Everything in this course is built from one kind of sentence: the kind that can be right or wrong about the world. Before you can ask whether a claim holds up, you have to be able to spot one. Most of the time that is easy. This section slows down for the two cases that are not: sentences that look like claims but aren't, and claims that nobody can check yet.
Which sentences are statements
Picture a fact-checker at a newspaper. On the desk sit two rubber stamps. One says TRUE and the other says FALSE. The job is simple to describe: take a sentence, check it against the world, and stamp it.
Now hand the fact-checker some sentences. "The pharmacy closes at six." That can be checked. Call the pharmacy, find out, stamp it. "Is the pharmacy open?" Neither stamp fits. A question asks for something. It doesn't tell you anything that could be right or wrong. "Close the window." No stamp either. Nobody gets the facts wrong by giving an order. "Wow, what a game!" is a feeling, not a report, so it gets no stamp.
That is what a statement is: a sentence the fact-checker could stamp. The stamp it deserves is called its truth value, which just means "true or false, whichever it is." Every statement gets one stamp. Never both, and never none.
Here is a quick test that does the same job. Imagine replying to the sentence with "That's true" or "That's false." After "The pharmacy closes at six," that reply is natural. After "Close the window," it is nonsense.
Three warnings. First, don't judge by the punctuation mark. "You finished the report?" asks something. "I asked if the bus was late" tells you about something that happened, so it can be stamped. Second, a wrong sentence still gets a stamp. "Earth has two moons" is a statement. Its stamp is FALSE. Third, some sentences need a speaker and a time before anyone can check them. "I'm hungry" depends on who says it and when. Once you know that, it can be stamped. At noon the stamp might be TRUE. After lunch it might be FALSE.
A statement is a sentence that says something is the case, and so is either true or false. Which of the two it is, true or false, is its truth value. In this course every statement has exactly one truth value: never both, never neither.
Many ordinary sentences are not statements, because they do not say that anything is the case:
- A question asks for information: "Is the pharmacy open?" It can be answered, but the question itself is neither true nor false.
- Commands are sentences that tell someone to act, and requests work the same way: "Close the window." "Please send the report by Friday." A command can be obeyed or ignored, not believed or doubted.
- An exclamation expresses a reaction: "Wow!" "What a game!" It reports no fact that could fail to hold.
A reliable test is the reply test: a sentence is a statement just when the reply "That's true" or "That's false" makes sense. "The pharmacy closes at six" passes. "Close the window" fails, since "That's false" is not a reply to an order.
Three refinements. First, the test concerns what a sentence does, not its punctuation. "You finished the report?" ends in a question mark and asks. "I asked whether you finished the report" reports an event, so it is a statement. Second, a false sentence is still a statement: "Earth has two moons" has a truth value, and that value is false. Being a statement means having a truth value, not having the value true.
Third, some sentences depend on who says them, where, and when: "I'm hungry," "It's raining here." Once the speaker, place, and time are fixed, each makes a definite claim and is a statement. Its truth value can differ from one moment to the next, which is why the context is fixed first.
Can it be stamped?
Sort each sentence: could a fact-checker stamp it true or false, or not?
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What this task checks
Structure checked automatically. Whether your ideas are convincing isn't graded, so reread with the checklist.
The compiler says
A model answer
Correct answer
Also accepted:
Why
Why
Worked example
Sorting a school notice
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1take one sentence at a time
A school sends home this note: "The field trip is on Friday. Bring a packed lunch. Who still needs a permission slip? Buses leave at 8:30." Decide which sentences are statements.
take one sentence at a time
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2
"The field trip is on Friday." Try the reply test: "That's true" is a natural answer. It is a statement.
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3
"Bring a packed lunch." This tells the reader to do something. "That's false" makes no sense as a reply to it. It is a command, not a statement.
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4
"Who still needs a permission slip?" This asks for information. You can answer it, but you can't call it true or false. Not a statement.
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5
"Buses leave at 8:30." This passes the reply test. So the note holds two statements, the first and last sentences, wrapped around a command and a question.
Worked example
A wrong sentence is still a statement
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1common trap
A classmate says: "'Every month has 31 days' isn't a statement, because it's false." Decide whether the classmate is right.
common trap
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2
Apply the reply test. "That's false" is a perfectly sensible reply to "Every month has 31 days." So the sentence has a truth value.
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3
Find the value. February has 28 or 29 days, so the truth value is false.
