The paper is a critique of Allan Gibbard’s impressively crafted monograph Meaning and Normativity. The book relies on a subtle form of logical empiricism, developing a normative verificationist semantics within a subjective Bayesian framework. I argue that the resulting account of synonymy is too fine-grained, since it counts clearly synonymous words in different languages as non-synonymous. For similar reasons, Gibbard’s account of analytic implication relies on postulating untenable connections between semantics and epistemology. I conclude that one of the main obstacles (...) to robust realism about normativity and morality, the supposed conceptual connections between normative language and action, is a myth. (shrink)

I problematize Grounding-based formulations of physicalism. More specifically, I argue, first, that motivations for adopting a Grounding-based formulation of physicalism are unsound; second, that a Grounding-based formulation lacks illuminating content, and that attempts to imbue Grounding with content by taking it to be a strict partial order are unuseful and problematic ; third, that conceptions of Grounding as constitutively connected to metaphysical explanation conflate metaphysics and epistemology, are ultimately either circular or self-undermining, and controversially assume that physical dependence is incompatible (...) with explanatory gaps; fourth, that in order to appropriately distinguish physicalism from strong emergentism, a Grounding-based formulation must introduce one and likely two primitives in addition to Grounding; and fifth, that understanding physical dependence in terms of Grounding gives rise to ‘spandrel’ questions, including, e.g., “What Grounds Grounding?”, which arise only due to the overly abstract nature of Grounding. (shrink)

Joyce (1998) gives an argument for probabilism: the doctrine that rational credences should conform to the axioms of probability. In doing so, he provides a distinctive take on how the normative force of probabilism relates to the injunction to believe what is true. But Joyce presupposes that the truth values of the propositions over which credences are defined are classical. I generalize the core of Joyce’s argument to remove this presupposition. On the same assumptions as Joyce uses, the credences of (...) a rational agent should always be weighted averages of truth value assignments. In the special case where the truth values are classical, the weighted averages of truth value assignments are exactly the probability functions. But in the more general case, probabilistic axioms formulated in terms of classical logic are violated—but we will show that generalized versions of the axioms formulated in terms of non-classical logics are satisfied. (shrink)

Recently, a number of epistemologists (notably Feldman [2007], [2009] and White [2005], [2013]) have argued for the rational uniqueness thesis, the principle that any set of evidence permits only one rationally acceptable attitude toward a given proposition. In contrast, this paper argues for extreme rational permissivism, the view that two agents with the same evidence may sometimes arrive at contradictory beliefs rationally. This paper identifies different versions of uniqueness and permissivism that vary in strength and range, argues that evidential peers (...) with different interests need not rationally endorse all the same hypotheses, argues that evidential peers who weigh the theoretic virtues differently can sometimes rationally endorse contradictory conclusions, and finally defends the permissivist appeal to standards against objections in the works of Feldman and White. (shrink)

The epistemic theory of causality is analogous to epistemic theories of probability. Most proponents of epistemic probability would argue that one's degrees of belief should be calibrated to chances, insofar as one has evidence of chances. The question arises as to whether causal beliefs should satisfy an analogous calibration norm. In this paper, I formulate a particular version of a norm requiring calibration to chances and argue that this norm is the most fundamental evidential norm for epistemic probability. I then (...) develop an analogous calibration norm for epistemic causality, argue that it is the *only* evidential norm required for epistemic causality, and show how an epistemic account of causality that incorporates this norm can be used to analyse objective causal relationships. (shrink)

This paper defends a new norm of assertion: Assert that p only if you are in a position to know that p. We test the norm by judging its performance in explaining three phenomena that appear jointly inexplicable at first: Moorean paradoxes, lottery propositions, and selfless assertions. The norm succeeds by tethering unassertability to unknowability while untethering belief from assertion. The PtK‐norm foregrounds the public nature of assertion as a practice that can be other‐regarding, allowing asserters to act in the (...) best interests of their audience when psychological pressures would otherwise prevent them from communicating the knowable truth. (shrink)

According to the doctrine of infallibility, one is permitted to believe p if one knows that necessarily, one would be right if one believed that p. This plausible principle—made famous in Descartes’ cogito—is false. There are some self-fulfilling, higher-order propositions one can’t be wrong about but shouldn’t believe anyway: believing them would immediately make one's overall doxastic state worse.

