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Timothy WILLIAMS
Knowledge and Its Limits
Oxford University Press
2002
Preface
If I had to summarize this book in two words, they would be: knowledge first. It takes the simple distinction
between knowledge and ignorance as a starting point from which to explain other things, not as something itself to be
explained. In that sense the book reverses the direction of explanation predominant in the history of epistemology.
Like many philosophers, I have long been impressed by the failure of attempts to find a correct analysis of the
notion of knowledge in terms of supposedly more basic notions, such as belief, truth, and justification. One natural
explanation of the failure is that knowledge has no such analysis. If so, I wondered, what follows? At first, I was
tempted to draw the conclusion that the notion of knowledge did not matter very much, because we could use those
other notions instead. Around 1986, however, I began to notice points at which philosophers had gone wrong through
using combinations of those other notions when the notion of knowledge was what their purposes really called for. That
raised the question: why did they not use the notion of knowledge when it was just what they needed? The first three
chapters of this book explain but do not justify this neglect of the distinction between knowledge and ignorance. They
do so by applying the lessons of recent philosophy of mind to epistemology and then using the result to enrich the
philosophy of mind. That provides a theoretical context for work I had already been doing on knowledge and its limits,
work in which the notion of knowledge figures as one of the main instruments of understanding. That work forms much
of the basis for the final nine chapters. These chapters also sketch applications to the philosophy of language, the
philosophy of science, and decision theory. The book suggests a way of doing epistemology in which the distinction
between knowledge and ignorance is central and irreducible, and we can still aspire to systematicity and rigour.
This book draws together work done in many places. There are traces of my time at Trinity College Dublin and
much more from that at University College Oxford, particularly from some periods of leave and partial teaching relief.
The majority of the material is far more recent, since my move to the University of Edinburgh, again with valuable
end p. v
periods of leave and partial teaching relief. The hospitality of other institutions was also important: I did some
of the work as a visiting professor at the Massachusetts Institute of Technology and Princeton University and as a
visiting fellow of the Australian National University and the University of Canterbury.
Most of the ideas in the book have been tried out in discussion on many occasions, both informally and at
graduate classes at Oxford, Edinburgh, Princeton, and Helsinki; talks at the University of Aberdeen, the Australian
National University, the University of Belgrade, the University of Bristol, the Cambridge Moral Sciences Club, the
University of Canterbury at Christchurch, Cornell University, the University of Delaware, the University of Edinburgh,
the University of Glasgow, Keele University, La Trobe University, the University of Leeds, the Classical University of
Lisbon, University College London, the Catholic University of Lublin, the Massachusetts Institute of Technology,
Melbourne University, the Instituto de Investigaciones Filosóficas of the Universidad Nacional Autónoma de México,
Monash University, the University of Michigan at Ann Arbor, the University of New Mexico, New York University,
the University of North Carolina at Chapel Hill, Ohio State University, the University of Oslo, the University of
Oxford, the University of St Andrews, the University of Sheffield, the University of Stirling, the University of Sussex,
Waikato University, the University of Wollongong, and Yale University; workshops on epistemology at the
Universities of London and Stirling; a conference in Glasgow on Achilles and the Tortoise; a conference on empiricism
and a meeting of the Scots Philosophical Club, both at Edinburgh; the 1999 Rutgers conference on epistemology; a
congress on analytic philosophy at the turn of the millennium at Santiago de Compostela. To anyone familiar with
analytic philosophy, it hardly needs to be emphasized how much there is to be learned from such occasions. The reader
must judge whether I have learned enough. Certainly some sections of the book emerged as answers to questions posed
by members of one or more of those audiences. I thank those audiences collectively. In addition, individual thanks are
due to many people: they include Michael Ayers, Michael Bacharach, Helen Beebee, Alexander Bird, Simon
Blackburn, Bill Brewer, Justin Broackes, John Campbell, Peter Carruthers, Paul Castell, Bill Child, Tim Cleveland, Earl
Conee, Jack Copeland, Neil Cooper, Paolo Crivelli, Jonathan Dancy, Keith DeRose, Harry Deutsch, Dorothy
Edgington, Jim Edwards, Matti Eklund, Kit Fine, Graeme Forbes, Elizabeth Fricker, Richard Fumerton, Manuel Garcia
Carpintero, Olav Gjelsvik, John Gibbons, Gilbert Harman, Pedro Hecht, James Higginbotham,
end p. vi
Matthias Hild, Richard Holton, Lloyd Humberstone, Frank Jackson, Mark Johnston, Peter Klein, Jon Kvanvig,
Igal Kvart, Rae Langton, Keith Lehrer, David Lewis, Peter Lipton, Michael Martin, Hugh Mellor, Peter Milne, Chad
Mohler, Adam Morton, Peter Mott, Nicholas Nathan, John O'Leary-Hawthorne, Philip Percival, Philip Pettit, Stathis
Psillos, Gideon Rosen, Mark Sainsbury, Nathan Salmon, Hyun Song Shin, Sydney Shoemaker, John Skorupski, Roy
Sorensen, Ernest Sosa, Jason Stanley, Helen Steward, Scott Sturgeon, Richard Swinburne, Charles Travis, Peter Unger,
Alan Weir, Ralph Wedgwood, Crispin Wright, and various anonymous referees. The lists are certainly both invidious
and incomplete; I apologize to those whom I have undeservedly omitted, and hope that they will take some satisfaction
from the improvements which they correctly guess themselves to have caused. Peter Momtchiloff has been helpful and
supportive as my editor at Oxford University Press, and Angela Blackburn meticulous as my copy editor. Elisabetta
Williamson enabled me to spend an excessive proportion of my days writing the book. Alice and Conrad were Alice
and Conrad.
