Abstract
This paper explores some consequences of Lewis’s (Australas J Philos 74(4):549–567, 1996) understanding of how knowledge is compartmentalized. It argues, first, that he underestimates how badly it impacts his view. When knowledge is compartmentalized, it lacks at least one of two essential features of Lewis’s account: (a) Elusiveness—familiar skeptical possibilities, when relevant, are incompatible with everyday knowledge. (b) Knowledge is a modality—when a thinker knows that p, there is no relevant possibility where p is false. Lewis proposes compartmentalized knowledge to keep treating knowledge as a modality while mitigating one of its unrealistic epistemological implications: In normal modal epistemic logic (and standard possible world semantics), a thinker always counts as knowing the strongest proposition that follows from the set of all the individual propositions that this thinker knows. Lewis’s compartmentalization proposal is that thinkers merely know the conjunctions of propositions that are known in each of, but not across, their compartments. The irony is that in avoiding overblown knowledge the view now allows for thinkers to attend to skeptical error possibilities and yet knowledge is present. The account avoids inflation of knowledge in one sense only to acquire another type of knowledge the view denies subjects can have. This problem motivates an inspection of knowledge accounts whose intra-compartment closure principles are weaker than those that are valid in normal modal-logic. The conclusion is that some formulations of closure can avoid the challenge Lewis’s view faces. Nevertheless, even these closure principles pose a barrier—perhaps an implausible barrier—for knowledge of ignorance. Even when the reasoning supporting the lack of knowledge is sound, a subject cannot always know she doesn’t know. Interestingly, this obstacle is one that knowledge of knowledge doesn’t seem to face.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
For instance, Williamson (2013) models Gettier cases in (normal) modal logic and regards the above strong closure of known propositions as a “harmlessly simplifying idealization of the models.” (2013, 4). In Sharon and Spectre (2013b) we argue that normal modal logic cannot adequately capture Gettier cases within some of the internalist views that validate Gettier’s assumptions. A salient problem, for instance, is suggested by Gettier’s (1963, 121) condition that a justified belief can be false. Since Williamson’s model has a non-reflexive doxastic accessibility relation, a justified belief can indeed be false. However, it will also be the case that justification is will be closed in the strong sense discussed in the main text. Though these two are not contradictory, it is difficult to reconcile the strong multi-premise justification closure with a view that accepts that false propositions are sometimes justified. Williamson (2015) resolves this issue by modeling Gettier cases with neighborhood rather than the standard possible world semantics. Multi-premise closure isn’t valid in these models, let alone the normal modal logic type of closure from the main text that doesn’t differentiate between known premises and known conclusions.
More carefully, it is not that knowledge “goes away” or “evaporates.” Rather, in those contexts, “know” expresses a relation between a subject and a proposition that almost never holds.
To see the difference I am speaking to here, think the role of attention in Lewis’s view. It is possible to rethink the idea that what a knowledge ascriber is thinking of makes a difference to whether the attribution is true. Attention—the focus of awareness, may or may not play this theoretical role. It isn’t up to the theoretician to say whether this attention is compartmentalized.
Lewis (1996, 556) explicitly rejects the claim that knowledge entails belief. So belief compartmentalization doesn’t necessarily translate into Comp-K. There are though, questions about how the two papers—Lewis (1982) and (1996)—can be combined. For instance, how do beliefs that are part of an inconstancy fit into the Comp-K picture?
One consequence of belief compartmentalization that deserves mention, is that on Lewis’s view believing \(\lnot {p}\) doesn’t entail (even if knowledge does entail belief) that a subject doesn’t know that p. However, regardless of compartmentalization, it doesn’t seem like Lewis’s view rules this possibility out in the first place. See Lewis (1996, 556).
Lewis also has “permissive rules” that tell us when we may properly ignore an EP. But if we may ignore an EP but are not, that would not matter to whether the subject knows that p. Attention says S will not know that p if we are attending to an EP that isn’t eliminated by her evidence regardless of whether we could have properly ignored it (legitimately). See quote in the main text.
