[ADMINISTRATIVE NOTE: MOVING TO THE FRONT (FROM AUGUST 15)]
Epistemic agents claim to know that-P within a context of competing alternative propositions, {A1, A2… An}, all of which would be as equally consistent with the facts as P, but necessarily exclude P, such that:
If some one member of {A1, A2… An} were true, then that-P would be false.
Thus, in order for S to know that-P, s/he must also know that not-{A1, A2… An}, which means S must be able to exclude {A1, A2… An}. If S cannot, then let us say S’s belief that-P is not knowledge. This is called the Underdetermination Principle (UP). Now, as noted above, vis-à-vis P there exist many alternatives. Indeed, in a manner of speaking, there exist an infinitude of logically possible alternatives to P; some of which- perhaps many- are unable to be excluded by S, e.g. dream-state and brain-in-the-vat arguments. If S cannot exclude all the possible alternatives to that-P, then how can s/he claim to know that-P? Quite simply, the skeptic says S cannot, and in the chance that S does possess a true belief, s/he does so merely accidentally. However, one proposed solution to this difficulty, and one that has become rather popular, is the relevant alternative theory of knowledge (RT). RT has it that epistemic agents need only exclude the relevant alternatives to that-P, and not every logically possible alternative, in order to claim properly to know that-P. To see it in action, consider the following.
A bird alights atop a branch relatively close to S’s position. To facilitate the argument, let us presume the following: (i) The environment within which S operates is optimal for visual perception, and, (ii) S is a shrewd field ornithologist. Thus, from the above, S justifiably believes the bird before her/him is a cardinal (C). However, someone may have painted a robin to appear as a cardinal (PR), which if were the case, S would be unable to differentiate C from PR.
RT purports that in one context (1) S does know C. That is to say, S is able to discriminate cardinals from bluebirds, Scarlet Tanagers, finches, robins, and like birds, and thus s/he may and can exclude those alternatives. What is more, within (1) PR is not a relevant alternative with which S need concern her/himself. If a skeptic insists otherwise, S need only respond that all s/he means by “know” is that s/he can accurately distinguish between contrary visual perceptions; nothing more, nothing less. So, in (1), deductive closure upholds (CP), as we see:
S knows that C
S knows that C logically entails not a bluebird, Scarlet Tanager, finch, robin, and like birds.
Therefore, S knows that not a bluebird, Scarlet Tanager, finch, robin, and like birds.
In another context (2), which is concurrent with (1), PR is a relevant alternative, and the truth of C entails its falsity. However, S does not know that not-PR; hence, S does not know C is true relative to not-PR. In this instance, (CP) is invalid, as may be observed:
S knows that-C
S knows that-C logically entails not-PR
However, S does not know that not-PR
We see that (CP) fails and thus leads to skepticism about contingent propositions. So, in order to prevent skepticism, many proponents of RT reject (CP). Implicit in the rejection of (CP) by most adherents of RT is the assumption that in order for one to know that-P, one must have evidence for that-P. Thus, if S does not have evidence that not-PR, then S may not properly claim to know that not-PR. But as we have seen from (1) all an agent need do in order to properly claim to know that-P is to eliminate all relevant alternatives within a specified context; and there seems to exist contexts in which PR is not a relevant alternative; similarly, there seem to be contexts wherein PR is a relevant alternative. In this way Dretske may implore us ‘to think of knowledge as an evidential state in which all relevant alternatives (to what is known) are eliminated’ (1981). Thus, from this, we may conclude that when the epistemic context changes, what is meant by the verb ‘to know’ also changes. If we so conclude, then we may in many circumstances avoid skepticism.
What are relevant alternatives? In brief, they are logically possible alternatives that are not irrelevant (I presume here irrelevant to be synonymous with not-relevant). Recollect that an alternative to that-P is some proposition that describes a state of affairs consistent with the given data, and if true, necessitates that not-P. Recall further that for that-P there exist some infinite set of logically possible alternative propositions {A1, A2… An}. Hence, a relevant alternative is a member of the set of all non-irrelevant alternatives {R1, R2… Rn}. Nevertheless, a skeptic may yet agree and insist that all logically possible alternatives are relevant. So, a further definition is required.
