis of infinite regression since we cannot go through an infinite number of reasons or proofs.

But, he concedes that any such regression will not be “epistemologically serious”, by which I suppose he means that we cannot learn anything new through such regressive arguments.²⁵⁷

In short, the gladiatorial interpretation sees the mode of infinite regress as an

257Barnes (1990, 51). My own example above is not “serious” in the sense that each sequent begs the question since the premise for each argument is simply the conclusion conjoined with some further claim. Hankinson (1995a) essentially follows Barnes' line of reasoning here, arguing that it is possible to imagine an infinitely regressive argument, but that any example will “pose no threat to the Infinite Regress Mode” (188-189).

appeal to a particular fallacy.²⁵⁸ Since a regressive argument is “unacceptable”, we should suspend judgment pending any further considerations.²⁵⁹ But as Morison points out, Barnes' view seems to commit Sextus to a belief – namely that regressive arguments are bad – about which he ought to suspend judgment if he is a good skeptic.²⁶⁰ And this is one reason to reject Barnes' version of the gladiatorial view.

The oppositional view raises its own questions. Morison – borrowing an idea from Barnes²⁶¹ – suggests that the regressive mode is meant to provide the skeptic with a way of generating equally opposing regressive arguments.²⁶² If a mathematician argues regressively that “two is even” because “four is even” because “eight is even” and so on, then the skeptic will oppose to this the parallel argument that “two is odd” because “four is odd” because “eight is odd” and so on. Since the arguments are completely parallel, there is no reason to prefer one to the other, so we must suspend judgment. I offer two objections to this line of reasoning. The first is textual: We do not see Sextus arguing like this anywhere in his writings. When he appeals to a regression to infinity, he never generates two parallel regressions. Rather, he simply notes the single regression and

258Barnes (1990, 44).

259This is why Thorsrud (2009) emphasizes the way in which this mode typically works in conjunction with other modes. He says, “Since few would rest their justification on an infinite regress in the first place, this mode is most commonly used in conjunction with the hypothetical and reciprocal modes”

(153).

260Hankinson (1995a) argues that the modes (it's not clear whether he means all five or only the 3 he calls

“Formal”, that is regression, reciprocity and hypothesis) are simply the codification of dogmatic canons of rationality and so they are meant to induce epochē in the dogmatist, not the skeptic (192). But this yields a strange result. According to Hankinson, the dogmatist who is committed to the validity and invalidity of certain argument forms – like regression – may suspend judgment on many questions. But once he suspends judgment about the invalidity of the forms that constitute the modes, then the modes will no longer work because the skeptic will not grant that, on her own view, infinite regress arguments are unacceptable. This tells against Hankinson's interpretation since Sextus seems happy to use the modes in his own investigation as much as in any discussion with a particular dogmatist.

261Barnes (1990, 51–56).

262Morison (forthcoming, 30).

sometimes indicates its unacceptability. The second objection involves thinking about how the modes were used. They were clearly meant to be used – at least in part – to engage with dogmatic philosophers. I submit that no dogmatic philosopher would have offered a regressive argument for precisely the reasons many scholars have given.²⁶³ If there are no regressive arguments to oppose, then there is no reason to think that Agrippa (or whoever) would have developed a mode to oppose such arguments. The mode would have been completely useless.

The pragmatic interpretation does not run into any of these problems. My

interpretation says that the skeptic suspends judgment on question p because she is in the midst of asking about the grounds of p, that is R1. But she cannot decide p unless she has established R1 , so she asks about the grounds for R1; call this R2. Why does she suspend judgment about p? She remains in the middle of the dialectic and will remain there until the dogmatist makes a move that settles the question. The interlocutors suspend judgment because a decision has yet to be made. But this does not commit the skeptic to any position regarding the logical status of infinitely long arguments. The skeptic need not even take a position about the status of said grounds, she merely requests support for each claim as long as the dogmatist is willing to provide it.