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4
Being a statement means having a stamp, either one. It does not mean getting the TRUE stamp. The classmate mixed up "is a statement" with "is a true statement." The sentence is a false statement.
Worked example
Fixing the speaker and time first
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1context-dependent sentence
Is "It's raining here" a statement?
context-dependent sentence
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2
As printed, nobody knows where "here" is or when it was said. So we can't check it yet, and the reason is missing context, not missing facts.
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3
Fix the context: Priya texts it from Denver at 3:00 p.m. on a Tuesday. Now the sentence claims that it was raining in Denver at that moment.
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4
That claim has a truth value, so the sentence is a statement once its context is fixed. The same words texted from a sunny beach would make a different claim, with a different stamp.
Check your understanding (counts toward your progress)
Which rewrite turns the question “Is the gym open on Sundays?” into a statement about the same topic?
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Adding words to a question still leaves a question. It asks which way things are without saying.
This tells someone to do something. You can obey it, but you can’t stamp it true or false.
A polite request is still a request. “That’s false” makes no sense as a reply to it.
Why
“The gym is closed on Sundays” says how things are, so it takes a stamp. It answers the question “no.” The rewrite “The gym is open on Sundays” would work just as well. Either answer to the question is a statement.
A statement tells how things are. Which choice says something about the gym instead of asking or instructing?
This group-chat message holds two statements. Select each one: click its first word, then its last word.
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What this task checks
Structure checked automatically. Whether your ideas are convincing isn't graded, so reread with the checklist.
The compiler says
A model answer
Why
The practice sentence and the flooding sentence each say something is the case. The cones sentence asks, and the last one orders, so neither of those can be stamped.
Correct answer
Also accepted:
Why
Look for the sentences that end in a period and say how things are.
One sentence asks and one gives an order. Skip those.
Which of these is NOT a statement?
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This one reports the speaker’s wish. That wish either exists or it doesn’t, so the sentence can be stamped.
This one says how many replies arrived: none. One reply would make it false, so it has a truth value.
“Might” makes a claim about what could happen, and that claim is itself true or false. It is a statement.
Why
“The meeting was canceled?” is a question in statement word order. It asks whether the meeting was canceled. The other three each say something is the case: about a wish, about replies, and about a chance of closing early.
Read each sentence out loud, paying attention to the end mark.
Which one is asking for information instead of giving it?
Which of these sentences is a statement?
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This asks about the museum instead of saying anything about it. You can answer it, but “That’s false” isn’t a reply to a question.
An instruction to visit can be followed or ignored. Nobody could stamp it true or false.
This expresses how the speaker feels. It reports no fact that could turn out wrong.
Why
“The museum is free on Sundays” says something is the case, so it gets a truth value: true or false, whichever it is. The others ask, instruct, or react.
Try replying “That’s true” or “That’s false” to each one. Which reply makes sense?
Practice: Can it be stamped? (5 problems · doesn’t affect your progress)
Which sentence can be stamped true or false?
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A question asks whether the book is there. It doesn’t say either way.
An instruction to check can be carried out, but it isn’t true or false.
This is a pure reaction. It says nothing is the case, so “That’s false” makes no sense as a reply.
Why
Only “The library has a copy of this book” says something is the case, so only it takes a stamp.
Use the reply test on each sentence.
The library has a copy of this book.
Each button is one whole sentence from a store’s website. Label every sentence.
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What this task checks
Structure checked automatically. Whether your ideas are convincing isn't graded, so reread with the checklist.
The compiler says
A model answer
Why
The shipping sentence says something is the case, so it is the statement. The site also gives an order, asks a question, and offers a greeting.
Correct answer
Also accepted:
Why
One sentence reports a fact about shipping.
“I’m tired.” Which is the best description?
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A report about how someone feels is still a report. If Jin says it wide awake, it’s false.
“I” just needs the context to say who is speaking. Then the sentence can be checked.
People sometimes say it when they aren’t tired. The stamp depends on the facts, not the habit.
Why
With the speaker and time fixed, “I’m tired” claims that this person is tired at this moment. That claim is true or false.
Fix the speaker and the time. Could the sentence then be right or wrong?
A statement once we know who says it and when.
This note on a fridge holds exactly one statement. Select it.
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What this task checks
Structure checked automatically. Whether your ideas are convincing isn't graded, so reread with the checklist.