Another way of stating this is by defining a (minimally reflexive) accessibility relation R between worlds in the set of worlds W. For this purpose, propositions can be coarse-grained sets of worlds in W. Knowledge that p in the \(<W, R>\) frame can be \(K(p)=\{w: wRx \models x\in {p}\}\). If \(p\vdash \lnot {q}\) then given the Attention rule, if S is attending to q then either S’s evidence eliminates it, or there is at least one q-world \(x'\) such that \(wRx'\). In which case since (\(wRx' \wedge x'\notin {p})\), \(\lnot {K(p)}\) in w. For more formal and detailed 5-tuple frame definition of Lewis’s accessibility relation, see Salow (2016, 1576) and references there to rival Lewisian knowledge definitions.
This isn’t quite right because attending doesn’t always make an uneliminated EP accessible (in the sense of the previous note). But the cases are odd or at least extraordinary. Moreover, it’s hard to see how they could work in first person knowledge attributions. See (Lewis 1996, 556) about the possibly a well trained dog shot a gun and hence the court doesn’t know it’s was the suspect who did it. This amusing example is presented in relation to the Belief rule, I don’t know how if it can sidestep the rule of Attention.
Since it is almost always the case that the subject/speaker is attending to what she is saying, we could also use the claim: “I know I’m not a brain in a vat.” is false whenever uttered.
Lewis uses the rule of resemblance in his attempt to resolve the “static” problems, why there isn’t knowledge in the Gettier cases, the fake barn case, the available but not yet perceived evidence case, and lottery cases. There is room, though, for shifts that are due to salience changes. See Hawthorne (2002) for a Lewisian solution to the preface paradox that hinges on salience in accordance with the rule of Resemblance. The point is, skepticism is mostly a matter of attention shifting and the solutions to other puzzles and paradoxes mostly employ other prohibitive rules.
Unfortunately things are not as neatly separable as my comments so far suggest. There are mixed cases that involve both properties. Cases, for instance, that are part deductive and part modal framework driven, for instance that a priori equivalences are indistinguishable regardless of whether the subject knows of these equivalences. Though we often know well enough what to treat seriously and what to hang on the framework, this isn’t always so. Not too much depends on this, but it looks like Lewis regards the Omniscience Problem as something he can think of in terms of idealization of rationality. See quotes below where he says that he cannot treat the Modal Closure issue in this way.
Lewis notes that this result also follows in any normal modal logic in footnote 21 of (Lewis 1996).
There are psychological facts about compartmentalization that need to be explored before we can be satisfied with an answer to the preface cases along the lines suggested in the main text. Or so it seems to me, at least.
CompModal-CL doesn’t itself entail Subject-K, it only does so assuming that it can provide a counter example to Modal-CL with only two compartments. To see this suppose S has three compartments A, B and C. p could be known in A and B, and q known in B and C. The criterion for subject knowledge could be: S knows that p (simpliciter), iff p is known in the majority of S’s compartments. We would then have the same counterexample to Modal-CL that Lewis gives but with no commitment to Subject-K. Nevertheless, the problems I will discuss below will also hold with this and similar compartment-to-subject-knowledge criteria. (But see the section on indexing Sect. 6.)
It isn’t easy to apply the case Lewis presents to third person knowledge ascriptions. Here is one stab at how it is supposed to work: Presumably, the compartmentalization that is relevant to the determination of the expressed relation is the attributer’s (and maybe also the third party listeners). What seems the most pertinent here is the operative compartment—the compartment from which the sentence is uttered (or more generally the compartment that guides the organisms behavior). Since this will determine the truth value of “S knows that p”, the way the subject is compartmentalized is immaterial (leaving to one side the rule of Belief). She doesn’t have the kind of relation that the philosophical compartment expresses. However, this should also be the case for everyday bushwalking-like compartments. And if so, it isn’t clear how supposing “S knows that p” and “S knows that q” are both true,“S doesn’t know that \(p\wedge q\)” can be true. It seems—in line with the argument in the main text—that Lewis can have CompModal-CL or Elusiveness but not both.