The reflections recorded in this paper arise from three moments in the theory of definition and of conceptual analysis. The moments are: Frege’s review of Husserl’s Philosophy of Arithmetic, the discussion there of the paradox of analysis, and the division that Frege marks, ensuing upon his distinction of Sinn/sense from Bedeutung/reference, between two different conceptions of definition; Leibniz’s still serviceable account of a distinction between the clarity and the distinctness of ideas---a distinction that prompts the suggestion that the guiding purpose (...) of lexical definition is Leibnizian clarity whereas that of real definition is inseparable from the pursuit of Leibnizian distinctness; Leibniz’s speculations concerning the limit or terminus of analysis. The apparent failure of these speculations, casting doubt as it does upon the aspirations that give rise to them, points to the long-standing need to reconfigure the philosophical business of enquiry into concepts. (shrink)

According to the subjective view of lying, speakers can lie by asserting a true proposition, as long as they believe this proposition to be false. This view contrasts with the objective view, according to which lying requires the actual falsity of the proposition asserted. The aim of this paper is to draw attention to pairs of assertions that differ only in intuitively redundant content and to show that such pairs of assertions are a reason to favour the subjective view of (...) lying over the objective one. (shrink)

Timothy Williamson has a marvelously precise account of epistemic justification in terms of knowledge and probability. I argue that the account runs aground on certain cases involving the probability values 0 and 1.

There has been much debate over whether to accept the claim that meaning is normative. One obstacle to making progress in that debate is that it is not always clear what the claim amounts to. In this paper, I try to resolve a dispute between those who advance the claim concerning how it should be understood. More specifically, I critically examine two competing conceptions of the normativity of meaning, rejecting one and defending the other. Though the paper aims to settle (...) a dispute among proponents of the claim that meaning is normative, it should be of interest to those who challenge it. After all, before one takes aim, one’s target needs to be in clear view. (shrink)

In a paper in this journal, I defend the view that truth is the fundamental norm for assertion and, in doing so, reject the view that knowledge is the fundamental norm for assertion. In a recent response, Littlejohn raises a number of objections against my arguments. In this reply, I argue that Littlejohn’s objections are unsuccessful.

The view that truth is the norm of assertion has fallen out of fashion. The recent trend has been to think that knowledge is the norm of assertion. Objections to the knowledge view proceed almost exclusively by appeal to alleged counterexamples. While it no doubt has a role to play, such a strategy relies on intuitions concerning hypothetical cases, intuitions which might not be shared and which might shift depending on how the relevant cases are fleshed out. In this paper, (...) I reject the knowledge view on principled grounds. More specifically, by appeal to a principle which is motivated independently of the debate over the norms of assertion and which is already accepted by many proponents of the knowledge view, I show the knowledge view to be false while simultaneously accounting for why it might seem to be true. In doing so, I provide a novel defence of the unfashionable truth view. (shrink)

A critical survey of recent work in epistemology on higher-order evidence. It discusses the nature of higher-order evidence, some puzzles it raises, responses to those puzzles, and problems facing them. It concludes by indicating connections between debates concerning higher-order evidence in epistemology and parallel debates in ethics and aesthetics.

What is a normative reason for acting? In this paper, I introduce and defend a novel answer to this question. The starting-point is the view that reasons are right-makers. By exploring difficulties facing it, I arrive at an alternative, according to which reasons are evidence of respects in which it is right to perform an act, for example, that it keeps a promise. This is similar to the proposal that reasons for a person to act are evidence that she ought (...) to do so; however, as I explain, it differs from that proposal in two significant ways. As a result, I argue, the evidence-based account of reasons I advance shares the advantages of its predecessor while avoiding many of the difficulties facing it. (shrink)

Suppose for reductio that I know a proposition of the form <p and I don’t know p>. Then by the factivity of knowledge and the distribution of knowledge over conjunction, I both know and do not know p ; which is impossible. Propositions of the form <p and I don’t know p> are therefore unknowable. Their particular kind of unknowability has been widely discussed and applied to such issues as the realism debate. It hasn’t been much applied to theories of (...) the nature of knowledge. That is what I’m going to do here. (shrink)

A number of prominent philosophers advance the following ideas: (1) Meaning is use. (2) Meaning is an intrinsically normative notion. Call (1) the use thesis, hereafter UT, and (2) the normativity thesis, hereafter NT. They come together in the view that for a linguistic expression to have meaning is for there to be certain proprieties governing its employment.1 These ideas are often associated with a third.

