Knowledge and Its Limits

Citation

Williamson, T. (2002). Knowledge and Its Limits. Oxford University Press.

Chapter Summary

The book consists of an Introduction (about twenty pages), twelve chapters, six short technical appendices (pp. 302–320), a bibliography and an index, about 340 pages in all. The publisher's summary describes its central move as reversing the traditional programme of analysing knowledge as belief plus truth plus justification: instead, knowledge is treated as explanatorily basic, belief as the state whose successful form is knowledge, and evidence as knowledge.

Introduction

Previews the main theses under five headings: unanalysable knowledge, knowing as a factive mental state, knowledge as what justifies belief and assertion, the "myth of epistemic transparency", and unknowable truths.

Chapter 1: A State of Mind

Proposes that knowing is a mental state, and specifically a factive one: only truths are known, whereas believing is non-factive. Knowledge is presented as the most general factive mental state, with perception and memory as sub-species. The chapter argues that knowledge cannot be analysed as a combination of belief, truth and further factors; belief is instead to be understood through knowledge, in the manner of disjunctive accounts of perception, so that to believe is roughly to act as though one knew.

Chapter 2: Broadness

Argues that if knowing is a mental state then internalism, which makes mental states depend only on what is inside the head, is false for this state. Attempts to find an internalist core of knowledge, such as belief or rational belief, are rejected, and the causal efficacy of knowing is defended with cases where knowing explains an extended action better than believing does.

Chapter 3: Primeness

Defines composite conditions (a purely internal condition conjoined with a purely external one) and prime conditions (those that are not composite), and gives a general method for showing that knowing and many other mental states are prime. The chapter connects this to Plato's Meno and uses correlation coefficients to explain why prime states are valuable in explaining action.

Chapter 4: Anti-Luminosity

A condition is luminous if whenever it obtains one is in a position to know that it does. The chapter argues, through gradual processes whose small changes fall below our powers of discrimination, that no non-trivial condition is luminous, and relates the argument to, but distinguishes it from, the sorites paradox. The result also supplies an objection to Dummett's attempt to characterise meaning through assertibility rather than truth.

Chapter 5: Margins and Iterations

Uses the anti-luminosity argument against the KK principle, that knowing implies being in a position to know that one knows, and traces further iterations of knowledge. The underlying phenomenon is diagnosed as a need for a margin for error and is related to safety, reliability and close possibility. The account is extended to knowledge of what others know.

Chapter 6: An Application

Applies margins for error to the Surprise Examination Paradox, and then to knowledge of rationality in the iterated Prisoner's Dilemma. Variants in which the pupils know only that the examination will not be expected are used to criticise rival accounts of the paradox.

Chapter 7: Sensitivity

Examines the view, associated with Nozick, that knowledge must be sensitive: if what one knew were false, one would not believe it. The chapter argues that no version of the constraint is correct, criticises Keith DeRose's contextualist variant, and addresses a Putnam-style argument about brains in vats.

Chapter 8: Scepticism

Analyses a leading sceptical argument, which assumes that one has the same evidence in the good case and the bad case. Williamson denies the assumption, since one is not always in a position to know what one's evidence is. The chapter then draws the unsettling consequences for rationality, treated through the sections on sameness of evidence, the sorites and the non-transparency of rationality.

Chapter 9: Evidence

Argues that one's total evidence is one's total knowledge. Because knowledge is not analysed in terms of justification, there is no circularity in using it to explain justification by evidence. The chapter argues that evidence must be propositional, with reference to falsification, inference to the best explanation and Bayesian confirmation.

Chapter 10: Evidential Probability

Builds a theory of evidential probability on the equation of evidence with knowledge, a form of objective rather than subjective Bayesianism, in which updating can lose as well as gain probability. It is integrated with possible-worlds models of epistemic logic, in which accessibility is not an equivalence relation.

Chapter 11: Assertion

Argues that assertion is governed by the rule to assert only what one knows, compares this with truth and reasonable-belief accounts (testing them on lottery cases), and examines objections and replies. The chapter also treats mathematical assertion and the point of having such a speech act.

Chapter 12: Structural Unknowability

Explores Fitch's paradox of knowability, which shows that if some truths are unknown then some truths are unknowable, and its challenge to verificationism and anti-realism. The chapter considers objections by Edgington, Kvanvig, Melia and others.

