Consider two cases. In the first, you are standing in the desert under the scorching sun. Beyond the dunes, you see an expanse of water and form the belief that there is water. In the second, your twin is standing in the desert under the scorching sun. Beyond the dunes, she sees a mirage suggesting an expanse of water, yet without knowing that it is a mirage that she is seeing. Like you, your twin forms the belief that there is water. To fix ideas, let us assume that your conditions, unlike your twin’s, could not easily be ones in which you witnessed a mirage. That is a matter of geography, meteorology, and ultimately physics.

The two cases differ in important respects. Your belief is true, your twin’s is false. All things being equal, in forming your belief, you come to know that there is water. Your twin, by contrast, acquires no such knowledge. The process by which you form your belief involves a suitable causal relation between you and the fact you believe. It is a case of perception. The process by which your twin forms her belief involves no such causal relation: your twin is in no position to perceive what is not there.

But there are also many respects in which these two cases are relevantly alike: the two of you are twins, you both stand in the desert under the scorching sun, gaze in the same direction, and the stimulation patterns on your retinas are very similar—so much so that, subjectively, they are indistinguishable and prompt belief in the very same proposition. I contend that, in addition, both of you are justified in believing what you do and that both of you had propositional justification for so believing before forming your respective beliefs. My reasons are as follows. Before and after you form your respective beliefs, neither of you is in a position to rule out that they are in a position to know that there is water. Once you have formed your respective beliefs, neither of you is in a position to rule out that they do in fact know that there is water.

According to the account set out in Justification as Ignorance (Rosenkranz, 2021; henceforth JAI), one is doxastically justified in believing p, if one does, iff one is in no position to know that one does not know p. Similarly, one has propositional justification for believing p iff one is in no position to know that one is in no position to know p. Accordingly, then, doxastic justification is some kind of epistemic possibility of knowing, and propositional justification is some kind of epistemic possibility of being in a position to know. I say ‘some kind of epistemic possibility’ because the epistemic possibility in question is to be understood in terms of one’s not being in a position to know rather than in terms of one’s not knowing. If you merely do not know that you do not know p, but are in a position to know that you do not know p, then your belief in p, if any, is not justified. At best, it is premature, at worst, it is reckless.

The proposal is controversial. One half is less controversial than the other. The less controversial half consists in the implications (a) that one is never doxastically justified in believing p if one is in a position to figure out that one does not know p, and (b) that one never has propositional justification for believing p if one is in a position to figure out that one is in no position to know p. The far more controversial half consists in the converse implications (c) that one already is doxastically justified in believing p when one is in no position to rule out that one knows p, and (d) that one already has propositional justification for believing p when one is in no position to rule out that one is in a position to know p.

The dead, the comatose, and the seriously inebriated are in a position to know nothing or very little about their epistemic situation. Similarly, someone who lacks the concept of knowledge is in no position to know that they do not know—or are in no position to know—p, for any proposition p. It does not follow that such subjects have justification for believing propositions aplenty. Therefore, suitable idealizations must be in place, restricting the account to epistemic subjects so idealized. Even with such an idealization in place, however, (c) and, in particular, (d) may be thought vulnerable to the threat of counterexample. In my reply to Waxman (2022) and Zhan (2022), I detail how formidable such threats may, after all, successfully be averted.

The account makes use of two epistemic notions, that of knowledge (k) and that of being in a position to know (K). Being in a position to know is perched somewhere on the line extending between the pole of knowledge and the pole of the mere feasibility of knowledge. Knowledge implies being in a position to know (i.e. ˹kp ⊃ Kp˺ holds). Like the mere feasibility of knowing, but unlike knowledge, being in a position to know does not imply belief. Like knowledge, but unlike the mere feasibility of knowing, being in a position to know is factive (i.e. ˹Kp ⊃ p˺ holds). The account accordingly implies that, if one knows p, one is doxastically justified in believing p (i.e. ˹kp ⊃ ¬K¬kp˺ holds). It likewise implies that, if one is in a position to know p, one has propositional justification for believing p (i.e. ˹Kp ⊃ ¬K¬Kp˺ holds).