An influential proposal is that knowledge involves safe belief. A belief is safe, in the relevant sense, just in case it is true in nearby metaphysically possible worlds. In this paper, I introduce a distinct but complementary notion of safety, understood in terms of epistemically possible worlds. The main aim, in doing so, is to add to the epistemologist’s tool-kit. To demonstrate the usefulness of the tool, I use it to advance and assess substantive proposals concerning knowledge and justification.

Objective reasons are given by the facts. Subjective reasons are given by one’s perspective on the facts. Subjective reasons, not objective reasons, determine what it is rational to do. In this paper, I argue against a prominent account of subjective reasons. The problem with that account, I suggest, is that it makes what one has subjective reason to do, and hence what it is rational to do, turn on matters outside or independent of one’s perspective. After explaining and establishing this (...) point, I offer a novel account of subjective reasons which avoids the problem. (shrink)

I summarize Timothy Williamson's theory of knowledge, construct some counterexamples to it, and try to diagnose the problem in virtue of which those counterexamples arise. Then I consider possible responses. It turns out that only one of those responses is tenable, and that that response renders Williamson's theory a continuous piece of, rather than a radical paradigmatic break from, recent mainstream work in the theory of knowledge.

Among other interesting proposals, Juan Comesaña’s _Being Rational and Being Right_ makes a challenging case that one’s evidence can include falsehoods. I explore some ways in which we might have to rethink the roles that evidence can play in inquiry if we accept this claim. It turns out that Comesaña’s position lends itself to the conclusion that while false evidence is possible and not even terribly uncommon, I can be rationally sure that I don’t currently have any and perhaps also (...) that I won’t get any, and (absent certain evidence to the contrary) you are not afflicted with any either. This conclusion might seem too good to be true. I finish by raising a puzzle about one of the main motivations for Comesaña’s view. (shrink)

It is common to hear talk of the aim of belief and to find philosophers appealing to that aim for numerous explanatory purposes. What belief 's aim explains depends, of course, on what that aim is. Many hold that it is somehow related to truth, but there are various ways in which one might specify belief 's aim using the notion of truth. In this article, by considering whether they can account for belief 's standard of correctness and the epistemic (...) norms governing belief, I argue against certain prominent specifications of belief 's aim given in terms of truth, and advance a neglected alternative. (shrink)

The truth-justification is an enduring explanation for valuing free speech. This paper seeks to advance an account of “assertion”, found in speech act theory, that can identify speech which contributes to truth-discovery in a nuanced way. I apply the dialectic theory of assertion which emphasises the language game of giving and asking for reasons to believe things as assertional social practice. In doing so, I consider what “moves” in this game make sense from a truth-discovery perspective, drawing together contemporary and (...) foundational work on assertion in linguistics to fit the normative context of law. Speech act theory is often invoked in current free speech literature to identify regulable speech, but less typically to identify speech that warrants legal protection. I contextualise my theory within this existing legal work and show how the model I advocate for applies across many formulations of the truth-justification to offer comprehensive explanatory and justificatory power. I also explore the potential appeal of alternative theories of assertion and explain why they are a poor fit in comparison to the dialectical account. (shrink)

It is widely acknowledged that some truths or facts don’t have a minimal full ground [see e.g. Fine ]. Every full ground of them contains a smaller full ground. In this paper I’ll propose a minimality constraint on immediate grounding and I’ll show that it doesn’t fall prey to the arguments that tell against an unqualified minimality constraint. Furthermore, the assumption that all cases of grounding can be understood in terms of immediate grounding will be defended. This assumption guarantees that (...) the proposed minimality constraint is significant for all cases of grounding. With its help one can get a clear grip on the relevance of grounding, a feature that will be put to use in the penultimate section. (shrink)

The surprise exam paradox is an apparently sound argument to the apparently absurd conclusion that a surprise exam cannot be given within a finite exam period. A closer look at the logic of the paradox shows the argument breaking down immediately. So why do the beginning stages of the argument appear sound in the first place? This paper presents an account of the paradox on which its allure is rooted in a common probabilistic mistake: the base rate fallacy. The account (...) predicts that the paradoxical argument should get less and less convincing as it goes along—a prediction I take to be welcome. On a bleaker note, the account suggests that the base rate fallacy may be more widespread than previously thought. (shrink)