Alvin Goldman (1976) provides a useful delineation between irrelevant and relevant alternatives, ‘idle’ and ’serious’, respectively. An alternative, R1, is relevant if S has good reason to think R1 obtains. Accordingly, an alternative, IR1, is irrelevant if S does not have good reason to think IR1 obtains. Dretske (1970) himself seems to provide a similar definition in ‘Epistemic Operators’ when he says, ‘A relevant alternative is an alternative that might have been realized in the existing circumstances if the actual state of affairs had not materialized.’ A further reading of Dretske indicates that what he means by ‘might’ is that some alternative state of affairs is nomologically possible, that is, consistent with the physical laws of nature:
‘[T]he difference between a relevant and an irrelevant alternative resides not in what we happen to regard as a real possibility (whether reasonably or not), but in the kind of possibilities that actually exist in the objective situation. Whether or not [a] bird-watcher knows that the bird he sees is a Gadwall depends on whether or not, in some objective sense, it could be a look-alike grebe (or any other similar looking creature)’ [emphasis added].
The definitions proffered by Goldman and Dretske are lacking and too permissive, respectively, although I am partial to their motivations. For I too think something is amiss with the skeptical concern, and in particular with the UP and its employment by skeptics. However, at the same time, if S claims to know that-P, then S must be able to eliminate the alternatives that serve as legitimate blocks to knowledge of that-P. Thus, RT possesses a very strong intuitive appeal, and I think is in principle correct. It certainly explains very well why, for instance, before claiming to know that Christ with the Adulteress is an authentic Vermeer, an art collector must first exclude the possibility that it is a clever forgery of Han van Meegeren. For Van Meegeren was a skilled forger who possessed a predilection for the works of Vermeer, was known to have forged Vermeer’s works before, and had access to many of the necessary conduits through which forgers peddled their works, not to mention a distinctive stroke that varied from Vermeer’s only subtly. Indeed, it seems (even before a clear definition has been formulated) RT explains quite well why a collector would be epistemically irresponsible if s/he did not first exclude the van Meegeren possibility, but not irresponsible if s/he failed to exclude the possibility that aliens from Alpha Centauri re-created the work and passed it off, via their secret liaison on Earth, as Vermeer’s.
Dretske’s definition seems to allow for the alien-alternative in the Vermeer case, which, for me, is too permissive. I suggest that an outline of a definition is here appropriate. Goldman’s definition, I think, serves as the most useful. Although, it is incomplete insofar as it does not address the problem of missing evidence; in other words, what are the necessary and sufficient conditions for the exclusion of some relevant alternative (although I think this criticism is itself too demanding, and in the end, I agree with Goldman almost entirely). Nevertheless, that problem may be set aside and addressed at a later time. At this time, however, I shall note two conceptual points from which I will draw a practical implication.
(i) For an alternative to be relevant it must be eliminable, both theoretically and practically. For the epistemic significance of an alternative is its manner of elimination; which is to say, if A requires S to empirically eliminate {A1, A2, A3} before being able to know that-P, S must possess the empirical means necessary to eliminate {A1, A2, A3}. If {A1, A2, A3} were so designed so as to make them uneliminable, S need not worry her/himself over the set. For example, if A claims S must first ensure that an invisible, inaudible, odorless, insipid, intangible, utterly imperceptible person was not in the room before s/he can properly know that s/he was alone, then how is S to address such an alternative? Furthermore, why should S concern her/himself over this logical possibility when it possesses no empirical import?
(i) should prove useful in setting aside the most pernicious skeptical arguments, namely the Cartesian evil-demon / perpetual dream-state argument, and the more fashionable brain-in-the-vat argument. If the skeptic wishes to participate in the epistemic debate, s/he must be prepared to do so fairly. In fact, when a skeptic poses an alternative to that-P, s/he ex hypothesi either sets forth the means by which it is to be eliminated, or eliminates it her/himself by not so doing.
(ii) It appears that if S wishes to claim to know that-P, s/he must first eliminate that not-P. The skeptic makes this point obvious and often, and we saw how it plays into (CP) failure. Therefore, even if a skeptic accepts the constraints of (i) s/he may still contend S does not know that-P because S does not know that not-P (this is due in large part to the potential for the infinitude of {R1, R2… Rn}, which I shall address next). The skeptic, however, is again, at best, being imprecise, or, at worst, dubious. To the former, if the skeptic selects a member of {R1, R2… Rn}, say, R2, and proposes that it blocks S’s knowledge of that-P, s/he may be asserting that S has good reason to suspect R2 may be true. However, at this point, the onus is now upon the skeptic to make precise what s/he means by “may… be true.” For I assert the skeptic, in postulating {R1, R2… Rn}, must do so within a framework of evidential merit. Which is to say, if the skeptic would like S to consider R2 as a potential defeater to knowing that-P, then s/he must have inferred the probability of R2 being true from some set of evidence. In brief, it is not enough for the skeptic to merely require S to have to eliminate that not-P, but rather, must offer legitimate evidential concerns to S knowing that-P. To put the matter another way, S asserts that-P and the skeptic asserts that-possibly-R2: it is incumbent upon both to provide good evidential reasons why either should be seriously considered.
