Week 5 · Chapter

Chapter 5 — Knowledge II: What Knowledge Is

Introduction to Philosophy Free sample edition

The module's primary reading · ~40–50 minutes · Objective 3 (explain central positions in metaphysics and epistemology — Plato's Forms, rationalism and empiricism, skepticism, and the analysis of knowledge — and evaluate the arguments for them), with Objective 2 (identify arguments, put them in standard form, judge whether they are valid, sound, or inductively strong, and test claims with counterexamples and thought experiments) carried forward · Read it first this week; the lecture, the slide deck, the tutorial, the quiz, and the Philosophy Workshop all build on it.

In plain language

This week asks what it takes to really know something, rather than to believe it and happen to be right. A famous answer says knowledge is justified true belief (a belief that is true and that you have good reason to hold). A short paper from 1963 described cases that seem to break that answer, because the belief in them is right only by luck. You also sort knowledge by where it comes from, and you meet three rival accounts of what good reason is. Your goal is to state each view fairly and test it, not to crown a winner.

Why you already care about this

You are hiking, and you reach a fork in the trail. A wooden sign says "Lake" with an arrow pointing left. You trust it and turn left. Twenty minutes later, there is the lake, flat and bright between the trees.

Here is what you never find out. A storm the night before knocked the sign loose, and it spun around on its post. It stopped, by pure chance, pointing at the left trail, the one that really does go to the lake. If the lake had been to the right, the sign would still have pointed left, and you would still have turned left.

So: you believed the left trail led to the lake, you had good reason, and you were right. Did you know it? Many people feel a tug both ways. In 1963 the philosopher Edmund Gettier published a three-page paper that turned that tug into one of the most discussed problems in the study of knowledge.

By the end of this chapter you will be able to:

state the justified true belief analysis and say why each of its 3 conditions seems needed;
explain why justification is good reason and not certainty, and key Dataset B's argument 1 for validity only;
explain why one counterexample can defeat a definition;
describe the Gettier cases and credit them correctly;
put a Gettier-style case in standard form and judge its validity;
sort a claim as a priori or a posteriori;
state the regress problem and three answers to it, each with its strongest objection and a reply.

Carry this line with you: right by luck is not the same as knowing.

Where we are

Already covered: Week 1, What Philosophy Is: Socrates and the Examined Life, gave you the counterexample test for a definition. Week 2, Arguments and Thought Experiments, gave you standard form, validity, and denying the consequent. Week 3, Plato: Reality and the Forms, asked how appearance differs from reality. Week 4, Knowledge I: Doubt, Reason, and Experience, asked what you can know for certain, and whether knowledge comes from reason or from experience.
This week: what knowledge is; justified true belief; the Gettier cases; a priori and a posteriori knowledge; and three theories of justification that answer the regress problem.
How they connect: Week 4 ended on an open question, whether knowledge requires certainty. This week offers a definition that asks for good reason instead, and then aims Week 1's counterexample test at that definition.
Where we're going next: Week 6, The Mind-Body Problem, begins a new unit on mind and self, and asks what a mind is.

Two tools from earlier weeks carry this chapter. From Week 1: a counterexample to a definition is a case the definition gets wrong. From Week 2: standard form numbers the premises P1 and P2 and gives the conclusion last, marked C and introduced by "So". You also need valid, which means the conclusion cannot be false if the premises are true, and the form called denying the consequent: if P then Q; not Q; so not P.

1. State the classic definition: justified true belief

Think about a nurse who says, "I know the person in bed 4 is allergic to penicillin." What would make that more than a guess? Three things seem to matter. The person really must be allergic. The nurse must actually believe it. And the nurse needs good reason, such as a chart entry the person confirmed out loud.

Take away any one, and "know" stops fitting. If the person is not allergic, the nurse did not know it, however sure she felt. If the nurse does not believe it, she does not know it. And if she only guessed, a lucky guess is not knowledge.

That is the idea behind the traditional and most famous definition of knowledge.

Justified true belief — the traditional analysis of knowledge: a person knows a claim when the claim is true, the person believes it, and the person is justified in believing it.

The definition has 3 conditions. The course numbers them so you can check them one at a time:

(1) Truth — the claim is true.
(2) Belief — the person believes it. A belief is a person's taking a claim to be true; beliefs can be true or false.
(3) Justification — the person has good reason to hold it. Justification is support for a belief, such as evidence, a reliable source, or sound reasoning.