John Hawthorne has suggested to me a way to avoid this problem. Suppose our mental life is similar to a Hydra with many heads each calling attention (in a non-technical sense) to itself. Imagine further that somehow, “I” manages to pick one head/compartment. If this were the case, it seems Lewis could claim that “I know I’m a brain in a vat” is false when referring to the epistemological compartment. So if the referring method picks out the right compartment, BIV-Elusiveness could still be true. We agree, however, that on this suggestion there is no counter example to Modal-Closure. We also agree that third person attributions are hard to make sense of here.
David Enoch suggested that there may be other principles that determine the relation between compartment and subject knowledge. For instance, a subject knows whatever is know in a relevant compartment. Like with the Hydra case of the previous footnote, I don’t deny that this is possible. I just don’t see—at least not without complete ad hocery what could motivate CompModal-CL without losing Elusiveness. In this case, Modal-CL is retained, it seems. I don’t want to deny the possibility of some combination of CompModal-CL with Elusiveness. Nor can I. What I do want to emphasize is that the epistemology as it stands makes incompatible commitments and that the shape it can take by rejecting one (or more) of them depends heavily on the principle governing the relation between compartment and subject knowledge. It seems to me that the psychology of attention and compartmentalization can contribute here.
But there is also a dissimilarity here because “as a” beliefs are also expressions of awareness of other (at least potential) roles. This is not typical of (and not always possible in) compartmentalization cases.
Moshe Halbertal has proposed the following type of case: A Captan of sinking ship is also the father of two of the young passengers. As a farther he will do anything to save his kids while as a Captan he must be impartial. We are not concerned with this kind of compartmentalization (assuming that it is). But it is useful to see that this kind of devision need not be unconscious.
In several contexts “belief that” combines well with “as a” but so would “belief in.” E.g., “As a reporter I believe in free speech, but not as a conservative.” In other contexts “as a” combines rather badly with “believe that.” In reference to the past (assuming there isn’t some backstory)“as a X I believe that” sound bad and is better when it comes to the future: “As a reporter I believe that it will rain tomorrow, but not as a reader.” “As a reporter I believe that it rained yesterday....” This might be because it is harder to imagine how the role is relevant. But it is not clear to me that this is the explanation.
I do not want to deny that there are other expression types that mark compartments (or index to compartments). I just don’t know of any. Is it possible that the indexing is subconscious? Here too, psychological data may be useful.
Let me say again that Comp-K can be true even if attention (or salience) has no impact on what is known or unknown. Comp-K can result from belief compartmentalization together with the view that knowledge entails belief. For instance, assuming I believe that p in compartment A and \(\lnot q\) in compartment B while \(p\vdash q\). I might then know that p in A but not in B. So though I cannot develop these ideas here, compartmentalization might have very wide epistemological implications.
Jason Stanley’s view (2005, 18–19) is vulnerable to this problem in cases where p and \((p\vdash {q})\) are known as a conjunction (i.e., \(K((p\vdash {q})\wedge {p})\)). Of course there is no problem stating the case in this way, but for clarity I will use the two-premise version. Stanley’s reason for focusing on the more restrictive principle is orthogonal to accepting his “single-premise closure” and how it differs from ClosedComp. So the problem concerns not merely possible but actual views.
Naturally, it is possible to plug in other knowledge obstructing attention or salience conditions.
I also note that even if there is a solution to this problem and the subject doesn’t in fact know that he will lose the lottery, the advocates of these views still need to get used to claims like the following: He knows he will not be able to afford a Safari trip but he doesn’t know that he will not win this money in the lottery.