(iii) The most alarming aspect of and the primary force behind UP is the (potential) infinite set of {R1, R2… Rn}. (Since {A1, A2… An} may be infinite, and {R1, R2… Rn} is a proper part of {A1, A2… An}, it seems entirely feasible that {R1, R2… Rn} may also be infinite.) Fortunately, (i) and (ii) in conjunction with one another ameliorate this concern. In brief, S need not concern her/himself with an infinite set of relevant alternatives. Rather, s/he need only concern her/himself with the set of relevant alternatives that possess good evidential reasons for their truth [I think this follows from (ii)].
To conclude, an alternative R is relevant iff R is theoretically and practically eliminable and some set of evidence warrants S in thinking R true. (I leave the question of the nature of the evidence in question for a later date.) From this, the following may be formulated: In any epistemic context, S may claim to know that-P if a belief in that-P was arrived at by reliable means inferred from reliable evidence, notwithstanding contrary alternatives that may be imagined, until further evidence justifies S in believing that not-P. But this requires further development for another time.
Fred Dretske, ‘Epistemic Operators’, 1970
Fred Dretske, ‘The Pragmatic Dimension of Knowledge’, 1981
Alvin Goldman, ‘Discrimination and Perceptual Knowledge,’ 1976
Aaron,
This seems right. That might not normally be worth much, but consider that I generally find the skeptic’s position appealing and consistent with many of my intuitions.
We agree that there is more to say regarding evidence and also, perhaps, inferences from evidence – but that in no way derails the argument in this post.
I think especially your (ii) above, paring down what we – or one pushing the skeptic’s agenda – may mean by relevant alternatives is effective. The skeptic might entirely reject that they have to show any evidence to suggest one of {R1, R2… Rn} is to be considered, but this just seems disingenuous.
Good stuff,
~Q
“In any epistemic context, S may claim to know that-P if a belief in that-P was arrived at by reliable means inferred from reliable evidence, notwithstanding contrary alternatives that may be imagined, until further evidence justifies S in believing that not-P. ”
Aaron,
Hi. Doesn’t this imply one can know what isn’t true. And since we’re relying on a lot intuition pumps to play this game, doesn’t that seem counterintuitive?
or does being able to claim knowledge not imply knowledge on your view?
suppose someone claims to know that the earth is flat and we all believe him. On your view, does that mean he knows the earth is flat, or is it just okay to claim it? Suppose no one brings up any in your sense relevant alternatives he can’t shoot down. Someone even says it might be round, and he merely points to the horizon and says, does that look round to you? again, everyone believes him. Does he know?
when i said, “…one can know what isn’t true,” i meant one can know that p even if it’s not the case that p.
That was careless. I wish you could edit this thing.
Chase,
Thank you for your response. In my post, I de-emphasized “truth” for a reason. My conception of “truth” is rather austere. Honestly, outside of certain mathematical and logical statements, I am not sure what it means for any proposition or hypothesis to be “true”. Beliefs and hypotheses come in varying degrees of accuracy and are more or less the result of certain reliable, causal processes, but are nevertheless fallible; some more so than others. All empirical propositions and thus beliefs involve inferences from evidence and therefore in one way or another may turn out to be wrong, whether from consideration of new perceptual evidence or reflection upon the set of perceptual evidence extant.
Many propositions may be indubitable (e.g. that I have before me on my desk a collection of Greek dramas), but none are certain; the former being a neurological brain-state, the latter an epistemic conception. Thus, beliefs that are based on good evidence obtained via reliable processes are “true” until justifiably revised. Many things follow from this, and some I (hope) am sure are counterintuitive. Any other notion of “truth” and its cognates is much too metaphysical for my tastes.