A definition like this one is called an analysis of knowledge: an account that tries to state the conditions that hold in every case of knowledge and in no other case.

Worked example — checking the 3 conditions. Run the nurse's claim through the list. (1) Truth: the person is allergic, so yes. (2) Belief: the nurse believes it, so yes. (3) Justification: a confirmed chart entry is good evidence, so yes. All 3 hold, so the analysis says the nurse knows. In words: on this definition, knowing is believing something true for a good reason.

Misconception check — belief is not the same as knowledge. Students often think that feeling sure is enough to know. It is tempting because "I know" and "I'm sure" sound alike in everyday talk. The cure is condition (1). A person can be completely sure and still wrong, and no one knows a falsehood. Belief is one condition of knowledge, not the whole of it.

2. Ask for good reason, not certainty

Week 4 left you with a hard standard. Descartes searched for a belief that no doubt could touch. If knowledge needs that kind of certainty, you know very little. Dataset B, the argument set (illustrative), has an argument that runs on exactly that worry. Its premises were written for teaching, and the course does not endorse them.

Worked example — Dataset B, argument 1, recalled. Lay it out, then name its form.

P1: If knowledge requires certainty, then I know very little.

P2: Knowledge requires certainty.

C: So I know very little.

The pattern is if P then Q; P; so Q. That is modus ponens, so the argument is valid. If both premises were true, the conclusion could not be false.

Now look at condition (3) of justified true belief. It asks for good reason, not for proof beyond all doubt. The nurse's chart entry could, in some strange case, be wrong. On the justified true belief analysis, she can still know. So a defender of the analysis rejects P2.

That does not settle the argument. Whether knowledge requires certainty is still an open question, and the skeptic has replies of their own. So the course keys argument 1 for validity only, never for soundness.

Misconception check — knowledge does not need certainty on this definition. Students often think you cannot know anything unless you are certain of it. It is tempting because certainty feels like the gold standard after Descartes. The cure is to read condition (3) word for word: justified, not certain. Many things you would happily say you know, such as where you parked or what you ate this morning, rest on good reason rather than on proof.

3. Aim a counterexample at a definition

A coach says, "A player is ready for the match if and only if they finished every practice." That sounds like a fair rule. Then a player finishes every practice and sprains an ankle the night before. Finishing every practice was not enough. One case broke the rule.

Definitions work the same way, because a definition makes a claim about every case. Two terms help you say exactly what it claims.

Necessary condition — a condition that must hold for something to be the case. Truth is a necessary condition for knowledge, because no one knows a falsehood.
Sufficient condition — a condition whose holding is enough, on its own, for something to be the case.

The justified true belief analysis treats each of its 3 conditions as necessary, and all 3 together as sufficient. So it claims: every justified true belief is knowledge.

Worked example — what it takes to defeat a universal claim. A claim of the form "every A is B" is false if even 1 A is not B. You do not need a pattern or a pile of cases. So to defeat the definition as stated, you need 1 counterexample: a single case that has all 3 conditions and is still not knowledge. In words: one case where justified true belief falls short of knowing is enough to show the definition, as written, fails.

That is Week 1's Socratic test, aimed at the most famous definition in this branch of philosophy.

Misconception check — one case is enough. Students often think a single odd example is too weak to defeat a definition. It is tempting because one case feels like an exception, and rules have exceptions. The cure is to read the definition's own claim: every justified true belief is knowledge. A claim about every case is false the moment one case fails. A definition can be repaired after that, but the version that failed has failed.

4. Meet the Gettier cases

Now the week's thought experiment, the Week 5 case on the course's thought-experiment roster.

In 1963, Edmund Gettier published "Is Justified True Belief Knowledge?" in the journal Analysis. The paper runs three pages. In it, Gettier described cases where a person has a belief that is justified and true, but true only by luck, so that the person seems not to know.

Gettier case — a case in which a person has a belief that is justified and true, but true only by luck, so that the person seems not to know; named for Edmund Gettier's paper of 1963.

The roster gives the cases a question: Is justified true belief enough for knowledge? The cases test the analysis of knowledge.

Worked example — placing the paper in time. Line up the date against Week 4's anchor.