Appendices

Six short appendices give technical support for earlier chapters: correlation coefficients, counting iterations of knowledge, a formal model of slight insensitivity, proofs about iterated probabilities in epistemic logic, a non-symmetric epistemic model, and distribution over conjunction.

Key Concepts

Introduction and Chapters 1–3: Knowing as a mental state

• Factive mental state: a state that can be had only when its content is true; knowing is the most general such state.
• Unanalysable knowledge: the thesis that knowledge cannot be decomposed into belief plus further conditions.
• Prime condition: a condition that is not a conjunction of purely internal and purely external parts.

Chapters 4–6: Luminosity and iteration

• Luminosity: a condition one is always in a position to know to obtain when it does; the book argues there are no non-trivial ones.
• Margin for error: the gap that knowledge requires between what is known and nearby cases where it would be false.
• KK principle: that knowing entails being in a position to know that one knows.

Chapters 7–10: Scepticism, evidence and probability

• Sensitivity: the counterfactual condition that one would not believe a proposition if it were false.
• E = K: one's total evidence is one's total knowledge.
• Evidential probability: probability conditional on one's total evidence, which the book identifies with one's total knowledge.

Chapters 11–12: Assertion and unknowability

• Knowledge norm of assertion: one should assert only what one knows.
• Fitch's paradox: the argument that unknown truths imply unknowable truths.

Critical Analysis

Strengths

• A single organising thesis. The central idea of knowledge as basic runs through the whole book, so each chapter applies it to a different topic (mind, scepticism, evidence, probability, assertion) and the pieces support each other.
• Direct engagement with named opponents. Chapters 7 and 11 test the author's view against Nozick-style sensitivity, contextualism and rival norms of assertion, and Chapter 12 answers specific objections to the knowability argument.
• Formal work is kept separate. Probability models, epistemic logic and proofs are largely placed in Chapter 10 and in the appendices, which lets readers follow the philosophical argument without the technical material.
• A preview in the Introduction. The first twenty pages set out the main claims under five headings, which gives a reader an overview before the detailed chapters.

Limitations

• Written for readers who already know epistemology. The arguments assume familiarity with analyses of knowledge, internalism and externalism, scepticism and Bayesian ideas; this is a research monograph and not a survey.
• Cumulative argument. The later chapters rely on the conclusions about mental states and anti-luminosity in Chapters 1 to 4, so reading out of order is difficult.
• Technical sections. Chapter 10 and the appendices use possible-worlds models, probability and correlation coefficients, which some epistemology students will need to supplement.
• One side of the debate. The book argues against sensitivity, internalism and the justified-true-belief programme, so the opposing positions have to be read elsewhere.

Where It Fits in the Course

This is the book for readers who have finished an introductory epistemology text. The introductions in the list prepare for it in different ways: Pritchard's What is this thing called Knowledge? is a self-contained first course with study questions, Nagel's Knowledge: A Very Short Introduction is a brief orientation, Lemos's An Introduction to the Theory of Knowledge sets out the main theories of knowledge and justification with objections, and Audi's Epistemology: A Contemporary Introduction is a systematic text from sources of knowledge to scepticism. Lemos or Audi provide the background on justification and analysis that Williamson rejects.

Sosa's A Virtue Epistemology is the natural companion monograph: it also gives a full account of knowledge, but through belief as an apt performance and the distinction between animal and reflective knowledge, so reading the two together shows two quite different ways of organising the subject.

How to Use This Book

The book suits graduate students and advanced undergraduates with a solid course in epistemology and some comfort with basic modal and epistemic logic.

A practical reading plan:

• Core: the Introduction and Chapters 1, 4, 8, 9 and 11. These give the thesis that knowing is a mental state, the anti-luminosity argument, its use against scepticism, the equation of evidence with knowledge, and the knowledge norm of assertion.
• Supporting chapters: Chapters 2 and 3 for the externalism and primeness arguments; Chapters 5 and 6 for margin for error and the KK principle; Chapter 7 for the rejection of sensitivity.
• Technical and optional: Chapter 10 and the appendices, for readers interested in probability and epistemic logic; Chapter 12 for the paradox of knowability.

Keep a short list of the claims defended in each chapter and check each against the objections the author discusses. Pair Chapter 7 with the sensitivity and contextualist literature it criticises, and Chapter 11 with the other proposed norms of assertion.