The KK Principle

In this paper I present a more refined analysis of the principles of deductive closure and positive introspection. This analysis uses the expressive resources of logics for different types of group knowledge, and discriminates between aspects of closure and computation that are often conflated. The resulting model also yields a more fine-grained distinction between implicit and explicit knowledge, and places Hintikka’s original argument for positive introspection in a new perspective.

There are many ordinary propositions we think we know. Almost every ordinary proposition entails some "lottery proposition" which we think we do not know but to which we assign a high probability of being true (for instance: “I will never be a multi-millionaire” entails “I will not win this lottery”). How is this possible - given that some closure principle is true? This problem, also known as “the Lottery puzzle”, has recently provoked a lot of discussion. In this paper I (...) discuss one of the most promising answers to the problem: Stewart Cohen’s contextualist solution which is based on ideas about the salience of chances of error. After presenting some objections to it I sketch an alternative solution which is still contextualist in spirit. (shrink)

_ Source: _Page Count 12 In a previous article, I argued against the widespread reluctance of philosophers to treat skeptical challenges to our a priori knowledge of necessary truths with the same seriousness as skeptical challenges to our a posteriori knowledge of contingent truths. Hamid Vahid has recently offered several reasons for thinking the unequal treatment of these two kinds of skepticism is justified, one of which is a priori skepticism’s seeming dependence upon the widely scorned kk thesis. In the (...) present article, I defend a priori skepticism against Vahid’s criticisms. (shrink)

The knowledge account of assertion - roughly: one should not assert what one does not know - can explain a variety of Moorean conjunctions, a fact often cited as evidence in its favor. David Sosa ("Dubious Assertions," Phil Studies, 2009) has objected that the account does not generalize satisfactorily, since it cannot explain the infelicity of certain iterated conjunctions without appealing to the controversial "KK" principle. This essay responds by showing how the knowledge account can handle such conjunctions without use (...) of the KK principle. (shrink)

The logic of common belief does not always reflect that of individual beliefs. In particular, even when the individual belief operators satisfy the KD45 logic, the common belief operator may fail to satisfy axiom 5. That is, it can happen that neither is A commonly believed nor is it common belief that A is not commonly believed. We identify the intersubjective restrictions on individual beliefs that are incorporated in axiom 5 for common belief.

This paper supersedes an ealier version, entitled "A Non-Standard Semantics for Inexact Knowledge with Introspection", which appeared in the Proceedings of "Rationality and Knowledge". The definition of token semantics, in particular, has been modified, both for the single- and the multi-agent case.

According to the KK-principle, knowledge iterates freely. It has been argued, notably in Greco, that accounts of knowledge which involve essential appeal to normality are particularly conducive to defence of the KK-principle. The present article evaluates the prospects for employing normality in this role. First, it is argued that the defence of the KK-principle depends upon an implausible assumption about the logical principles governing iterated normality claims. Once this assumption is dropped, counter-instances to the principle can be expected to arise. (...) Second, it is argued that even if the assumption is maintained, there are other logical properties of normality which can be expected to lead to failures of KK. Such failures are noteworthy, since they do not depend on either a margins-for-error principle or safety condition of the kinds Williamson appeals to in motivating rejection KK. “Introduction: KK and Being in a Position to Know” Section formulates two versions of the KK-Principle; “Inexact Knowledge and Margins for Error” Section presents a version of Williamson’s margins-for-error argument against it; “Knowledge and Normality” and “Iterated Normality” Sections discuss the defence of the KK-Principle due to Greco and show that it is dependent upon the implausible assumption that the logic of normality ascriptions is at least as strong as K4; finally, “Knowledge in Abnormal Conditions” and “Higher-Order Ignorance Inside the Margins” Sections argue that a weakened version of Greco’s constraint on knowledge is plausible and demonstrate that this weakened constraint will, given uncontentious assumptions, systematically generate counter-instances to the KK-principle of a novel kind. (shrink)