Descartes' Meditations on First Philosophy: 1641.
Gettier's paper: 1963.
The gap: 1963 − 1641 = 322 years.

In words: Gettier's challenge came 322 years after Descartes' search for certainty. Descartes asked whether anything can be known for sure; Gettier asked whether the standard definition of knowledge is even right.

A note on sources. This chapter does not retell the details of Gettier's own cases. It works through cases written for this course on the same shape, and each one is labelled as a variation. The shape is what matters: justified, true, and right by luck.

Misconception check — a famous definition is not a settled one. Students often treat justified true belief as the agreed definition of knowledge, the one to memorize and move on from. It is tempting because it is old, tidy, and widely taught. The cure is the Gettier cases themselves. They are why philosophers still debate what knowledge is, and the course keys no answer to that debate.

5. Run the trail sign as a Gettier-style case

Go back to the fork in the trail. The trail sign is a variation written for this course, built on the shape of Gettier's cases, not one of Gettier's own.

Worked example — the 3 conditions, one at a time. Take the claim "the left trail leads to the lake".

(1) Truth: the left trail does lead to the lake. Yes, that is 1.
(2) Belief: the hiker believes it and turns left. Yes, that is 1 more.
(3) Justification: a posted trail sign is good evidence. Yes, 1 more.
The tally: 1 + 1 + 1 = 3, so all 3 conditions hold.

Yet the belief is true only by luck. The storm-spun sign would have pointed left whichever trail led to the lake. What made the hiker's belief true, the lie of the land, had nothing to do with what justified it, the sign.

Worked example — the challenge in standard form. Here is the course's reconstruction (illustrative).

P1: If every justified true belief is knowledge, then the hiker knows that the left trail leads to the lake.

P2: The hiker does not know that the left trail leads to the lake.

C: So not every justified true belief is knowledge.

Name the form. Let P be "every justified true belief is knowledge" and Q be "the hiker knows". The pattern is if P then Q; not Q; so not P. That is denying the consequent, the form of Dataset B's argument 2. So the argument is valid: if P1 and P2 are true, C cannot be false.

Is it sound? P1 follows from what the definition says, since the hiker's belief has all 3 conditions. P2 is the hard part. It is an intuition about a thought experiment, and some philosophers resist it. So the course keys the validity and never the answer to the case.

Here is an honesty note. You may feel that the hiker did know, in a loose sense. That reaction is worth stating and defending. The point of the case is to make you say what knowledge requires, not to hand you a verdict.

Misconception check — the case does not say the hiker was careless. Students often think the hiker should have checked more carefully, so the belief was not really justified. It is tempting because we want to blame someone for a lucky outcome. The cure is to keep condition (3) honest. A posted sign is the kind of evidence anyone would rely on, and nothing looked wrong. The case works because the justification is good and the truth still arrives by luck.

6. Spot the shared shape: two more lucky beliefs

Once you see the shape, you start finding it everywhere. Here are 2 more variations written for this course.

The study partner. A student checks a homework answer against a study partner's, because the partner is careful and usually right. The question asks how many minutes are in 3 hours and 20 minutes. The correct working is 3 × 60 = 180, then 180 + 20 = 200. The partner slipped twice: they wrote 170 for the 3 hours, then added 30 instead of 20, and 170 + 30 = 200. The 2 slips cancel. The student believes that 200 is correct, has good reason to trust the partner, and is right. But the partner's working did not reach 200 for the right reason.

The help-desk light. A help-desk worker tells a caller the server is running, because the status light on the rack shows green. The worker does not know that the light has been stuck on green for a week. As it happens, the server is running. The belief is true, believed, and backed by a light that is normally good evidence. It is right by luck.

Worked example — finding the shape. For each case, name what justified the belief and what made it true.

The trail sign: justified by the sign; made true by where the trail goes.
The study partner: justified by the partner's track record; made true by correct arithmetic the partner did not do.
The help-desk light: justified by the light; made true by the server's actual state.

In words: in all 3 cases, what justifies the belief is not what makes it true, and the two line up only by luck.

Misconception check — a false belief is not a Gettier case. Students often call any case where evidence misleads someone a Gettier case. It is tempting because the cases all involve misleading evidence. The cure is condition (1). If the help-desk worker had said "running" while the server was down, the belief would be false, and the definition already says that is not knowledge. A Gettier case needs the belief to come out true.

