Propositional and doxastic justification

Drawing on the results of previous chapters, the proposal is made to interpret the complex operator ⌜¬K¬K⌝ as encoding propositional justification and the complex operator ⌜¬K¬K⌝ as encoding doxastic justification—where in each case justification is understood to be justification all things considered. Accordingly, not only propositional but also doxastic justification is construed as a feature of one’s epistemic situation rather than a feature of one’s beliefs. On this view, both types of justification are non-factive. The proposed account is defended against a number of putative counterexamples, the allegation that it confuses epistemic permissibility with epistemic blamelessness, and the charge that it fails to heed plausible reliabilist constraints on justification. At crucial junctures this defence relies on the availability of theorems governing the aforementioned complex operators that were proved in chapter 5.

Competing views

The present account, which construes justification as a kind of epistemic possibility of knowing, or of being in a position to know, competes with three recently advanced theories of justification. Of these competitors, the first two construe doxastic justification as the metaphysical possibility of knowing. While they differ in some details, these views share certain problematic features: they fail to yield a corresponding account of propositional justification, have trouble vindicating an intuitive principle of closure for justified belief, and fail to comply with the independently plausible principle that if one has a justified belief, one is in no position to rule out that one has knowledge. The present account does not have these problematic features. According to the third competitor, |φ‎| is propositionally justified in one’s situation just in case it would be abnormal—and so require explanation—if |φ‎| were to be false in the presence of the evidence that one possesses in that situation. This normic theory of justification validates the principle that propositional justification agglomerates over conjunction, and in so doing, violates the constraint that propositions of the form ⌜φ‎ & ¬Kφ‎⌝ never be justified. It likewise contradicts the independently plausible principle that whenever |φ‎| is propositionally justified all things considered, |¬Kφ‎| is not. The present account does not face these problems, since it rejects the relevant agglomeration principle and treats the condition encoded by ⌜¬K¬Kφ‎⌝ as luminous.

On being in a position to know

The notion of being in a position to know contrasts with that of knowledge, and yet, both notions are intimately related. Just as one can only know what is true, one can only be in a position to know what is true. To the extent that knowledge requires safe belief, being in a position to know implies being in a position to safely believe. For any p, if one knows p, one is in a position to know p, whereas the converse does not hold. Doing the best that one is in a position to do to decide a given question may be less than doing everything that one is in a position to do to decide that question, because one cannot do every such thing at once. If one is in a position to know p, one has the opportunity to come to know p upon doing the best that one is in a position to do to decide whether p holds. It is explained what this opportunity involves and what is involved in seizing it.

What’s wrong with internalism?

Extant internalists are either accessibilists or mentalists. Accessibilists standardly claim that whenever p is justified, one is in a position to know this fact by reflection alone or else this fact has grounds that are accessible in this way. The argument for this claim assumes that one ought to believe p only if p is justified; that therefore, grounds for justification must be luminous; and that only facts accessible by reflection fit the bill. It founders already because too few conditions are luminous. A non-standard version of accessibilism avoids this problem by conceiving of the grounds for justification as facts about what one is in a position to know by reflection alone. The argument marshalled in its favour fails to show why they cannot be facts about what one is in a position to know by other means. Mentalists claim that whenever p is justified this fact is grounded in facts about one’s mental states. One argument contends that only mentalism can account for certain structural features of justification. It founders because the present account explains these features equally well. Another argument contends that only mentalism heeds our intuitions about sceptical cases. It founders because mental states can help to confer justification only if they are arrived at in certain ways—a fact not itself determined by such states. Accessibilism and mentalism lack sufficient support and incur costs internalists do better without. The present account delivers all the goods that internalists should wish for, without making justification an internal condition.

Two systems of epistemic logic

Drawing on the results of chapters 2 to 4, two non-normal, multimodal axiomatic systems for both knowledge (k) and being in a position to know (K) are introduced—an idealized system and a weaker, more realistic system. Both share important theorems governing the complex operators ‘¬K¬K’ and ‘¬K¬K’, whose availability will be of crucial importance in later chapters. Unlike the realistic system, the idealized system requires subjects to be logically omniscient and must therefore ultimately be rejected in favour of the realistic system. A semantic characterization of the idealized system is devised that shows it to be sound and allows us to invalidate principles we previously found unacceptable for independent reasons. Since the realistic system is weaker, this result implies that it too has these features. Both systems imply that each of ⌜¬K¬Kφ‎⌝, ⌜K¬Kφ‎⌝, and ⌜¬K¬Kφ‎⌝ encodes a luminous condition. The scenario of the unmarked clock presents a prima facie case against this implication. It is shown that the relevant anti-luminosity argument presupposes the principle that being in a position to know (K) distributes across provable conditionals—a principle that has been shown to be deeply problematic and that the realistic system is designed to flout.