The logic of justification piggy-backs on a bimodal logic for ‘k’ and ‘K’. I consider two such bimodal systems, an idealized one and a more realistic one. The idealized system incorporates the principle that, if one is in a position to know p, one is in a position to know each logical implication of p. In my reply to Rossi (2022), I detail some of the reasons why I think this principle requires too strong idealizations and should be rejected. Accordingly, the logic for ‘K’ cannot be a normal modal logic. The realistic system still incorporates some consequences of the aforementioned principle, e.g. the plausible thesis that, if one is in a position to know p, one is also in a position to know that one is in no position to know p’s negation (i.e. ˹Kp ⊃ K¬K¬p˺). There are others of a comparable degree of plausibility that can be assumed to hold, at least for reasonably idealized agents.

On the account proposed, propositional justification is non-factive, as ˹¬K¬Kp ⊃ p˺ proves invalid. The same goes for doxastic justification. The by far most controversial claim of JAI is that propositional justification is also luminous, i.e. that ˹¬K¬Kp ⊃ K¬K¬Kp˺ holds. In a nutshell, the argument for the claim is this. A case in which ˹K¬Kp˺ holds—and in which one does the best one is in a position to do in order to decide whether one is in a position to know p—will be a case in which one believes ˹¬Kp˺. Such a case, I submit, will not be a case in which one also believes ˹¬K¬Kp˺. At least for knowledge-seeking subjects, believing both ˹¬Kp˺ and ˹¬K¬Kp˺ would be blatantly irrational. Every epistemic logic comes with some idealizations. That the targeted subjects are not irrational in this regard is one such idealization I put in place. Arguably, however, doing the best one is in a position to do in order to decide whether ˹¬K¬Kp˺ holds implies doing the best one is in a position to do in order to decide whether ˹¬Kp˺ holds. So, if one truly believes ˹¬K¬Kp˺ on the basis of doing the former, there would not be a close case in which one falsely believes ˹¬K¬Kp˺ on that kind of basis. For, believing anything on that kind of basis, one would then also do the latter and, if ˹K¬Kp˺ held, would accordingly come to believe ˹¬Kp˺ on that basis. Given the foregoing rationality constraint, one would not then also believe ˹¬K¬Kp˺. More must evidently be said in order to defend the luminosity of ˹¬K¬Kp˺ against Williamson-style arguments (e.g. that one is in a position to believe ˹¬K¬Kp˺ upon doing the best one is in a position to do in order to decide the matter, whenever ˹¬K¬Kp˺ holds). Such efforts are made in JAI, but this précis is not the place to rehearse them. However, I will say more below on the matter in my reply to Smith (2022).

Further principles are added to the epistemic logic that cannot all be reviewed here either. Suffice it to say that, with the sole exception of ˹¬K¬Kp ⊃ K¬K¬Kp˺ and one further principle in the same ballpark that allows for a similar kind of rationale (viz. ˹kp ⊃ K¬K¬kp˺), the epistemic logic is rather weak. Even so, the resulting logic for propositional justification turns out to be as strong as D45. That is to say, where ˹Jp˺ is ˹¬K¬Kp˺, it licenses all of the following: ˹J¬p ⊃ ¬Jp˺, ˹Jp ⊃ JJp˺, and ˹¬Jp ⊃ J¬Jp˺. If ˹Jp˺ is interpreted as saying that one has propositional justification for p, the latter two of these three correspond to principles of positive and of negative introspection for propositional justification. In my reply to Dutant (2022), I address one type of worry about ˹J¬p ⊃ ¬Jp˺ that puts pressure on that interpretation.

One further result is that the absence of propositional justification, too, proves luminous (i.e. ˹¬Jp ⊃ K¬Jp˺ holds). Another crucially important result is that the following agglomeration principle for justification fails: ˹Jp ˄ Jq ⊃ J(p ˄ q)˺. One may be in a position to know each of p and q individually—and hence be in no position to know one is in no such position—and nonetheless know that one is in no position to know their conjunction. Examples are legion (for one example, see Heylen, 2016).