7. Sort knowledge by its source: a priori and a posteriori

Try two claims. "Every triangle has 3 sides." "The left trail leads to the lake." You could check the first one sitting in a dark room, with no map and no window. The second you can only learn by going out, looking at a map, or trusting someone who has walked it.

Philosophers name the difference.

A priori — knowable independently of experience, as in mathematics. It describes how a claim is known, not when a person first learned it.
A posteriori — knowable only through experience, such as what the senses report about the world.

You met this divide from the other side in Week 4. Rationalists hold that some substantive knowledge of the world is a priori; empiricists hold that all knowledge of the world is a posteriori.

Worked example — sorting 2 claims. "Every triangle has 3 sides" is a priori: understanding what a triangle is lets you see it is true, with no survey of triangles needed. "The left trail leads to the lake" is a posteriori: nothing in the words tells you where the trail goes, so only experience can.

Misconception check — "a priori" does not mean "learned first". Students often read a priori as "known before other things" or "learned early". It is tempting because "prior" means "before". The cure is to ask how the claim is known, not when. A person who first learns that 12 ÷ 4 = 3 at age forty still knows it a priori, because the knowing does not rest on experience of the world.

8. Follow the chain of reasons: the regress problem

A child asks a parent, "Why do you think it will rain?" "Because the forecast says so." "Why trust the forecast?" "Because it is usually right." "How do you know it is usually right?" Every reply is another belief, and the child can always ask again.

That game of "why?" points at a real problem about justification. A belief is often justified by another belief. But then that belief needs a justification too.

Regress problem — the problem that if every justified belief needs another belief to justify it, the chain of reasons seems to go on forever, loop back on itself, or stop at something unsupported.

The skeptic, a person who argues that we know far less than we think, presses the problem hard. An endless chain never finishes, so it seems to give no support. A loop seems to use a belief to support itself, like the circular argument of Week 4. A chain that stops at an unsupported belief seems to rest on nothing. So, says the skeptic, no belief is justified, and so no belief is knowledge.

Worked example — the 3 ways a chain can go. Picture the forecast chain.

It goes on forever: every reason has a further reason, with no last one.
It loops: at some point, "the forecast is usually right" is supported by a belief that depends on trusting the forecast.
It stops: some belief at the bottom has no further reason behind it.

In words: the skeptic says each of these 3 options fails, and each theory of justification you meet next says one option, or a new picture, can work.

Misconception check — the regress is not about stubborn children. Students often treat the regress as a word game that ends when someone gets tired of asking "why?". It is tempting because the child's version is funny. The cure is to see what is at stake: if every route fails, then nothing you believe is justified, and the justified true belief analysis says nothing is known. That is a serious skeptical conclusion, and the next section gives three serious replies.

9. State three answers to the regress

Here are the 3 theories of justification this week compares, each stated the way its best defenders would. Each one is an answer to the regress problem and a reply to the skeptic.

Foundationalism. Think of a building: the upper floors rest on lower ones, and the lower floors rest on a foundation that rests on nothing else in the building.

Foundationalism — the theory of justification that holds that some beliefs are basic and support the rest, so the chain of reasons comes to an end.
Basic belief — in foundationalism, a belief that is justified without resting on any other belief, and that helps support the beliefs built on it.

A foundationalist might offer "it looks to me as if there is a sign here" or "every triangle has 3 sides" as candidates for basic beliefs. The reply to the skeptic: the chain stops, and it stops somewhere solid.

Coherentism. Think of a jigsaw puzzle. No single piece holds up the rest, but each piece is supported by how well it fits the others.

Coherentism — the theory of justification that holds that beliefs are justified by fitting together in a system of beliefs that support one another, so no belief has to come first.

The reply to the skeptic: the regress pictures justification as a line, but it is really a web, and a web needs no first strand.

Reliabilism. Think of a thermometer you trust. You trust it not because it gives you reasons, but because it tends to read the right temperature.

Reliabilism — the theory of justification that holds that a belief is justified when it is produced by a reliable process, one that tends to produce true beliefs.

Good eyesight in daylight, careful memory, and sound reasoning are examples of reliable processes. The reply to the skeptic: justification does not need a chain of reasons you can recite at all; it depends on how the belief was formed.