At one stage I envisaged a collection of previously published papers, cluttered with additional footnotes and
postscripts. Subsequently dissatisfied with that prospect, I reworked, expanded, and integrated the material. Some
repetitions have been eliminated, terminology has been made uniform, and interconnections signalled. The original
sources are listed below; the bibliography contains full details of the papers mentioned. I should have made few of these
improvements had it not been for Mima Andjelković, who refused to believe that I had already done my best; she was
right. She also caught many errors at proof stage.
The introduction is new.
Chapter 1 is based on parts of 'Is knowing a state of mind?', Mind 104 (1995), with extensive rewriting. There
is significant new material in sections 1.1 , 1.2 , 1.3 , and 1.5 .
Most of Chapter 2 is based on parts of 'Is knowing a state of mind?', with some material in sections 2.1 and 2.2
from 'The broadness of the mental: some logical considerations', Philosophical Perspectives 12 (1998). There is
extensive new material in section 2.3 and some in each of the other sections.
The majority of Chapter 3 is based on 'The broadness of the mental'. Section 3.2 contains significant new
material, section 3.3 is largely new, and section 3.8 is wholly new.
Most of Chapter 4 is based on 'Cognitive homelessness', The Journal of Philosophy 93 (1996), with rewriting.
Section 4.4 is new.
Of Chapter 5 , sections 5.1 and 5.2 are based on parts of 'Inexact
end p. vii
knowledge', Mind 101 (1992), with extensive reworking. The reworking differentiates those sections from
sections 8.2 and 8.3 of my Vagueness , which were also based on 'Inexact knowledge'. Sections 5.4 and 5.5 are based on
'Margins for error: a reply', Philosophical Quarterly 50 (2000). Section 5.3 is new.
Chapter 6 is based on parts of 'Inexact knowledge'.
Most of Chapter 7 is new. Sections 7.4 and 7.5 overlap 'Skepticism, semantic externalism, and Keith's mom',
Southern Journal of Philosophy 38 (2000).
Chapter 8 is mainly based on 'Scepticism and evidence', Philosophy and Phenomenological Research 60
(2000), with some additional material expanded from 'Is knowing a state of mind?' in section 8.2 .
Chapter 9 is a revised version of 'Knowledge as evidence', Mind 106 (1997). There is significant new material
in sections 9.2 , 9.7 , and 9.8 .
Chapter 10 is based on 'Conditionalizing on knowledge', British Journal for the Philosophy of Science 49
(1998), except for section 10.5 , which is based on part of 'Inexact knowledge'.
Chapter 11 is a revised version of 'Knowing and asserting', Philosophical Review 105 (1996), with some brief
new passages.
Of Chapter 12 , sections 12.1 and 12.2 draw on 'Verificationism and non-distributive knowledge', Australasian
Journal of Philosophy 71 (1993), with amplifications and some reference to results in 'Two incomplete anti-realist
modal epistemic logics', Journal of Symbolic Logic 55 (1990). Section 12.5 reworks 'On the paradox of knowability',
Mind 96 (1987), and 'On knowledge of the unknowable', Analysis 47 (1987). Sections 12.3 and 12.4 are new.