The principle itself, even without knowledge of its truth, is weaker than the K-axiom \(K(p\supset {q})\supset {(K}p\supset {K}q)\) that with the inferences and assuming knowledge is retained is equivalent to MPC. It is stronger, though than SPC.
I am assuming that there is no problem in a compartment that has nothing to do with skeptical scenarios or whatever—there is no problem for me coming to know that my plane is stoping in Chicago. After all, if I didn’t reason a priori in the first compartment we would not think of denying that I can know this in the second.
Much of what follows I owe to Daniel Rothschild.
Socrates (or Plato’s Socrates) probably never states the paradoxical claim that in popular culture is often attributed to him: that the only thing he knows is that he knows nothing. The name, then, shouldn’t be taken too seriously.
References
Cohen, S. (1999). Contextualism, skepticism, and the structure of reasons. Philosophical Perspectives, 13(s13), 57–89.
Egan, A. (2008). Seeing and believing: Perception, belief formation and the divided mind. Philosophical Studies, 140(1), 47–63.
Gettier, E. L. (1963). Is justified true belief knowledge? Analysis, 23(6), 121–123.
Greco, D. (2015). Iteration and fragmentation. Philosophy and Phenomenological Research, 91(3), 656–673.
Hawthorne, J. (2002). Lewis, the lottery and the preface. Analysis, 62(3), 242–251.
Hawthorne, J. (2003). Knowledge and lotteries. Oxford: Oxford University Press.
Lewis, D. (1982). Logic for equivocators. Noûs, 16(3), 431–441.
Lewis, D. (1996). Elusive knowledge. Australasian Journal of Philosophy, 74(4), 549–567.
Norby, A. (2014). Against fragmentation. Thought: A Journal of Philosophy, 3(1), 30–38.
Salow, B. (2016). Lewis on iterated knowledge. Philosophical Studies, 173(6), 1571–1590.
Sharon, A., & Spectre, L. (2013a). Epistemic closure under deductive inference: What is it and can we afford it? Synthese, 190(14), 2731–2748.
Sharon, A. & Spectre, L. (2013b). Models of internalism. MS.
Sharon, A., & Spectre, L. (2017). Evidence and the openness of knowledge. Philosophical Studies, 174(4), 1001–1037.
Spectre, L. (2009). Knowledge closure and knowledge openness: A study of epistemic closure principles. PhD thesis, Department of Philosophy, Stockholm University.
Stalnaker, R. (1984). Inquiry. Cambridge: MIT.
Stanley, J. (2005). Knowledge and practical interests. Oxford: Oxford University Press.
Williamson, T. (2000). Knowledge and its limits. Oxford: Oxford University Press.
Williamson, T. (2013). Gettier cases in epistemic logic. Inquiry, 56(1), 1–14.
Williamson, T. (2015). A note on gettier cases in epistemic logic. Philosophical Studies, 172(1), 129–140.
Acknowledgements
I presented several versions of this paper at Lund University; Stockholm University’s 2016 international epistemology workshop; Israel’s 2017 Philosophical Association conference; The Logic, Language, and Cognition Center at the Hebrew University; ECUP 9 at LMU Munich; University of Arizona; and University of Sheffield. I would like to thank everyone who attended. For discussions, comments, objections, and suggestions that significantly improved this paper I’m indebted to Stewart Cohen, Juan Comesaña, Julien Dutant, David Enoch, Paul Faulkner, Mikael Janvid, Moshe Halbertal, John Hawthorne, Maria Lasonen-Aarnio, Ofra Magidor, Ittay Nissan-Rozen, Erik J Olsson, Peter Pagin, Baron Reed, Daniel Rothschild, and Assaf Sharon.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Spectre, L. Compartmentalized knowledge. Philos Stud 176, 2785–2805 (2019). https://doi.org/10.1007/s11098-018-1151-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11098-018-1151-2