The compiler says
A model answer
Why
“The plumber comes at noon” says something is the case. “Please buy milk” is a request, and the egg sentence asks.
Correct answer
Also accepted:
Why
Skip the request and the question.
A coworker writes, “You finished the slides?” Is this a statement?
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Word order isn’t what decides it. This sentence asks you something, and you would answer “yes” or “no,” not “that’s true.”
A finished set of slides answers the question. It doesn’t make the question true.
Why
The coworker is asking. A natural reply is “Yes” or “Not yet,” not “That’s true,” so the reply test says it isn’t a statement.
What would you naturally say back: “that’s true” or “yes”?
No. Its word order looks like a claim, but its job is asking.
Statements nobody can settle yet
Back to the fact-checker's desk. Some sentences arrive that can't be checked today. "It snowed in Oslo on March 3, 1650." No weather records go back that far. "The package will arrive on Thursday." It's only Monday. "There is life on another planet." Nobody has looked everywhere. "Dana is thinking of the number 7." Only Dana knows.
The fact-checker doesn't throw these away. They go into a tray marked PENDING. Each one will get one stamp and only one, TRUE or FALSE. We just can't tell yet which stamp is the right one. A statement counts as settled once somebody has found out which stamp fits. Until then it waits in PENDING, even when the fact itself was fixed long ago, like the Oslo snow. A statement is a sentence that a stamp fits, not a sentence someone has already stamped.
Compare a question on the same topic: "Is there life on another planet?" That one goes in the trash, not the pending tray. Even if astronauts find life tomorrow, the question still won't be true or false. It will have an answer. The answer is a new statement: "There is life on another planet."
So when you meet a sentence nobody can check, ask one question: if we learned everything about the world, would a stamp fit it? If yes, it's a statement, pending or not. This matters later. Most claims worth thinking hard about are the ones nobody has settled yet.
Whether a sentence is a statement depends on whether it has a truth value, not on whether anyone knows that value. In this course a statement is settled once someone has found out which truth value it has, and unsettled until then. A fixed fact about the past that nobody has checked still counts as unsettled. A statement can be unsettled for several different reasons:
- Lost facts. "It snowed in Oslo on March 3, 1650." Nobody recorded it, but it either snowed or it didn't.
- The future. "The package will arrive on Thursday." Thursday will settle it. This course treats such predictions as statements.
- Open questions. "There is life on another planet." No one knows, yet the sentence describes a way the universe either is or isn't.
- Private facts. "Dana is thinking of the number 7." Only Dana can check.
Contrast each of these with a question on the same topic. "Is there life on another planet?" has no truth value at all, and nothing we could learn would give it one. "There is life on another planet" has a truth value that no one has found yet. The topic is the same; the job the sentence does is different.
This matters because much of careful reasoning is about unsettled claims. Evidence, reasons, and later tests all work on statements whose truth values are not known in advance. A reader who throws out every unsettled sentence throws out the very claims most worth thinking about.
Settled, pending, or no stamp
Sort each sentence: a statement whose truth is already settled, a statement nobody can settle yet, or not a statement at all.
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What this task checks
Structure checked automatically. Whether your ideas are convincing isn't graded, so reread with the checklist.
The compiler says
A model answer
Correct answer
Also accepted:
Why
Why
Worked example
A prediction about next week
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1the future
Is "The package will arrive on Thursday" a statement, said on a Monday?
the future
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2
Ask whether a stamp would fit if we knew everything. On Thursday night we will know whether it arrived. So yes, a stamp fits.
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3
Nobody knows the stamp on Monday. That makes the sentence unsettled, not stampless.
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4
It is a statement. Its truth value is unknown on Monday and settled by Friday.
Worked example
Same topic, different job
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1common trap
Compare "Is there life on another planet?" with "There is life on another planet." Nobody knows the answer to either. Are both statements?
common trap
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2
Try the reply test on the question. "That's false" is not a reply to a question. It has no truth value, so it is not a statement.
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3
Try it on the second sentence. "That's false" is a sensible reply, even if nobody can back it up yet. It has a truth value that no one has found.
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4
Only the second is a statement. What separates them is the job the sentence does. Whether anyone knows the answer plays no part.
Check your understanding (counts toward your progress)
The fact-checker’s PENDING tray holds sentences that…
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Questions go in the trash, not the pending tray. No stamp will ever fit a question.
Every statement in the tray is true or false. We just can’t tell which yet.