Worked example — one belief, three accounts. Take a lifeguard's belief that a swimmer is waving for help.

A foundationalist says: the belief rests on a basic belief about what the lifeguard sees right now, and that basic belief needs no further support.
A coherentist says: the belief is justified because it fits with everything else the lifeguard believes, such as the rough water and the swimmer's distance from shore.
A reliabilist says: the belief came from trained eyesight in clear daylight, a process that tends to get such things right.

In words: the three theories can agree that the lifeguard is justified while disagreeing about what makes the belief justified.

Misconception check — the three theories are not three steps. Students often treat foundationalism, coherentism, and reliabilism as a sequence, where each one fixes the last and the newest wins. It is tempting because the chapter lists them in order. The cure is to see them as rivals. They give different accounts of what justification is, and each still has defenders.

10. Test each answer: objections and replies

The fair way to weigh rival views is the course's way: each view in its strongest form, its strongest objection, and a reply from its own side.

Three theories of justification compared: central claim, strongest objection, and a reply from each side
Theory	Central claim	Strongest objection	Reply from its side
Foundationalism	Some beliefs are basic and support the rest.	If nothing supports a basic belief, stopping there looks arbitrary.	A basic belief is supported by experience or by being self-evident, not by another belief, so the stopping point is not arbitrary.
Coherentism	Beliefs are justified by fitting together in a system that supports itself.	A made-up story can fit together perfectly and still be false.	A real person's system includes beliefs from perception, which the world keeps supplying, so it must fit experience too.
Reliabilism	Beliefs are justified when produced by reliable processes.	A person whose process is reliable, but who has no idea it is reliable, does not seem justified.	A young child knows a parent's face without being able to defend the process, so demanding reasons a person can recite sets the bar where the skeptic wants it.

Worked example — the reply count. Count what the table gives you: 3 theories, 3 objections, and 3 replies. So each theory gets 3 ÷ 3 = 1 objection and 1 reply. In words: no theory is left facing an objection without an answer from its own side.

Read the rows one at a time. The foundationalist worry is that a stopping point with no support is a stopping point chosen by fiat. The reply says basic beliefs have support, only not from another belief. The coherentist worry is a detailed novel: every chapter fits the others, yet none of it happened. The reply says your web is tied to the world, because perception keeps adding beliefs you did not choose. The reliabilist worry is a person with a reliable process and no clue that it is reliable. The reply points to young children and to everyday knowledge that no one could defend step by step.

A caveat to keep in view: whether any of these theories also solves Gettier's problem is a further open question. The course keys no verdict on which theory of justification is right.

Where do the three disagree, in one plain sentence? They disagree about whether justification comes from a foundation, from fit, or from a reliable process.

Misconception check — an objection with a reply is still open. Students often think the last objection mentioned is the one that wins. It is tempting because the order of a table feels like a ranking. The cure is to read the reply column with the same care as the objection column. Every theory here has a serious objection and a serious reply, and that is what an open question looks like.