Concluding Remarks

According to the account of epistemic justification developed in this book, one has propositional justification for p just in case one is in no position to know that one is in no position to know p; and one has doxastic justification for p just in case one is in no position to know that one does not know p. The account gives internalists much of what they want from a theory of justification—in particular, a notion of justification according to which propositional justification is non-factive and luminous, underwrites principles of positive and negative introspection, and remains available to the victims of systematic deception. All the while, that notion is explained in terms of other notions that clearly belong to the knowledge-firsters’ toolkit, and coheres with an externalist account of the grounds for justification.

Grounds for justification

We must distinguish between the condition of a proposition’s being justified in one’s situation and the metaphysical grounds determining that this condition obtains. While the former is luminous, the latter need not be. It is argued that knowing is a strict full ground for doxastic justification, and being in a position to know is a strict full ground for propositional justification. It follows that facts about one’s evidence that serve as strict partial grounds for knowing are strict partial grounds for doxastic justification, and facts about one’s evidence that serve as strict partial grounds for being in a position to know are strict partial grounds for propositional justification. Even if only partial, such evidential grounds can only be assumed to be available in some, but not all, cases in which one has doxastic justification without knowing, and propositional justification without being in a position to know. A more comprehensive account identifies facts about evidential probabilities as facts that yield strict full grounds for justification. While one’s evidence is the totality of what one is in a position to know, the evidential probability of p equals the probability of p conditional on one’s evidence. The account requires taking the notion of evidential probability as primitive. It uniformly applies to all cases of justification, including the bad cases envisaged by radical scepticism. Degrees of strength of justification are explained in terms of facts about evidential probabilities. Just as their grounds, degrees of strength of justification are not luminous, even if justification is.

Principles of epistemic logic I: Knowledge

All epistemic logics come with some idealizations. Not all such idealizations seem acceptable. A large family of epistemic logics assume that if ⌜φ‎⌝ and ⌜ψ‎⌝ are logically equivalent, so are ⌜One knows that φ‎⌝ and ⌜One knows that ψ‎⌝. This assumption, characteristic of normal epistemic logics but also of many non-normal ones, is acceptable only if the objects of knowledge can be construed as sets of possible worlds known under some mode of presentation or other, where knowledge-ascriptions do not yet make those modes explicit. Unlike fine-grained conceptions that reject the assumption, such coarse-grained conceptions of the objects of knowledge have the untoward consequence that failures of logical omniscience are no longer expressible in the logic. But even on coarse-grained conceptions, epistemic logic cannot be expected to be normal. Fine-grained conceptions allow for failures of logical omniscience to be expressible in the logic. On balance, fine-grained conceptions are to be preferred. Against this backdrop, candidate principles for inclusion in the logic of knowledge are critically reviewed in the light of general epistemological considerations. Very few survive closer scrutiny.

Principles of epistemic logic II: Being in a position to know

Principles of being in a position to know that are candidates for inclusion in a combined logic for knowledge and being in a position to know are critically reviewed. Some are disqualified for reasons similar to those that already disqualified their counterparts for knowledge, others for other reasons, since being in a position to know, unlike knowledge, does not imply belief. Of those that survive closer scrutiny, some are restricted versions of more general principles that ought to be rejected. Two unfamiliar principles are singled out and given a detailed defence. Since one of them affirms outright that some non-trivial condition is luminous, its defence involves demonstration that, at least for this isolated case, the anti-luminosity argument devised in Williamson (2000) can be resisted. Throughout, and in line with the results of chapters 2 and 3, it is being assumed that knowledge requires safe belief, and correspondingly, that being in a position to know requires being in a position to safely believe.

Outline of a theory of justification

Core theses of the novel account of justification to be developed are first stated: one has propositional justification for p just in case one is in no position to know that one is in no position to know p; and one has doxastic justification for p just in case one is in no position to know that one does not know p. Unlike other theories that conceive of justification in terms of the metaphysical possibility of knowing, the present account thus construes it as a distinctive kind of epistemic possibility. It treats propositional justification as non-factive, both its presence and its absence as luminous conditions, and by assuming a weak non-normal modal logic for knowledge and being in a position to know, validates principles of positive and negative introspection for it. The account thereby attributes features to justification that internalists care about. But it does so without construing justification as an internal condition. The account allows one to systematically distinguish between the condition of being justified and the metaphysical grounds for its obtaining, thereby heeding externalist insights into the difference between the good cases and the bad cases envisaged by radical scepticism. Lines of argument that show the account’s potential, e.g. in dealing with the preface and lottery paradoxes, are previewed, and so are lines of defence against challenges and objections, including prominent anti-luminosity arguments.