Now to address your particular example. S may claim to know the Earth is flat (P) iff S believes that-P and that-P is the result of a reliable process (e.g. experience, memory, testimony, deduction, induction, and so forth) based upon good evidence (E). However, E, in this case the appearance of the horizon, is not good evidence. In fact, it is strikingly poor evidence. For as many classical Greeks have noted the visibility of objects on or just past the horizon are better explained by a spherical Earth. Combined with other evidence, for instance, the observation made by Aristotle that during its phases a straight line was not caste upon the Moon by Earth’s shadow (which is a logical entailment of a flat-Earth hypothesis), the horizon evidence should have compelled a flat-Earth proponent to revise her/his belief.
Thus: “On your view, does that mean he knows the earth is flat, or is it just okay to claim it?” No, s/he is not justified in claiming to know the Earth is flat.
“Suppose no one brings up any in your sense relevant alternatives he can’t shoot down.” I did not address this point explicitly in my post, but I hold relevant alternatives to be objective, rather than contextually based. Therefore, the relevant alternatives remain whether one is aware of them or not.
I leave unaddressed the matter of “missing” or “overlooked” evidence, which arises quite naturally from your concern. (In other words, how much evidence is necessary before one may claim properly to know some proposition.) The issue of evidence is really the most interesting epistemological discussion.
so, hmm. there’s always going to be countervailing and relevant evidence that will count against a false belief whether it’s practically available or not. so if you believed in truth and falsity, your view would just be reliablism. S knows that p just in case S’s belief that p was produced by a reliable method and p is true.
But you don’t believe in truth because you’re some kind of crazy positivist or scientific relativist or something. And you don’t index possible countervailing evidence to context or, if I understand your reply, to practical availability. And you say you leave open how much evidence is needed before S can properly claim know that p.
So you’re left with a view which says that S can’t claim to (doesn’t?) know that p unless S’s belief that p was produced by a reliable method and there is not much possible evidence, none which is practically available, that would count against p, and S has ruled out relevant alternatives.
Do I have this right? if so, i have 2 points.
1. I just don’t think it’s going to be hard to construct a getiier case as a counterexample unless you just beg the question about relevance. As soon you drop truth, getiier comes back. My flat earth case might not be the best given the scientific mumbo jumbo about the horizon line you mentioned, but it shouldn’t be hard to come up with a case we intuitively would not say is a case of knowledge but which is allowed as knowledge on your view. You might demand that I do it, and that would be fair, i suppose.
2. I feel like you’re oscillating between saying S can claim to know that p and saying S knows that p. One is socio-linguiistic, the other is metaphysical or logical. It could be correct to claim knowledge even if one doesn’t actually have it. So is your view one that tells us when it’s okay or acceptable for us to say S knows that p, or is your view about whether S knows that p, or are you collapsing that distinction?
Your stuff on relevant
Chase,
First of all, I am worried that some of your last comment was cut off, the last bit seems like a fragment, and you might want to at least re-read it and make sure everything you wanted to say was included.
In response to your comment, I do not think that your assertion about the Gettier type problem is right. Of course, I may not have understood you correctly, and if that is the case, please correct me and explain your view further. Gettier’s problem was for justified, true, beliefs. So the exclusion of truth does not bring Gettier into the debate in a new way, as you asserted it would. You might, using Aaron’s view, be able to come up with a counterintuitive example of knowledge, but that would not have the force of a logical counter example, and that would in no way force him to drop or change his view. Anyway, there are a number of ways to get around Gettier type problems, causal accounts of how we can justifiably come to know that-p, tracking theories, etc.. One could also just bite the bullet about Gettier-type example’s and say “I guess Smith did know that the man with ten coins in his pocket would get the job”(admittedly, that is not a desirable option). Based off of Aaron’s comment that “[m]any things follow from this, and some I (hope) am sure are counterintuitive,” a mere counter intuitive view of knowledge would not necessarily be a relevant alternative (sorry about the pun).
Amy,
Thanks for that. I’m used to a looser format. I’ll straight to sit up straighter. The part that was cut off should read — Your stuff on relevant alternatives, the main contribution, is interesting. Most of what you’re getting from me here are points of clarification.
And I’m glad you pointed it out because it certainly changes the tone. “crazy positivist” is meant as a friendly ribbing, by the way. I’m a fan of wittgenstein. Ever read wittgenstein’s poker? Anyway …
In response about gettier, you’re correct. The point from gettier is about justifiaction. So I strike the sentence “as soon as you drop truth …” , but i retain the rest.