Epistemic transparency tells us that, if an agent S knows a given proposition p , then S knows that she knows that p . This idea is usually encoded in the so-called KK principle of epistemic logic. The paper develops an argument in favor of a moderate version of KK , which I dub quasi-transparency , as a normative rather than a descriptive principle. In the second Section I put forward the suggestion that epistemic transparency is not a demand of (...) ideal rationality, but of ideal epistemic responsibility, and hence that ideally responsible agents verify transparency principles of some sort; I also contend that their satisfaction should not be tied to an internalist epistemology. The central argument in favor of transparency is then addressed in Sections 3 to 8, through the development of a formal system. I show that, in a well-behaved formal setting, a moderate version of transparency is imposed upon us as a result of a number of independent decisions on the structure of higher-order probabilities, as long as we request that our probability and knowledge attributions cohere with each other. Thus I give a rationale to build a model for a hierarchy of languages with different levels of knowledge and probability operators; we obtain an analogous to KK for successive knowledge operators without actually demanding transitivity. The formal argument reinforces the philosophical intuition that epistemic transparency is an important desideratum we should not be too ready to dismiss. (shrink)

The KK principle is typically rejected in externalist accounts of knowledge. However, a standard general argument for this rejection is in need of a supportive explication. In a recent paper, Samir Okasha argues that the standard externalist argument in question is fallacious. In this paper I start off with some critical discussion of Okasha’s analysis before suggesting an alternative way in which an externalist might successfully present such a case. I then further explore this issue via a look at how (...) Fred Dretske’s externalist epistemology, one of the exemplifying accounts, can explain failure of the KK principle. (shrink)

An important question in epistemology is whether the KK principle is true, i.e., whether an agent who knows that p is also thereby in a position to know that she knows that p. We explain how a “transparency” account of self-knowledge, which maintains that we learn about our attitudes towards a proposition by reflecting not on ourselves but rather on that very proposition, supports an affirmative answer. In particular, we show that such an account allows us to reconcile a version (...) of the KK principle with an “externalist” or “reliabilist” conception of knowledge commonly thought to make that principle particularly problematic. (shrink)

Roy Sorensen introduced the concept of an epistemic blindspot in the 1980s. A proposition is an epistemic blindspot for some individual at some time if and only if that proposition is consistent but unknowable by that individual at that time. In the first half of this paper, I extend Sorensen work on blindspots by arguing that there exist blindspots that essentially involve hopes. In the second half, I show how such blindspots can contribute to and impair different pursuits of self-understanding. (...) My arguments throughout this paper draw on Luc Bovens’s account of hope. (shrink)

In chapter 5 of Knowledge and its Limits, T. Williamson formulates an argument against the principle (KK) of epistemic transparency, or luminosity of knowledge, namely “that if one knows something, then one knows that one knows it”. Williamson’s argument proceeds by reductio: from the description of a situation of approximate knowledge, he shows that a contradiction can be derived on the basis of principle (KK) and additional epistemic principles that he claims are better grounded. One of them is a reflective (...) form of the margin for error principle defended by Williamson in his account of knowledge. We argue that Williamson’s reductio rests on the inappropriate identification of distinct forms of knowledge. More specifically, an important distinction between perceptual knowledge and non-perceptual knowledge is wanting in his statement and analysis of the puzzle. We present an alternative account of this puzzle, based on a modular conception of knowledge: the (KK) principle and the margin for error principle can coexist, provided their domain of application is referred to the right sort of knowledge. (shrink)

Williamson (2000a) has argued that posi- tive introspection is incompatible with in- exact knowledge. His argument relies on a margin-for-error requirement for inexact knowledge based on a intuitive safety prin- ciple for knowledge, but leads to the counter- intuitive conclusion that no possible creature could have both inexact knowledge and posi- tive introspection. Following Halpern (2004) I put forward an alternative margin-for-error requirement that preserves the safety require- ment while blocking Williamson’s argument. I argue that the infallibilist conception of knowledge (...) that underlies the new require- ment provides a better account of inexact knowledge and higher-order knowledge than both Williamson’s and Halpern’s. (shrink)

relevant alternatives: I take it that a process is reliable in the actual world iff, in the actual set of outcomes (i.e. beliefs being formed), the frequency of successes (those beliefs being true) is much greater than the frequency of failures (those beliefs being false). One may wish to run a more sophisticated kind of reliabilism, where one demands that a reliable process also be reliable in counterfactual situations, but one need not, and I won’t here. If perception is a (...) reliable belief forming process, then I can know things on the basis of perception. So let’s say I know p on the basis of perception. To know that I know p involves, first, knowing that I believe p, and second, knowing that I believe p on the basis of a reliable belief forming process, by the definition of knowledge. But can I know either of these things? (shrink)