Appendix 1 reprints the appendix to 'The broadness of the mental: some logical considerations'. Appendix 2 is
a revised version of the appendix to 'Inexact knowledge'. Appendix 3 is new. Appendices 4 and 5 reprint the appendices
to 'Conditionalizing on knowledge'. Appendix 6 is a revised version of the appendix to 'Verificationism and non-
distributive knowledge'.
I thank the editors concerned (and Cornell University in the case of Philosophical Review ) for permission to
use this material.
For the paperback edition, a few words or symbols have been corrected on pages 53, 90, 95, 97, 136, 141, 147,
150, 151, and 305; thanks go to Alexander Bird, Owen Greenhall, Richard Holton, and Philip Pegan.
T. W.
end p. viii
Contents
Introduction 1
1 Knowing and acting 1
2 Unanalysable knowledge 2
3 Factive mental states 5
4 Knowledge as the justification of belief and assertion 8
5 The myth of epistemic transparency 11
6
Unknowable truths 18
1
A State of Mind 21
1.1 Factive attitudes 21
1.2 Mental states, first-person accessibility, and scepticism 23
1.3 Knowledge and analysis 27
1.4 Knowing as the most general factive mental state 33
1.5
2
Broadness 49
2.1 Internalism and externalism 49
2.2 Broad and narrow conditions 51
2.3 Mental differences between knowing and believing 54
2.4
The causal efficacy of knowledge 60
3
Primeness 65
3.1 Prime and composite conditions 65
3.2 Arguments for primeness 66
3.3 Free recombination 73
3.4 The explanatory value of prime conditions 75
3.5 The value of generality 80
3.6 Explanation and correlation coefficients 83
3.7 Primeness and the causal order 88
3.8 Non-conjunctive decompositions 89
end p. ix
4
Anti-Luminosity 93
4.1 Cognitive homes 93
4.2 Luminosity 94
4.3 An argument against luminosity 96
4.4 Reliability 98
4.5 Sorites arguments 102
4.6 Generalizations 106
4.7 Scientific tests 109
4.8
Assertibility conditions 110
5
Margins and Iterations 114
5.1 Knowing that one knows 114
5.2 Further iterations 120
5.3 Close possibilities 123
5.4 Point estimates 130
5.5
Iterated interpersonal knowledge 131
6
An Application 135
6.1 Surprise Examinations 135
6.2
Conditionally Unexpected Examinations 143
7
Sensitivity 147
7.1 Preview 147
7.2 Counterfactual sensitivity 148
7.3 Counterfactuals and scepticism 150
7.4 Methods 152
7.5 Contextualist sensitivity 156
7.6
Sensitivity and broad content 161
8
Scepticism 164
8.1 Plan 164
8.2 Scepticism and the non-symmetry of epistemic accessibility 164
8.3 Difference of evidence in good and bad cases 169
8.4 An argument for sameness of evidence 170
8.5 The phenomenal conception of evidence 173
8.6 Sameness of evidence and the sorites 174
8.7 The non-transparency of rationality 178
8.8
Scepticism without sameness of evidence 181
9
Evidence 184
9.1 Knowledge as justifying belief 184
9.2 Bodies of evidence 186
Knowing and believing 41
end p. x
9.3 Access to evidence 190
9.4 An argument 193
9.5 Evidence as propositional 194
9.6 Propositional evidence as knowledge 200
9.7 Knowledge as evidence 203
9.8
Non-pragmatic justification 207
10
Evidential Probability 209
10.1 Vague probability 209
10.2 Uncertain evidence 213
10.3 Evidence and knowledge 221
10.4 Epistemic accessibility 224
10.5 A simple model 228
10.6
A puzzling phenomenon 230
11
Assertion 238
11.1 Rules of assertion 238
11.2 The truth account 244
11.3 The knowledge account 249
11.4 Objections to the knowledge account, and replies 255
11.5 The BK and RBK accounts 260
11.6 Mathematical assertions 263
11.7
The point of assertion 266
12
Structural Unknowability 270
12.1 Fitch's argument 270
12.2 Distribution over conjunction 275
12.3 Quantification into sentence position 285
12.4 Unanswerable questions 289
12.5
Trans-world knowability 290
Appendix 1
Correlation Coefficients 302
Appendix 2
Counting Iterations of Knowledge 305
Appendix 3
A Formal Model of Slight Insensitivity Almost Everywhere 307
Appendix 4
Iterated Probabilities in Epistemic Logic (Proofs) 311
Appendix 5
A Non-Symmetric Epistemic Model 316
Appendix 6
Distribution over Conjunction 318
Bibliography 321
Index 333
end p. xi
Introduction
Everyone by nature desires to know.
