3.1. Fantl and McGrath’s response

Fantl and McGrath (Reference Fantl and McGrath2012, pp.487–9) raise a number of points to resist this argument. First, they contend that it’s unclear why S should sell all his stock at the final stage of the cycle. Certainly, KA doesn’t imply this. After all, even if S no longer knows STOCKUP, he may still know that BXD will probably rise, and that may justify keeping much of his investment.

However, this response doesn’t avoid the criticism. Suppose S has adopted the principle that he’ll invest in BXD if and only if he knows it will go up. Again, a Dutch book can be opened against him given SSI. Besides, as Reed points out (2012, pp.469–70), given SSI, the broker can undermine S’s knowledge that BXD will probably rise by offering a high-stakes bet on it, thus removing any rationale for staying invested.

Fantl and McGrath urge that, if the example is taken realistically, it’s unlikely that S would know STOCKUP at all—our epistemic position on stocks isn’t usually that strong. But they concede that we could imagine a case, which “needn’t even be that unrealistic” (2012, p.488) where the evidence is stronger such that S would know. But in that case, they argue, S would be reasonable to invest all his assets when the broker invites him to do so. After all, we very plausibly know that our bank won’t go belly-up and are reasonable to leave all our money in its care.

Fantl and McGrath’s point seems to be that either S wouldn’t know STOCKUP in the first place or, if he did, he’d be reasonable to invest all his assets. Either way, the Dutch book problem doesn’t arise. This stance is hard to square with the central idea of SSI: that there can be case-pairs in which a “low-stakes subject” (as it were) knows that p while a “high-stakes subject” with the same strength of epistemic position fails to know it. Granting this, it seems possible for S to know STOCKUP when low-value investments are being considered but not know it when high-stakes investments are on the table. That’s all we need for Reed’s problem to take hold.

Fantl and McGrath argue the case (2012, p.488) by appeal to their principle KJ: if you know that p, then p is warranted enough to justify ϕ-ing, for any ϕ. This principle underpins their contention that if S knows STOCKUP to begin with, he would be reasonable to invest all his assets. They suggest that to resist this contention, one would need to resist their argument for KJ and complain that “…we’re left in the dark [by Reed] about which step of the argument for KJ is supposed to go wrong.” (p.488).

In fact, however, KJ doesn’t support the contention in question at all. We can see this by considering how Fantl and McGrath themselves deal with KJ in relation to hypothetical gambles (2009, pp.226–9). They consider an example in which, when stakes are low, a subject knows that her granddad smoked a pipe (“PIPE” henceforth). Still, they accept that if she were asked to bet the farm on it, her warrant would fall short – the stakes would be too high. I.e., she would no longer know it if the stakes were significantly raised – exactly the kind of knowledge loss the Dutch Book problem relies on.

What about KJ? That principle implies that if the subject knows PIPE to begin with, her warrant for it must be enough to justify any action, including betting the farm. So, now it seems that KJ commits Fantl and McGrath to denying that she could lose knowledge of PIPE through a change in stakes after all. What’s going on?

Here Fantl and McGrath affirm that KJ doesn’t have these implications. Given that the subject knows that PIPE when stakes are low, KJ implies that her warrant suffices to justify betting the farm when stakes are low (and the gamble is merely hypothetical). However, if she were actually presented with such a gamble, that would transform her practical context into a high-stakes one. Her warrant would not suffice to bet the farm in this context and she would not know that PIPE. Consequently, even granting KJ, somebody can go from knowing a proposition when stakes are low to not knowing it when stakes become high. The fact that they have warrant enough to bet the farm when stakes are low doesn’t mean they have warrant enough to bet the farm when stakes increase.

Parallel points can be applied in Reed’s example. S knows that STOCKUP when it’s a low-stakes matter of investing 25%. Given KJ, S’s warrant for STOCKUP suffices at this point to justify investing all his assets in BXD. But when the broker actually invites him to invest all his assets, that puts S in a high-stakes situation. His warrant for STOCKUP no longer suffices to justify investing all his assets, and he no longer knows STOCKUP. Fantl and McGrath’s appeal to KJ was meant to block this last point and establish that if S knows STOCKUP at the start, his warrant should justify “going all in” at the end. But it should now be clear that KJ has no such implication. Fantl and McGrath are at pains to point out as much in their discussion of hypothetical gambles. Hence, their Dutch book problem remains.

3.2. Beddor’s response

More recently, Bob Beddor (Reference Beddor2021) has argued that having a Dutch book opened against you through a series of bets does not necessarily imply that you are acting irrationally. If your evidence is being manipulated, you may be acting rationally given the evidence available to you throughout the process. If that’s right, SSI might be off the hook. Perhaps its defenders can agree that S has been Dutch-booked in Reed’s example but insist that it is an unproblematic, “perfectly rational form” (p.193) of Dutch book.