One main argument that has been offered in support of the Knowledge Account of Assertion is that it successfully makes sense of a variety of Moorean-paradoxical claims. David Sosa has objected to the Knowledge Account by arguing that it does not generalize satisfactorily to make sense of the oddity of iterated conjunctions of the form “p but I don’t know whether I know that p”. Recently, Martin Montminy has offered a defense of the Knowledge Account. In this paper, I show (...) that both Montminy’s and Sosa’s arguments fail. First, I argue that Montminy does not offer a good reply to Sosa; then I show that Sosa’s objection actually does not constitute a real threat to the Knowledge Account. (shrink)

Dorr et al. present a case that poses a challenge for a number of plausible principles about knowledge and objective chance. Implicit in their discussion is an interesting new argument against KK, the principle that anyone who knows p is in a position to know that they know p. We bring out this argument, and investigate possible responses for defenders of KK, establishing new connections between KK and various knowledge-chance principles.

We show that if an agent reasons according to standard inference rules, the truth and introspection axioms extend from the set of non-epistemic propositions to the whole set of propositions. This implies that the usual axiomatization of partitional possibility correspondences is redundant, and provides a justification for truth and introspection that is partly based on reasoning.

This paper argues for several related theses. First, the epistemological position that knowledge requires safe belief can be motivated by views in the philosophy of science, according to which good explanations show that their explananda are robust. This motivation goes via the idea—recently defended on both conceptual and empirical grounds—that knowledge attributions play a crucial role in explaining successful action. Second, motivating the safety requirement in this way creates a choice point—depending on how we understand robustness, we'll end up with (...) different conceptions of safety in epistemology. Lastly, and most controversially, there's an attractive choice at this point that will not vindicate some of the most influential applications of the safety-theoretic framework in epistemology, e.g., Williamson's arguments against the KK principle, and luminosity. (shrink)

In this paper I present a qualified defense of the KK principle. In section one I introduce two popular arguments against the KK principle, along with an example in which these arguments seem to prove too much. In section two I provide a simple formal model of knowledge in which KK holds, and which I argue provides an attractive analysis of the example from section one. I go on argue that when this model is combined with contextualism, we can retain (...) our attractive analysis of the example, while also explaining away the appeal of the aforementioned arguments against KK. I use the same maneuver contextualists have used to defend epistemic closure principles--I argue that KK holds within contexts, but can fail across contexts. (shrink)

This chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. No previous exposure to epistemic logic is assumed. Epistemic-logical topics discussed include the language and semantics of basic epistemic logic, multi-agent epistemic logic, combined epistemic-doxastic logic, and a glimpse of dynamic epistemic logic. Epistemological topics discussed include Moore-paradoxical phenomena, the surprise exam paradox, logical omniscience and epistemic closure, formalized theories of knowledge, debates about higher-order knowledge, and issues of knowability raised by Fitch’s paradox. The references (...) and recommended readings provide gateways for further exploration. (shrink)

Knows-knows principles in epistemology (KK principles for short) say that if you know some proposition, then you are in a position to know that you know it. This paper examines the viability of analogous principles in ethics, which I call ought-ought principles (OO principles for short). Several epistemologists have recently offered new defenses of KK principles and of other related principles and there has recently been an increased interest in examining analogies between ethics and epistemology and so it seem natural (...) to examine whether defenses of KK and related principles carry over to OO principles. In this paper I introduce two OO principles and I show how some arguments in favor of KK carry over to them. Then I show how these OO principles can be used to shed light on a much-discussed case in ethics, that of Professor Procrastinate. (shrink)

In a recent paper, Murali Ramachandran endorses a principle that he thinks can help us solve the surprise test puzzle and cause problems for a Williamsonian argument against KK principles. But in this paper I argue that his principle is false and as a result it cannot do either.