The account can be applied to a number of epistemological puzzles and problem cases. I here focus on three such applications. First, with the full logic in place, the structural features of justification already ensure that the Moorean conjunction ˹p ˄ ¬Kp˺ and others like it are never justified. Second and third, the account also lends itself to fairly straightforward solutions to the lottery and preface paradoxes. Given what one knows about the fair lottery before the draw takes place or is announced, one is in a position to know that one is in no position to know, of any particular ticket, that it is a loser. Hence, on the present account, one has no justification for believing, of any particular ticket, that it is a loser. The lottery paradox does not get off the ground. One may be in no position to rule out that one is in a position to know p, for each individual p written in the main body of one’s work, and yet be in a position to know, and coherently say so in the preface, that one is in no position to know their conjunction. Justification does not agglomerate over conjunction, which is why the preface paradox poses no threat.

We must distinguish between the condition of having justification (of either variety) and the factors that conspire to determine that this condition obtains—i.e. its metaphysical grounds. That propositional justification is luminous does not imply that so are its metaphysical grounds. What grounds your justification for believing that there is water is the availability of a knowledge-producing perceptual process whose input is the expanse of water beyond the dunes and whose output is your belief that there is water. This fact puts you in a position to know that there is water and prevents you from ruling out that you are in a position to know that there is. What grounds your twin’s justification for believing that there is water is her being in a position to see a mirage without being in a position to see through it. This fact prevents your twin from ruling out that she is in a position to know that there is water. (If your twin was in a position to know that she sees a mirage when looking beyond the dunes, she would after all be in a position to know that she is in no position to know that there is water.)

The example suggests that the grounds for one’s justification for p in cases in which one is in a position to know p systematically differ from the grounds for one’s justification for p in all other cases. That is true. But one and the same fact may have several metaphysical grounds, depending on the levels of metaphysical explanation to which one descends. The example does not suggest that there is no level of metaphysical explanation at which we find common grounds for either case. A more sophisticated account that identifies such common grounds is provided in JAI. The account conceives of the evidential probability of q as already being 1 if one is merely in a position to know q and treats facts about evidential probability as more basic than facts about what one is in no position to know. The account’s key claim is that if one has propositional justification for p, this fact is grounded in the fact that the evidential probability of ˹K¬Kp˺ equals 0. Since, ex hypothesi, both ˹¬K¬Kp˺ and ˹K¬Kp˺ encode luminous conditions, this delivers the right results. A different, yet similar, account is given of the common grounds for doxastic justification.

Unlike their externalist opponents, internalists tend to take propositional justification to be both non-factive and luminous and to underwrite principles of positive and negative introspection. The proposed account vindicates all three of these key internalist assumptions. Extant internalists go further, though. They take justification to be internal in at least one of two senses. In the first sense, justification is internal iff it is already fully grounded in the subject’s mental states. That justification is internal in this first sense is the core claim of mentalism. In the second sense, justification is internal iff its presence or its grounds are accessible to the subject by reflection alone. That justification is internal in this latter sense is the core claim of accessibilism. Insofar as these internalist theses are meant to best explain why justification is both non-factive and luminous and underwrites principles of positive and negative introspection, they are unmotivated. For, the proposed account explains the latter features without conceiving of justification as internal in either sense. The argument for luminosity, for instance, is quite compatible with the finding that in order to figure out that one has propositional justification, mere reflection would not do. You and your twin must use your outer senses in order to figure out that you are in no position to rule out that you are in a position to know that there is water. Similarly, the proposed account predicts that justification is not fully grounded in mental states. Collections of facts that jointly determine that you are in a position to perceive water, or that your twin is in a position to see a mirage without being able to see through it, will not always reduce to facts about your actual mental states. To the extent that vindicating the three key internalist assumptions is what makes an account deserving of the label ‘internalist’, the proposed account accordingly is a version of internalism. It nevertheless foregoes commitment to the idea that justification is internal. As we may put it, JAI promotes internalism without the internal.