Pending says nothing about which way the stamp will go. It only says nobody knows yet.
Why
A pending sentence is a statement: exactly one stamp fits it. The only thing missing is our knowledge of which stamp that is.
What does “pending” mean for a stamp that will eventually be applied?
What separates “Is there a cheaper flight?” from “There is a cheaper flight”?
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Both are unchecked right now, but that isn’t what matters. A search could stamp the second one; the first would still just be a question.
Politeness has nothing to do with it. A question, however polite, doesn’t claim anything.
Being unsettled doesn’t stop a sentence from being a statement. It only means we don’t know its stamp yet.
Why
The topic is the same, but the jobs differ. “There is a cheaper flight” claims something, and a search would stamp it. The question only asks.
Same topic, different job. Which sentence tells you something?
It’s Monday. Which rewrite turns “Will it rain at the picnic on Saturday?” into a statement nobody can settle yet?
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That is a statement, but the news report already settled it. The task asks for one nobody can settle yet.
Rewording the question keeps it a question. It still gets no stamp.
An instruction can be followed or ignored, not stamped true or false.
Why
“It won’t rain at the picnic on Saturday” makes a prediction. Saturday will stamp it TRUE or FALSE; until then it is pending. “It will rain at the picnic on Saturday” would work just as well. The question never gets a stamp.
Look for the choice that says what will happen, instead of asking or instructing.
Which sentence is a statement whose truth value nobody knows yet?
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This asks the question. It will never have a truth value, however much anyone learns.
This is an instruction. There’s nothing in it to be true or false.
This one is a statement, but its truth is already settled.
Why
“There is life on another planet” has a truth value that no one has found yet. The question and the instruction have no truth value, and the boiling-point sentence is already settled.
Two choices aren’t statements at all. Of the other two, which one hasn’t been settled?
Practice: Stampable, even when nobody knows the stamp (5 problems · doesn’t affect your progress)
“There are more than 500 fish in Miller’s Pond.” Nobody has counted. Is it a statement?
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Nobody knowing is different from no stamp fitting. Counting would settle it.
It tells you how many fish there are; it doesn’t ask. A question about the pond would end in a question mark and ask.
Why
The pond has some number of fish, so the sentence is true or false. It is a statement whose stamp is pending.
If someone drained the pond and counted, would a stamp fit?
Yes. The pond holds some definite number of fish.
Sort each sentence about a school play.
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What this task checks
Structure checked automatically. Whether your ideas are convincing isn't graded, so reread with the checklist.
The compiler says
A model answer
Why
The opening date is fixed. The sell-out prediction waits for Saturday. The question and the instruction never get a stamp.
Correct answer
Also accepted:
Why
Which sentence is a prediction?
Which pair shows the same topic doing two different jobs?
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These two do the same job, reporting, about different things.
These two do the same job, giving an order, about different things.
Why
Both sentences are about the keys, but only the second says something is the case. The first asks, so it has no truth value, even though nobody knows the answer to either.
Look for one sentence that asks and one that tells, on the same subject.
“Did anyone find my keys?” and “Someone found my keys.”
Turn this question into a statement about the same topic: “Is there a snack machine on the third floor?”
AI grading isn't configured on this deployment.
Explanation
Say how things are instead of asking.
Which sentence should NOT go in the PENDING tray?
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This prediction will be settled next spring, so it belongs in PENDING.
A tree’s age is a definite fact. Until someone checks, this statement waits in PENDING.
Birth records might settle it; until then it is a pending statement.
Why
The question about the park is not a statement at all, so it goes in the trash, not PENDING. The other three are statements whose stamps nobody knows yet.
The PENDING tray only takes statements.
Could the new park open next spring?
Where this shows up later in the course
Where this goes next
This course
Chapter 1 builds the course's main object out of statements. It is a group of statements in which some are offered as reasons for another. Section 3 of that chapter sets this up. A question or a command can't be a reason, and it can't be the thing the reasons back. So spotting statements is the first move every time. Chapter 2 then handles a question that is really a claim in disguise, like "Who wouldn't want free shipping?" You write out the statement it makes.
Chapter 9 starts naming whole statements with single capital letters. Chapter 12's tables list every way those statements could be stamped. Both only work because each statement gets a single truth value, never two, even when nobody knows which. The pending tray is where most of that later work happens. The claims in a product review, a news story, or a job offer are usually ones you can't check on the spot.