I propose that testimony is subject to a norm that is backed by a credibility sanction: whenever the norm is violated, it is appropriate for the testifier to lose some credibility for their future testimony. This is one of a family of sanction-based norms, where violation of the norm makes it appropriate to lose some power; in this case, the power to induce belief through testimony. The applicability of the credibility norm to testimony follows from the epistemology of testimony, in (...) that false or unjustified testimony weakens the reason for belief that is provided by the speaker's future testimony. (shrink)

Many philosophers working on the branches of philosophy that deal with the normative questions have adopted a " Reasons First" program. This paper criticizes the foundational assumptions of this program. In fact, there are many different concepts that can be expressed by the term 'reason' in English, none of which are any more fundamental than any others. Indeed, most of these concepts are not particularly fundamental in any interesting sense.

Here is a definition of knowledge: for you to know a proposition p is for you to have an outright belief in p that is correct precisely because it manifests the virtue of rationality. This definition resembles Ernest Sosa’s “virtue theory”, except that on this definition, the only virtue that must be manifested in all instances of knowledge is rationality, and no reductive account of rationality is attempted—rationality is assumed to be an irreducibly normative notion. This definition is compatible with (...) “internalism” about rationality, and with a form of “pragmatic encroachment” on the conditions of rational outright belief. An interpretation is given of this definition, and especially of the sense of ’because’ that it involves. On this interpretation, this definition entails that both safety and adherence are necessary conditions on knowledge; it supports a kind of contextualism about terms like ‘knowledge’; and it provides resources to defend safety, adherence, and contextualism, against some recent objections. (shrink)

What is the connection between justification and the kind of consequence relations that are studied by logic? In this essay, I shall try to provide an answer, by proposing a general conception of the kind of inference that counts as justified or rational.

There are three well-known models of how to account for perceptual belief within a probabilistic framework: (a) a Cartesian model; (b) a model advocated by Timothy Williamson; and (c) a model advocated by Richard Jeffrey. Each of these models faces a problem—in effect, the problem of accounting for the defeasibility of perceptual justification and perceptual knowledge. It is argued here that the best way of responding to this the best way of responding to this problem effectively vindicates the Cartesian model. (...) Finally, it is argued that, given the best interpretation of the probabilistic framework, that the Cartesian model is not vulnerable to the main criticisms that have been raised against it. (shrink)

Unknown peers create a problem for those epistemologists who argue that we should be conciliatory in cases of peer disagreement. The standard interpretation of ‘being conciliatory’ has it that we should revise our opinions concerning a specific subject matter whenever we encounter someone who is as competent and well informed as we are concerning this subject matter (and thus is our peer) and holds a different opinion. As a consequence, peers whom we have never encountered and who are hence unknown (...) to us are not taken into account. This, however, appears odd; not only because it is an accidental matter which peers we happen to encounter and which not, but also because it would allow people to deliberately isolate themselves from any kind of intellectual exchange on the topic under consideration. The paper argues that we should take the problem of unknown peers seriously, and that disregarding the problem is an instance of the more general mistake of assuming that evidential quality and justified believability can be dealt with separately. Moreover, a solution to the problem of unknown peers is suggested. (shrink)

Intuitively, Gettier cases are instances of justified true beliefs that are not cases of knowledge. Should we therefore conclude that knowledge is not justified true belief? Only if we have reason to trust intuition here. But intuitions are unreliable in a wide range of cases. And it can be argued that the Gettier intuitions have a greater resemblance to unreliable intuitions than to reliable intuitions. Whats distinctive about the faulty intuitions, I argue, is that respecting them would mean abandoning a (...) simple, systematic and largely successful theory in favour of a complicated, disjunctive and idiosyncratic theory. So maybe respecting the Gettier intuitions was the wrong reaction, we should instead have been explaining why we are all so easily misled by these kinds of cases. (shrink)