This essay defends a principle that promises to help illuminate the nature of reflective knowledge. The principle in question belongs to a broader category called knows-knows principles, or KK principles for short. Such principles say that if you know some proposition, then you're in a position to know that you know it.KK principles were prominent among various historical philosophers and can be fruitfully integrated with many views in contemporary epistemology and beyond—and yet almost every contemporary analytic epistemologist thinks that they (...) are false.Regarding their historical pedigree: they've been endorsed by Plato, Aristotle, Augustine, Averroes, Aquinas, Spinoza, and Schopenhauer, among others.1Regarding... (shrink)

According to Fred Dretske's externalist theory of knowledge a subject knows that p if and only if she believes that p and this belief is caused or causally sustained by the information that p. Another famous feature of Dretske's epistemology is his denial that knowledge is closed under known entailment. I argue that, given Dretske's construal of information, he is in fact committed to the view that both information and knowledge are closed under known entailment. Hence, if it is true (...) that, as Dretske also believes, accepting closure leads to skepticism, he must either embrace skepticism or abandon his information theory of knowledge. (shrink)

In the current discussion on epistemic value, several philosophers argue that understanding enjoys higher epistemological significance and epistemic value than knowledge—the epistemic state the epistemological tradition has been preoccupied with. By noting a tension between the necessary conditions for understanding in the perhaps most prominent of these philosophers, Jonathan Kvanvig, this paper disputes the higher epistemological relevance of understanding. At the end, on the basis of the results of the previous sections, some alternative comparative contrasts between knowledge and understanding are (...) briefly explored, including one in which an analogue to the KK-principle for knowledge, the “UU-principle”, does not hold for a different reason than that for which the former principle fails. (shrink)

ABSTRACT: In this paper, I revisit arguments for and against various theses concerning higher-order knowledge in order to fully gauge their impact on the principles of positive and negative introspection. I argue that the expression has at least two salient understandings: the more common one, labelled, validates the principle of positive introspection, while the other which is less common, labelled, supports some of the arguments against this principle.

The Surprise Exam Paradox continues to perplex and torment despite the many solutions that have been offered. This paper proposes to end the intrigue once and for all by refuting one of the central pillars of the Surprise Exam Paradox, the 'No Friday Argument,' which concludes that an exam given on the last day of the testing period cannot be a surprise. This refutation consists of three arguments, all of which are borrowed from the literature: the 'Unprojectible Announcement Argument,' the (...) 'Wright & Sudbury Argument,' and the 'Epistemic Blindspot Argument.' The reason that the Surprise Exam Paradox has persisted this long is not because any of these arguments is problematic. On the contrary, each of them is correct. The reason that it has persisted so long is because each argument is only part of the solution. The correct solution requires all three of them to be combined together. Once they are, we may see exactly why the No Friday Argument fails and therefore why we have a solution to the Surprise Exam Paradox that should stick. (shrink)

We present a new logic -based approach to the reasoning about knowledge which is independent of possible worlds semantics.? k is a non- Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom K i??? and some minimal conditions concerning common knowledge in a group. Knowledge is explicit and all forms of the logical omniscience problem (...) are avoided. Various stronger epistemic properties such as positive and/or negative introspection, the K-axiom, closure under logical connectives, etc, can be restored by imposing additional semantic constraints. This yields corresponding sublogics for which we present sound and complete axiomatizations. As a useful tool for general model constructions we study abstract versions of some 3-valued logics in which we interpret truth as knowledge. We establish a connection between? k and the well-known syntactic approach to explicit knowledge proving a result concerning equi-expressiveness. Furthermore, we discuss some self - referential epistemic statements, such as the knower paradox, as relaxations of variants of the liar paradox and show how these epistemic "paradoxes" can be solved in? k. Every specific? k - logic is defined as a certain extension of some underlying classical abstract logic. (shrink)

If we hold that perceiving is sufficient for knowing, we can raise a powerful objection to dreaming skepticism: Skeptics assume the implausible KK-principle, because they hold that if we don’t know whether we are dreaming or perceiving p, we don’t know whether p. The rejection of the KK-principle thus suggests an anti-skeptical strategy: We can sacrifice some of our self-knowledge—our second-order knowledge—and thereby save our knowledge of the external world. I call this strategy the Self-Knowledge Gambit. I argue that the (...) Self-Knowledge Gambit is not satisfactory, because the dreaming skeptic can avail herself of a normative counterpart to the KK-principle: When we lack second-order knowledge, we should suspend our first-order beliefs and thereby give up any first-order knowledge we might have had. The skeptical challenge is essentially a normative challenge, and one can raise it even if one rejects the KK-Principle. (shrink)