Aristotle, Metaphysics A1 980a21 (modernized)
1 Knowing and Acting
Knowledge and action are the central relations between mind and world. In action, world is
adapted to mind. In knowledge, mind is adapted to world. When world is maladapted to mind, there
is a residue of desire. When mind is maladapted to world, there is a residue of belief. Desire aspires
to action; belief aspires to knowledge. The point of desire is action; the point of belief is knowledge.
Those slogans are not platitudes—unless platitudes can be generally contested. According to
many philosophers, desire aspires only to satisfaction, and belief only to truth. Action is a
systematic way to satisfied desire, and knowledge to true belief, but desires can also be satisfied and
beliefs true by chance. There is satisfied desire without action and true belief without knowledge.
Why ask for more? Satisfaction and truth already constitute the required match between mind and
world, with the appropriate directions of fit. Of course, we sometimes desire to act; those desires are
satisfied only if there is action. We sometimes believe ourselves to know; those beliefs are true only
if there is knowledge. But such cases are special; our desires and beliefs frequently concern states of
the world of which actions and beliefs are not themselves constituents.
Although desires can be satisfied as well by chance as by action, that is no reason to
marginalize the category of action in the understanding of mind. The place of desire in the economy
of mental life depends on its potential connection with action. Similarly, although beliefs can be
true as well by chance as by knowledge, that is no reason to marginalize the category of knowledge
in the understanding of mind. This book develops a conception on which the place of belief in the
economy of mental life depends on its potential connection with knowledge.
The foregoing vague phrases will later be partially replaced by something
end p. 1
more precise. But that is not the purpose of this introduction, which is painted with a broad
brush. Its aim is to give the reader a rough overall picture in which the layout of the main parts is
visible. Subsequent chapters fill in details in the parts. Even they will amount to nothing like a proof
that the picture is correct. Epistemological theories are not usually susceptible of proof. This book
shows how to understand cognitive phenomena on the basis of some simple but generally
overlooked ideas. The reader will judge those ideas by their fruit.
2 Unanalysable Knowledge
Contemporary accounts of mind tend to marginalize the category of knowledge, sometimes
not mentioning it at all; they certainly make it less central than the category of action. As a reverse
counterpart of the output from mind to world in action, they admit the input from world to mind in
perception. The latter is a more restricted category than knowledge; it excludes the products of
memory and conscious inference. Perception is the reverse counterpart of action if both are single
episodes of causal interaction with the environment. But acting, in the sense of intentionally making
something the case, includes far more complex and mediated adaptations of world to mind over
extended periods. The reverse counterpart of action in that sense is knowledge. It includes far more
complex and mediated adaptations of mind to world over extended periods than perception does.
On contemporary accounts of mind, the general category for states with the mind-to-world
direction of fit is belief. The belief is true if it fits the world, false otherwise. Although true and
false belief are the same mental state in different worlds, the place of belief in the economy of
mental life depends on its potential connection with truth. Knowledge is merely a peculiar kind of
true belief. Since Gettier showed that even justified true belief is insufficient for knowledge,
epistemologists have expended vast efforts attempting to state exactly what kind of true belief
knowledge is, but that programme is assigned no significance for the philosophy of mind. On such a
view, knowledge is to be explained in terms of belief, and belief is what matters for the
understanding of mind. The converse attempt to explain belief in terms of knowledge sounds
eccentric and perverse. To summarize this orthodoxy: belief is conceptually prior to knowledge.
The orthodox claim is frequently taken for granted, rarely supported by argument. Why
should we suppose that belief is conceptually prior
end p. 2
to knowledge? One argument is that since knowledge entails belief but not vice versa, the
entailment should be explained by the assumption that we conceptualize knowledge as the
conjunction of belief with whatever must in fact be added to belief to yield knowledge—truth and
other more elusive features. The conjuncts are conceptually prior to the conjunction. Given that
knowledge entails belief, it is trivial that one knows p if and only if (1) one believes p ; (2) p is true;
and (3) if one believes p and p is true, then one knows p . But that equivalence is useless for
establishing that belief is conceptually prior to knowledge, for it is circular: 'know' occurs in (3).
The received idea is that we can conceptualize the factors whose conjunction with belief is
necessary and sufficient for knowledge independently of knowledge; we can think of the former
without already thinking of the latter, even implicitly. But the argument does not show that such
independent conceptualization is possible, for a necessary but insufficient condition need not be a

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