Beddor gives a convincing example involving memory manipulation (p.195-6). The subject in this example sees her colleague, Constance, enter the office and thereby acquires Constance is in the office (“OFFICE” henceforth) as part of her evidence. Moreover, she knows that conditional on OFFICE there’s a 50% chance that Constance parked on Main Street (“PARKED” henceforth) and that PARKED is definitely false if OFFICE is. The subject is then offered a bet on PARKED – she wins $1 if PARKED is true and loses the same amount if it’s false. It’s reasonable for her to take the bet given her evidence. But then the bookie wipes OFFICE from the subject’s memory. Now the bet looks much riskier. The bookie offers to release her from the bet for a penny. The subject, quite rationally given her present (lack of) evidence, pays up.

It is plausible that this subject is rational throughout her Dutch-booking. Beddor argues that Reed’s example works in similar fashion by manipulating the subject’s evidence, albeit through changing stakes rather than erasing memories. At the start, S’s evidence includes STOCKUP since he knows STOCKUP at that time. Hence, he’s rational to make the low-stakes investment. But when the stakes get high, that crucial evidence disappears, and it becomes rational for him to divest.

Beddor is right that given how manipulating the stakes affects S’s evidence on SSI, S is responding rationally to his changing evidence throughout the Dutch-booking. But this doesn’t solve the problem for SSI. It is the problem for SSI! In the PARKED example, it is clear that the subject loses the evidence that made her initial bet rational and so is rational to buy-out. But in Reed’s example, it isn’t plausible that S loses the evidence supporting his initial investments when the broker raises the stakes; nor is it plausible that he is rational to divest. Instead, it seems that his initial investments are just as well supported as ever and that the rational thing for him to do is keep those investments but not increase them further. The problem is that SSI cannot capture any of this but implies, implausibly, that the subject is rational to go through cycles of investing and divesting. This seems to be the point of Reed’s remark that SSI “can rationalize actions that are intuitively quite irrational.” (p.469) What’s needed is a theory that avoids this consequence. Beddor merely doubles down on the result and fails to get SSI out of trouble.Footnote ⁹

Beddor claims that the Dutch book problem confronts both SSI and EC. The next section shows that, unlike SSI, EC can escape the difficulty.

4.1. Context-relative knowledge?

Given the knowledge-action link at the heart of SSI (KA: you know that p iff you can treat p as a reason for action) the above idea would imply that S knows STOCKUP and simultaneously does not know it, which is contradictory, or that he knows it relative to one context but doesn’t know it relative to another. Some authors dismiss the idea of relativizing knowledge to different contexts out of hand. Jessica Brown (Reference Brown2014), having described the multi-tasking problem, writes:

Brown doesn’t elaborate on why knowledge shouldn’t be relativized to contexts (or “actions,” as she puts it).

Reed is similarly dismissive of the “unappealing” (2012, p.468) suggestion and writes:

The contention here is that ordinary knowledge-talk shows no evidence of context relativity, and the fact that Reed’s example sounds so strange is meant to count strongly against the idea.

Considering multi-tasking cases, Fantl and McGrath (Reference Fantl and McGrath2012) follow Brown’s suggestion and affirm that the more demanding practical context determines the knowledge standard. Thus, in the BXD example, when the broker invites S to invest 100% of his assets, that high-stakes context determines the standard for knowing STOCKUP across the board. Consequently, S doesn’t know, and cannot rely on, STOCKUP period (and so ought to divest).

4.2. Context-relative knowledge and SSI

Two questions arise here. Is relativizing knowledge really plausible—recall the earlier dismissals from Brown and Reed? And, if it is, is it a really an option for SSI?

Starting with the first, we saw that Reed finds this strategy “unappealing” because, “We never do say things like, “Relative to that guy, I know my BAC is under the limit. But, relative to the cop standing next to him, I don’t know it.” However, granting that this way of talking sounds strange, it’s not clear that the strangeness is due solely to the relativized knowledge claims. For one thing, the BAC example is described very briefly. To give relativization a fair shot, we’d want a fairly realistic example in which there seem to be multiple, clearly distinguishable practical contexts in play where different practical standards seem clearly to be operative. Now, one can imagine different standards applying to the question of whether one is under the alcohol limit when dealing with a police officer as compared to chatting with friends. But it may be hard to apply different standards in a case like Reed’s where there is a “cop standing next to” your friend. In that situation, the higher standard might naturally come to dominate thereby making it seem inappropriate to make Reeds’ relative knowledge claims.

Another problem with Reed’s example is that the speaker relativizes his knowledge to different people, which sounds strained, rather than to different standards or situations or actions. He says that he knows it relative to that guy but not relative to that cop. In contrast, DeRose affirms that Jane knows she’ll be back next year well enough to assert it to her friend but not with enough certainty to make it irrational to take the trouble to get the insurance. Here, Jane’s knowledge is relativized to certain kinds of behavior, which sounds more felicitous.