I argue that a version of the so-called KK principle is true for principled epistemic reasons; and that this does not entail access internalism, as is commonly supposed, but is consistent with a broad spectrum of epistemological views. The version of the principle I defend states that, given certain normal conditions, knowing p entails being in a position to know that you know p. My argument for the principle proceeds from reflection on what it would take to know that you (...) know something, rather than from reflection on the conditions for knowledge generally. Knowing that you know p, it emerges, is importantly similar to cases of psychological self-knowledge like knowing that you believe p: it does not require any grounds other than your grounds for believing p itself. In so arguing, I do not rely on any general account of knowledge, but only on certain plausible and widely accepted epistemological assumptions. (shrink)

A number of related fully quantified epistemic-doxastic logics are developed from a study of various epistemic principles. These logics countence constructions such as "Everyone knows that ...", hence are more expressive then Hintikka's epistemic-doxastic logic. A two sorted presupposition-free base logic is employed to distinguish those things capable of knowledge and belief from those which are not, and to distinguish denoting from non-denoting terms. Logics for both concurrent and virtual senses of "Knowledge" and "belief" are developed, both axiomatically and semantically. (...) The logic of occurrent knowledge and belief requires only that knowledge entail both truth and belief. Inconsistent belief sets are permitted. The logics for virtual knowledge and belief require in addition logical omniscience, and optionally the KK-thesis. Three sorts of epistemic contexts are considered, transparent, opaque in the sense of Hintikka, and fully opaque contexts. At various points, both frame-theoretic and truth-value semantic accounts are employed. Soundness and completeness theorems are provided for representative logics, the latter being of the Henkin sort. (shrink)

Epistemic theories of truth, such as those presumed to be typical for anti-realism, can be characterised as saying that what is true can be known in principle: p → ◊Kp. However, with statements of the form “p & ¬Kp”, a contradiction arises if they are both true and known. Analysis of the nature of the paradox shows that such statements refute epistemic theories of truth only if the the anti-realist motivation for epistemic theories of truth is not taken into account. (...) The motivation in a link of understandability ans meaningful- ness suggests to change the above principle and to restrict the theory to logically simple sentences, in which case the paradox does not arise. This suggestion also allows to see the deep philosophical problems for anti-realism those counterexamples are pointing at. (shrink)

We are often in no position to know whether p is true but, it is widely held, where we do know that p, we are always in a position to know that we know that p: knowledge is luminous. In Chapter 4 of Knowledge and Its Limits Williamson argues that knowledge is not luminous and with this conclusion in hand he hopes to see off the sceptic, amongst other things.

Eighteen leading philosophers offer critical assessments of Timothy Williamson's ground-breaking work on knowledge and its impact on philosophy today. They discuss epistemological issues concerning evidence, defeasibility, scepticism, testimony, assertion, and perception, and debate Williamson's central claim that knowledge is a mental state.

This paper considers, and rejects, three strategies aimed at showing that the KK-principle fails even in most favourable circumstances (all emerging from Williamson’s Knowledge and its Limits ). The case against the final strategy provides positive grounds for thinking that the principle should hold good in such situations.

Timothy Williamson (2000 ch. 5) presents a reductio against the luminosity of knowing, against, that is, the so-called KK-principle: if one knows p, then one knows (or is at least in a position to know) that one knows p.1 I do not endorse the principle, but I do not think Williamson’s argument succeeds in refuting it. My aim here is to show that the KK-principle is not the most obvious culprit behind the contradiction Williamson derives.