Without a more robust notion of truth, Aaron’s right, a lot of counterintuitive things follow. Some of them we can no doubt allow if we’re otherwise moved, but some not. And there is discussion to be had there.
Aaron’s view, simplified, is that S can claim to know that p if S believes that p and her belief is the result of a reliable belief forming process. So basically he’s saying S can claim to know that p if S has a justified belief that p.
My point here is that it is clearly conceivable that S could come to believe that p even if it isn’t so that p. And surely it is further conceivable that S’s coming to believe that p was the result of a belief forming process that S has utilized effectively in past and that everyone would agree has proven reliable.
So? In such a case, does S
1. know that p
2. not know that p but can rightly claim to know that p,
3. not know that p?
Just intuitively, I would say 3. If he goes with 1, it seems like he’s going to have to press too hard on the notions of reliability in terms of belief forming and relevance in terms of evidentiary support / alternative explanations for the data. But maybe not.
If he goes with 2, I think he stops doing philosophy and starts doing something like anthropology.
But hey, I don’t deny the principle of epistemic closure. I know I’m not a BIV (if it’s true). Which is more plausible, that I am a BIV or that I”m not?
Chase,
My intention was not to formulate a condition(s) to supplement
1. P is true
2. S believes that-P
3. S believes that-P justifiably
so as to avoid Gettier-like cases- at least, not directly- therefore I need not concern myself with their avoidance.
Instead, I sought only to provide a preliminary definition of relevant alternatives so as to make clear why S need not exclude all logically possible alternatives to that-P in order to claim properly to know that-P. The issue of relevant alternatives is one tied closely to matters of evidence, i.e., the definition of evidence, the quality of evidence, the amount and kind of evidence required to justify S’s belief in that-P, etc. However, no matter the specifics, it seems to follow that the evidence must be good and obtained via reliable processes. Thus, I say: beliefs that are based on good evidence obtained via reliable methods are “true” until other, further evidence obtained via reliable methods warrants a revision. To re-iterate, come what may concerning intuition, I think it is neither appropriate nor desirable to proffer a robust notion of “truth”.
Having said that, I find strange your question about distinguishing between saying when S may properly claim to know that-P and determining when S knows that-P. Who makes such a distinction? In offering substantial conditions for ‘S knows that-P’, have we not also set forth conditions for saying when S is justified in claiming to know that-P, and vice versa?
P.S. You do not need to worry yourself over the brain-in-the-vat hypothesis, because it is not a relevant alternative.
P.P.S. I did not take offense at the “crazy positivist” jibe (I consider myself a neo-logical positivist of sorts). And, yes, I have read Wittgenstein’s Poker; it’s a good book.
here’s some thoughts.
I don’t worry about the BIV case, I use it to help me understand what knowledge is. besides, I know I have hands.
your notion of truth feels obscure and question begging, but i have no idea what you’re talking about. So I’m ignoring it until it’s explained further … and argued for. why do you feel the need to scare quote, for instance? i reckon it’s because further evidence, correctly understood, doesn’t tell against true propositions. Though, by your lights, it tells against “true” propositions, whatever those are. I guess you mean socially acceptable.
“In offering substantial conditions for ‘S knows that-P’, have we not also set forth conditions for saying when S is justified in claiming to know that-P”
yes, but not necessary conditions.
“and vice versa”
No, not at all. It’s okay to say you know lots of things in lots of different situations, but whether or not you in fact know seems another matter entirely. If you knew the way home, we wouldn’t be lost. it was fine when you told me earlier that you knew though. i don’t hold it against you. but you were wrong.
“The issue of relevant alternatives is one tied closely to matters of evidence, i.e., the definition of evidence, the quality of evidence, the amount and kind of evidence required to justify S’s belief in that-P, etc”
the evidence is the same for me with these two conflicting cases:
1. i’m not a biv
2. i’m a biv.
what’s different here is the explanations for the data.
“However, no matter the specifics, it seems to follow that the evidence must be … obtained via reliable processes. ”
What makes for a reliable process? one that has proved reliable in the past? maybe that process is grue-reliable, reliable and used before tomorrow or unreliable and not used before tomorrow.
Further, if it’s the case that I’m a BIV, isn’t any process which leads me to believe that I am a BIV more reliable than one that doesn’t, at least in this case?
so i don’t see how I can rule out the BIV case given what you’ve said.
p.s. i already acknowledged that i misspoke about gettier. i wasn’t thinking about gettier cases, so drop it already. sheesh.
p.s.s. you should leave dead enough alone. go shout metafisik! at your grandma! lol.