Consider an adaptation of another of DeRose’s examples (2009, pp.4–5). Louise, in her brief visit to work one day, sees that John’s hat and coat are hung inside his office and overhears conversations strongly suggesting that John is at work (which he in fact is). In the tavern later that day, Louise claims correctly and appropriately to know that John was at work (“JOHN” henceforth) in order to claim her winnings in a low-stakes bet on whether John would show up to work that day. Later, when questioned by the police in relation to a very serious matter about which the question of whether JOHN is of great importance, Louise claims not to know, reflecting that she never actually saw him at work. We can imagine that, while the officer scribbles in a notebook, Louise’s friend, who paid-up in the bet at the tavern, pulls Louise aside and starts protesting: “Wait a minute, you just admitted you don’t know that John was at work! So you can’t claim your winnings from me!” And we can imagine Louise replying: “Oh come off it; you can’t be serious! I’d have to be really certain to testify to the police that John was at work. I don’t know it by those high standards. But, for the purposes of the bet, of course, I know he was at work! I saw his hat and coat in the office and heard people talking about him like he was there. He clearly was there, and I’m fully entitled to my winnings.”

Louise’s reply sounds far less jarring than what is said in Reed’s example. This time, the knowledge claim is relativized not to people but to standards and practical contexts (though, as with Reed’s examples, the contexts involve a police-officer and an ordinary civilian.) Plus, the example is described in more detail than Reed’s. The different practical contexts involved are made clear, as is the fact that different standards seem appropriate to them. Consequently, Louise’s relative-knowledge claims are much more intelligible than Reed’s. To my ear, while Reed’s relative-knowledge claims sound jarring and hard to make sense of, what Louise says seems acceptable and easy to understand.Footnote ¹⁴

Our next question was: is DeRose’s relativization of knowledge an option for SSI? DeRose defends EC. Quite generally, on his view the truth-conditions of knowledge-attributions of the sort “S knows that p” are determined by contextual factors. “S knows that p” might be true relative to one conversational context and at the same time false relative to another even though “S” and “p” are used to pick out the very same person and proposition respectively. Hence, knowledge ascriptions are already implicitly context-relative for EC.

DeRose affirms that his response to the walking-talker example “seems available whether SSI or contextualism is accepted.” (2009, p.272) But, on reflection, that doesn’t seem correct. Adopting DeRose’s response would mean conceding that if two speakers separately asserted, “Jane knows that she’ll survive the year,” one could assert a true proposition by speaking with Jane’s phone conversation in mind while the other could assert a false proposition by speaking with the life-insurance in mind. Thus, the truth conditions of the assertion would prove to be context-dependent in a way which is incompatible with the invariantism of SSI. (Recall: invariantism is a rejection of EC’s semantic thesis that the truth conditions of knowledge attributions vary with context.)

Defenders of SSI might be willing to cede ground here. When discussing a different problem which also impugns invariantism (one relating to third-person knowledge ascriptions, to be discussed below), Fantl and McGrath consider surrendering SSI and falling back on a defense of impurism:

As we’ve seen, that’s not the option they take in response to multi-tasking cases. But, given the Dutch book difficulties that beset their preferred strategy, it may be advisable to “reach into the contextualist’s playbook” to handle these cases too.

4.3. Impurist EC

How might that work exactly? Here is a sketch. Impurists might argue that knowledge is a three-place relation, relating a subject to a proposition and a practical context the subject faces. If the knowledge-standard is affirmed to vary with features of the subject’s practical context, that would make it an impure relation, as desired, as well as being a subject sensitive relation. A modified version of the knowledge-action principle might then be offered along the following lines:

Turning to semantic matters, impurists might affirm that utterances of “S knows that p” implicitly assert that S knows that p relative to a practical context salient to the speaker. Such utterances might be claimed to be true if and only if S knows that p relative to that context (as explained in KA*) and false otherwise. This yields the contextualist thesis that the truth conditions of knowledge attributions vary with context. One person asserting, “Jane knows she’ll survive the year,” where Jane’s phone conversation in salient would assert correctly that Jane knows SURVIVE relative to her phone conversation, while another person making the same utterance where Jane’s signing up for life-insurance is salient would assert incorrectly that Jane knows SURVIVE relative to that context. This approach also accommodates the more explicitly context-relative knowledge claims DeRose employs dealing with the walking talker (along the lines of “S knows that p well enough for this context but not well enough for the standards relevant to that context.”) It thereby provides a way to avoid the Dutch book problem: S knows STOCKUP and can rely on it relative to low-stakes contexts but doesn’t know it and cannot rely on it relative to going all in. Thus, he can sensibly keep his initial investments but cannot sensibly invest the remainder.

More details would need to be filled in. But this sketch suggests one way that those sympathetic to SSI might develop a fallback, impurist theory to handle multi-tasking cases and the Dutch book problem while ceding ground to EC.