The Sleeping Beauty puzzle provides a nice illustration of the approach to self-locating belief defended by Robert Stalnaker in Our Knowledge of the Internal World (Stalnaker, 2008), as well as a test of the utility of that method. The setup of the Sleeping Beauty puzzle is by now fairly familiar. On Sunday Sleeping Beauty is told the rules of the game, and a (known to be) fair coin is flipped. On Monday, Sleeping Beauty is woken, and then put back to (...) sleep. If, and only if, the coin landed tails, she is woken again on Tuesday after having her memory of the Monday awakening erased.1 On Wednesday she is woken again and the game ends. There are a few questions we can ask about Beauty’s attitudes as the game progresses. We’d like to know what her credence that the coin landed heads should be (a) Before she goes to sleep Sunday; (b) When she wakes on Monday; (c) When she wakes on Tuesday; and (d) When she wakes on Wednesday? Standard treatments of the Sleeping Beauty puzzle ignore (d), run together (b) and (c) into one (somewhat ill-formed) question, and then divide theorists into ‘halfers’ or ‘thirders’ depending on how they answer it. Following Stalnaker, I’m going to focus on (b) here, though I’ll have a little to say about (c) and (d) as well. I’ll be following orthodoxy in taking 1 2 to be the clear answer to (a), and in taking the correct answers to (b) and (c) to be independent of how the coin lands, though I’ll briefly question that assumption at the end. An answer to these four questions should respect two different kinds of constraints. The answer for day n should make sense ‘statically’. It should be a sensible answer to the question of what Beauty should do given what information she then has. And the answer should make sense ‘dynamically’. It should be a sensible answer to the question of how Beauty should have updated her credences from some earlier day, given rational credences on the earlier day. As has been fairly clear since the discussion of the problem in Elga (2000), Sleeping Beauty is puzzling because static and dynamic considerations appear to push in different directions.. (shrink)

I argue that what evidence an agent has does not supervene on how she currently is. Agents do not always have to infer what the past was like from how things currently seem; sometimes the facts about the past are retained pieces of evidence that can be the start of reasoning. The main argument is a variant on Frank Arntzenius’s Shangri La example, an example that is often used to motivate the thought that evidence does supervene on current features.

Recently, Timothy Williamson has argued that considerations about margins of errors can generate a new class of cases where agents have justified true beliefs without knowledge. I think this is a great argument, and it has a number of interesting philosophical conclusions. In this note I’m going to go over the assumptions of Williamson’s argument. I’m going to argue that the assumptions which generate the justification without knowledge are true. I’m then going to go over some of the recent arguments (...) in epistemology that are refuted by Williamson’s work. And I’m going to end with an admittedly inconclusive discussion of what we can know when using an imperfect measuring device. (shrink)

Pragmatic encroachment theories have a problem with evidence. On the one hand, the arguments that knowledge is interest-relative look like they will generalise to show that evidence too is interest-relative. On the other hand, our best story of how interests affect knowledge presupposes an interest-invariant notion of evidence. -/- The aim of this paper is to sketch a theory of evidence that is interest-relative, but which allows that ‘best story’ to go through with minimal changes. The core idea is that (...) the evidence someone has is just what evidence a radical interpreter says they have. And a radical interpreter is playing a kind of game with the person they are interpreting. The cases that pose problems for pragmatic encroachment theorists generate fascinating games between the interpreter and the interpretee. They are games with multiple equilibria. To resolve them we need to detour into the theory of equilibrium selection. I’ll argue that the theory we need is the theory of risk-dominant equilibria. That theory will tell us how the interpreter will play the game, which in turn will tell us what evidence the person has. The evidence will be interest-relative, because what the equilibrium of the game is will be interest-relative. But it will not undermine the story we tell about how interests usually affect knowledge. (shrink)

A contribution to a symposium on Herman Cappelen's Philosophy without Intuitions.

I consider the problem of how to derive what an agent believes from their credence function and utility function. I argue the best solution of this problem is pragmatic, i.e. it is sensitive to the kinds of choices actually facing the agent. I further argue that this explains why our notion of justified belief appears to be pragmatic, as is argued e.g. by Fantl and McGrath. The notion of epistemic justification is not really a pragmatic notion, but it is being (...) applied to a pragmatically defined concept, i.e. belief. (shrink)

In his Principles of Philosophy, Descartes says, Finally, it is so manifest that we possess a free will, capable of giving or withholding its assent, that this truth must be reckoned among the first and most common notions which are born with us.