Key terms

Justified true belief — The traditional analysis of knowledge: a person knows a claim when the claim is true, the person believes it, and the person is justified in believing it. (first used: 1. State the classic definition: justified true belief)
Belief — A person's taking a claim to be true; a belief can be true or false, and can be held with good reason or with none. (first used: 1. State the classic definition: justified true belief)
Justification — Good reason or support for holding a belief, such as evidence, a reliable source, or sound reasoning; it can fall short of certainty. (first used: 1. State the classic definition: justified true belief)
Analysis of knowledge — An account that tries to state the conditions under which a person knows a claim, so that the conditions hold in every case of knowledge and in no other case. (first used: 1. State the classic definition: justified true belief)
Necessary condition — A condition that must hold for something to be the case; being true is a necessary condition for being known, because no one knows a falsehood. (first used: 3. Aim a counterexample at a definition)
Sufficient condition — A condition whose holding is enough, on its own, for something to be the case; the justified true belief analysis claims that its three conditions together are sufficient for knowledge. (first used: 3. Aim a counterexample at a definition)
Gettier case — A case in which a person has a belief that is justified and true, but true only by luck, so that the person seems not to know; named for Edmund Gettier's paper of 1963. (first used: 4. Meet the Gettier cases)
A priori — Knowable independently of experience, as in mathematics; it describes how a claim is known, not when a person first learned it. (first used: 7. Sort knowledge by its source: a priori and a posteriori)
A posteriori — Knowable only through experience, such as what the senses report about the world. (first used: 7. Sort knowledge by its source: a priori and a posteriori)
Regress problem — The problem that if every justified belief needs another belief to justify it, the chain of reasons seems to go on forever, loop back on itself, or stop at something unsupported. (first used: 8. Follow the chain of reasons: the regress problem)
Skeptic — A person who argues that we know far less than we think, or that our beliefs lack the justification that knowledge needs. (first used: 8. Follow the chain of reasons: the regress problem)
Foundationalism — The theory of justification that holds that some beliefs are basic and support the rest, so the chain of reasons comes to an end. (first used: 9. State three answers to the regress)
Basic belief — In foundationalism, a belief that is justified without resting on any other belief and that helps support the beliefs built on it. (first used: 9. State three answers to the regress)
Coherentism — The theory of justification that holds that beliefs are justified by fitting together in a system of beliefs that support one another, so no belief has to come first. (first used: 9. State three answers to the regress)
Reliabilism — The theory of justification that holds that a belief is justified when it is produced by a reliable process, one that tends to produce true beliefs. (first used: 9. State three answers to the regress)

Summary

Justified true belief: knowing a claim means it is true, you believe it, and you are justified.
Justification is good reason, not certainty; Dataset B's argument 1 is keyed valid and never sound.
A definition claims every case, so 1 counterexample defeats it as stated.
Gettier's 1963 paper described justified true beliefs that are true only by luck.
In a Gettier case, what justifies the belief is not what makes it true.
A priori means knowable independently of experience; it does not mean learned first.
The regress problem: every reason seems to need a further reason.
Foundationalism, coherentism, and reliabilism are rival answers, each with an objection and a reply.

Check your understanding

Work these before looking at the answers — they are ungraded, and the answers (with reasoning) are at the bottom of the page.

A commuter checks a station's departure board, which shows a train as on time. Unknown to the commuter, the board froze an hour ago. The train is in fact on time. Check the 3 conditions of justified true belief for the commuter's belief, and explain whether this is a Gettier-style case.
Sort each claim as a priori or a posteriori: (a) "If every jar on the shelf is full and this is a jar on the shelf, then this jar is full." (b) "The pharmacy on the corner closes at nine." (c) "12 ÷ 4 = 3."
A club rule says, "A member may vote if and only if they have paid this year's dues." Describe one case that would show paying dues is not a sufficient condition for voting, and explain why one case is enough.
Name the theory of justification each speaker is using. (a) A gardener: "My belief that this leaf is yellow rests on how it looks to me right now, and that needs no further reason." (b) A pharmacist: "My belief about this order is justified because it fits everything else I believe about this customer." (c) A birdwatcher: "My belief came from sharp eyesight in good light, a process that tends to get birds right."

Answers (worked reasoning — read after attempting)

(1) Truth: the train is on time, so yes. (2) Belief: the commuter believes it, so yes. (3) Justification: a departure board is normally good evidence, so yes. All 3 conditions hold. It is a Gettier-style case, because the board froze an hour ago: what justified the belief, the frozen board, is not what made it true, the train's actual running. The belief is right only by luck.
(a) A priori: you can see it is true from the words alone, with no need to look at the shelf. (b) A posteriori: only experience, such as reading the sign or asking, tells you the closing time. (c) A priori: the arithmetic does not rest on experience of the world, however late a person first learned it.
A member pays this year's dues but has been suspended for breaking club rules, so the club does not let them vote. That case has paying dues without the right to vote, so paying is not enough on its own. One case is enough because the rule makes a claim about every member: a claim about every case is false if a single case fails.
(a) Foundationalism: the gardener treats a belief about how things look right now as basic, needing no further support. (b) Coherentism: the pharmacist's justification is fit with the rest of their beliefs. (c) Reliabilism: the birdwatcher points to a process that tends to produce true beliefs.

Next up in this module: the Readings & Resources page, the lecture tutorial, the practice set, the quiz, the discussion, and the assignment. Next week, the Turing test and the Chinese room carry the question from what we know to what a mind is.

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