Suppose you’d like to believe that p, whether or not it’s true. What can you do to help? A natural initial thought is that you could engage in Intentionally Biased Inquiry : you could look into whether p, but do so in a way that you expect to predominantly yield evidence in favour of p. This paper hopes to do two things. The first is to argue that this initial thought is mistaken: intentionally biased inquiry is impossible. The second is (...) to show that reflections on intentionally biased inquiry strongly support a controversial ‘access’ principle which states that, for all p, if p is part of our evidence, then that p is part of our evidence is itself part of our evidence. (shrink)

The status of the knowledge iteration principles in the account provided by Lewis in “Elusive Knowledge” is disputed. By distinguishing carefully between what in the account describes the contribution of the attributor’s context and what describes the contribution of the subject’s situation, we can resolve this dispute in favour of Holliday’s claim that the iteration principles are rendered invalid. However, that is not the end of the story. For Lewis’s account still predicts that counterexamples to the negative iteration principle ) (...) come out as elusive: such counterexamples can occur only in possibilities which the attributors of knowledge are ignoring. This consequence is more defensible than it might look at first sight. (shrink)

Timothy Williamson has famously argued that the principle should be rejected. We analyze Williamson's argument and show that its key premise is ambiguous, and that when it is properly stated this premise no longer supports the argument against. After canvassing possible objections to our argument, we reflect upon some conclusions that suggest significant epistemological ramifications pertaining to the acquisition of knowledge from prior knowledge by deduction.

In ‘The normative role of knowledge’ (2012), Declan Smithies defends a ‘JK-rule’ for belief: One has justification to believe that P iff one has justification to believe that one is in a position to know that P. Similar claims have been defended by others (Huemer, 2007, Reynolds, forthcoming). In this paper, I shall argue that the JK-rule is false. The standard and familiar way of arguing against putative rules for belief or assertion is, of course, to describe putative counterexamples. My (...) argument, though, won’t be like this – indeed I doubt that there are any intuitively compelling counterexamples to the JK-rule. Nevertheless, the claim that there are counterexamples to the JK-rule can, I think, be given something approaching a formal proof. My primary aim here is to sketch this proof. I will briefly consider some broader implications for how we ought to think about the epistemic standards governing belief and assertion. (shrink)

Justification logics are modal logics that include justifications for the agent's knowledge. So far, there are no decidability results available for justification logics with negative introspection. In this paper, we develop a novel model construction for such logics and show that justification logics with negative introspection are decidable for finite constant specifications.

Some time ago I wrote a paper about conceivability and knowledge. An anonymous referee rejected it on the grounds that the result had already been established in a short story by Jorge Luis Borges. Intrigued, I looked for the story but found no mention of it in Louis and Ziche’s extensive bibliography. I spent months consulting archives and electronic records to no avail. I had begun to doubt whether the story even existed when I had the curious good luck to (...) encounter Sir Thomas Browne of Pembroke College, Oxford, who assured me of the piece’s authenticity and introduced me to Brother Christian Rosenkreuz of Invisible College who in turn generously put me into correspondence with Borges himself. The literary defects in what follows reflect not a diminution of Borges’s undoubted power as a storyteller, but merely my limited ability as an amateur translator. Whatever the translation’s literary faults may be, I hope the story’s philosophical interest—i.e., an argument that ideal conceivers have higher-order knowledge of necessary truths—remains. [Trans.]. (shrink)

Can we turn the screw on counter-examples to the KK principle (that if one knows that P, one knows that one knows that P)? The idea is to construct cases in which one knows that P, but the epistemic status for one of the proposition that one knows that P is much worse than just one’s not knowing it. Of course, since knowledge is factive, there can’t be cases in which one knows that P and knows that one doesn’t know (...) that P (we can’t strengthen ¬KKp to K¬Kp)! If we can construct such cases, we may be able to use them to understand some puzzling epistemic phenomena. (shrink)

§I schematises the evidence for an understanding of ‘know’ and other terms of epistemic appraisal that embodies contextualism or subject-sensitive invariantism, and distinguishes between those two approaches. §II argues that although the cases for contextualism and sensitive invariantism rely on a principle of charity in the interpretation of epistemic claims, neither approach satisfies charity fully, since both attribute metalinguistic errors to speakers. §III provides an equally charitable anti-sceptical insensitive invariantist explanation of much of the same evidence as the result of (...) psychological bias caused by salience effects. §IV suggests that the explanation appears to have implausible consequences about practical reasoning, but also that applications of contextualism or sensitive invariantism to the problem of scepticism have such consequences. §V argues that the inevitable difference between appropriateness and knowledge of appropriateness in practical reasoning, closely related to the difference between knowledge and knowledge of knowledge, explains the apparent implausibility. (shrink)