Perspectivists hold that what you ought to do is determined by your perspective, that is, your epistemic position. Objectivists hold that what you ought to do is determined by the facts irrespective of your perspective. This paper explores an influential argument for perspectivism which appeals to the thought that the normative is action guiding. The crucial premise of the argument is that you ought to φ only if you are able to φ for the reasons which determine that you ought (...) to φ. We show that this premise can be understood in different ways. On one reading, it provides no support for perspectivism. On another reading, the premise lacks support. So, the argument fails. An important upshot of the paper is that the objectivist can embrace the thought about guidance. (shrink)

In this paper, we claim that, if you justifiably believe that you ought to perform some act, it follows that you ought to perform that act. In the first half, we argue for this claim by reflection on what makes for correct reasoning from beliefs about what you ought to do. In the second half, we consider a number of objections to this argument and its conclusion. In doing so, we arrive at another argument for the view that justified beliefs (...) about what you ought to do must be true, based in part on the idea that the epistemic and practical domains are uniform, in a sense we spell out. We conclude by sketching possible implications of our discussion for the debates over what is wrong with akrasia and pragmatic encroachment on justified belief and knowledge. (shrink)

Enkratic reasoning—reasoning from believing that you ought to do something to an intention to do that thing—seems good. But there is a puzzle about how it could be. Good reasoning preserves correctness, other things equal. But enkratic reasoning does not preserve correctness. This is because what you ought to do depends on your epistemic position, but what it is correct to intend does not. In this paper, I motivate these claims and thus show that there is a puzzle. I then (...) argue that the best solution is to deny that correctness is always independent of your epistemic position. As I explain, a notable upshot is that a central epistemic norm directs us to believe, not simply what is true, but what we are in a position to know. (shrink)

My aim in this paper is twofold: to establish that Kierkegaard's so‐called theory of the leap strongly anticipates a line of argument that is central to Wittgenstein's so‐called rule‐following considerations; and to begin to show how Kierkegaard's work has fruitful contributions of its own to make to on‐going discussions about rules and rule‐following. The paper focuses throughout on the question of how, if at all, human rule‐following can be distinguished from behaviour that is merely mechanical or instinctual. I identify a (...) central line of argument in Wittgenstein that problematizes this question by establishing the basis our ability to follow rules in our spontaneous responses. I argue that Kierkegaard not only strongly anticipates this line of argument but also offers a distinctive story about what, at bottom, makes the difference between human rule‐following and behaviour that is merely mechanical or instinctual. In a word, on Kierkegaard's story, what makes the difference is: anxiety. (shrink)

This is a paper about the nature of metaphysical laws and their relation to the phenomenon of vagueness. Metaphysical laws are introduced as analogous to natural laws, and metaphysical indeterminism is modeled on causal indeterminacy. This kind of indeterminacy is then put to work in developing a novel theory of vagueness and a solution to the sorites paradox.

This paper formulates a general epistemological argument against what I call non-causal realism, generalizing domain specific arguments by Benacerraf, Field, and others. First I lay out the background to the argument, making a number of distinctions that are sometimes missed in discussions of epistemological arguments against realism. Then I define the target of the argument—non-causal realism—and argue that any non-causal realist theory, no matter the subject matter, cannot be given a reasonable epistemology and so should be rejected. Finally I discuss (...) and respond to several possible responses to the argument. In addition to clearing up and avoiding numerous misunderstandings of arguments of this kind that are quite common in the literature, this paper aims to present and endorse a rigorous and fully general epistemological argument against realism. (shrink)

What should knowledge first theorists say about the value of knowledge? In this paper I approach this issue by arguing for a single ‘modest knowledge first claim’ about the value of knowledge. This is that the special value of knowledge isn’t merely instrumental value relative to true belief. I show that MKF is inconsistent with the version of the Platonic stability theory that Williamson defends in Knowledge and its Limits. I then argue in favour of MKF by arguing that Williamson’s (...) stability theory fails for reasons that plausibly generalise to any theory of the value of knowledge that is inconsistent with MKF. Crucial to this argument is a putative adequacy condition on philosophical theories of the value of knowledge: that, in order to fully explain the special value of knowledge, a theory must identify respects in which knowledge is more valuable than true belief that give enquirers adequate reason for preferring knowledge to true belief. I conclude by suggesting that this adequacy condition is the source of a more general dilemma for proponents of philosophical theories of the value of knowledge. (shrink)