In saying “S is justified in claiming to know that-P”, we at the very least deem appropriate (1) the evidence on which S ostensibly predicates her/his belief, (2) the method by which the evidence was obtained and the belief formed, and (3) the accuracy of that-P with the putative facts. While I agree we have not established necessary conditions for “S knows that-P,” we certainly commit ourselves to the above. So, in your example, when I managed to get us lost I provided further evidence that my prior “knowledge” was indeed not knowledge. As I see it, in initially saying I may claim to say that I knew how to get home, you committed yourself to (1) – (3). Moreover, I assert you commit yourself to agreeing that I fulfilled whatever necessary and sufficient conditions to knowledge that you hold. If not, then why would you agree that I am justified in thinking that I knew that-P? It seems to me you would have to say, “No, you are not justified in believing that-P.” Do we not do just that when the religious purport to have spoken to God directly?
In saying that the putative evidence speaks equally as well for the brain-in-vat hypothesis as for that-P, you seem to be saying that the BIV hypothesis serves as a block to S knowing that-P, and therefore the BIV hypothesis is a relevant alternative- under the RA theory, at least. However, the BIV hypothesis, while a logically possible alternative, is not a relevant alternative, for an alternative R is relevant iff R is theoretically and practically eliminable. Whether I am or am not a BIV neither cognitively significant nor constructive for heuristic purposes. Consider the following. I see a cardinal and thus know that I see a cardinal. However, is it not possible that what I see is not a cardinal but instead a gostem? If what I am observing is a gostem, and gostems, while appearing as cardinals and being otherwise indistinguishable from cardinals in every conceivable way, are not cardinals, then I am not seeing a cardinal, and thus I do not know that what I see is a cardinal. Is there not something unapproachable about this alternative? What empirical import does the gostem alternative have? I assert it has no cognitive significance and therefore may not serve as a block to knowing that what I see is, in fact, a cardinal. Similarly for the BIV and perpetual dream-state hypotheses. Evidential concerns arise when and only when we are considering cognitively significant alternatives.
I find your attempt to smuggle in a grue-like difficulty for reliability amusing. With the exception of deduction, reliability is a concern for the here-and-now and premised upon a track record of empirical performance. Maybe the day will come when clairvoyance, extispicy, and every other claptrappery under the sun will prove a reliable means by which humans gain and retain knowledge… but we can cross that bridge when we come to it.
Hi everybody,
Sorry, I am not a Florida student, but am working in epistemology. Sorry also that I didn’t have time to read all the replies (although I plan to), but I want to comment on the original post to get some feedback on my current thoughts.
One thing that is important to note is that if one is faced with a non-cardinal painted as a cardinal, there are no circumstances in which one ‘knows’ that x is a cardinal, i.e. there are no alternatives that one can rule out that will amount to knowledge that the bird is a cardinal.
The relevant alternatives theory seems to provide a decent theory of justification — providing some (yet controversial) threshold for when one has good reasons for believing.
One area that I am looking at these days is the relationship between practical interests and relevant alternatives. If we are sitting in the backyard having a beer and birdwatching, then it seems that one does not have to rule out painted birds in order to have a justified belief that x is a cardinal (if it is true that the bird is a cardinal, then I say we have knowledge). If we are out in the field taking statistics on kinds of birds in the area, it seems that our threshold for justification that x is a cardinal should be a bit higher. Our bird expert should investigate a ‘bit deeper’ — although she needn’t have painted birds in mind. If our painted bird is such that upon investigation it is indistinguishable from a cardinal, then while our bird expert does not have knowledge, her belief is not unreasonable given her circumstances (while just looking at the bird from 20 yards and marking ‘cardinal’ on her worksheet, would be a bit unreasonable given her expertise and job).
This points to the problem with closure. If we hold to a very high standard for knowledge then scenarios can always be constructed in which there are relevant alternatives that cannot be ruled out that must be ruled out to have knowledge (the higher the standard…the more possibilities must be ruled out). If we do not take practical interests into account (and want to hold onto closure) then we will turn out to not know most ordinary claims to knowledge. In some practical interests scenarios (scientific investigation for instance) the standards ought to be quite high…in which case knowledge may be ruled out — but justified belief will be stronger.