The last section asked whether a sentence can be stamped at all. This one asks what a stamp depends on. Everyday talk runs on guesses about what people mean, and most of the time those guesses help. Careful reading sets them aside. It holds a sentence to what its words promise, and to nothing more.
Promises and hints
Suppose a friend texts you: "Some of the cookies are gone." You get home and the jar is empty. Did your friend say something false?
It feels a bit false. You expected a few cookies left. But look at what the fact-checker from the last section would do. That's the person with two stamps, TRUE and FALSE, who checks a sentence against the world. The fact-checker checks only the words. Are some cookies gone? Yes, all of them are, which certainly includes some. Stamp: TRUE.
What happened is that the sentence gave you a hint, and the hint was wrong. People usually say "all" when they know it's all. So "some" made you guess "not all." But your friend never said "not all." A promise is what the words say. A hint is a guess the listener adds.
Here is a quick way to tell a promise from a hint. Add "in fact, all of them are" to the end. "Some of the cookies are gone. In fact, all of them are." That sounds fine: new information, not a clash. So "not all" was only a hint. Now try "All of the cookies are gone. In fact, one is left." That contradicts itself. So "every cookie is gone" was a real promise.
In this course we stamp sentences by their promises. Hints matter in real life, and someone can mislead you with a hint without saying one false word. But the stamp depends only on what the words commit to.
A statement commits its speaker to the conditions under which it is true. Those conditions are fixed by the words. They are separate from what a listener might guess the speaker had in mind.
Take "Some of the concert tickets sold." A listener usually concludes that not all of them sold, since a speaker who knew the show was sold out would normally say so. That extra meaning is a hint, not a commitment. The sentence is still true if every ticket sold.
A useful test separates the two. Try adding a sentence that cancels the extra meaning: "Some of the tickets sold. In fact, every one did." If the added sentence reads as more information rather than a clash, the extra meaning was only a hint. Compare "Every ticket sold. In fact, one is still available." That added sentence contradicts the first one, so "every ticket sold" is a real commitment.
Careful reading means judging a statement by its commitments alone. Hints still matter in conversation, and a speaker who leans on one can mislead without saying anything false. But the truth value of the sentence depends only on what it commits to.
Worked example
Promise or hint: “I finished most of the report”
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1basic
Kenji tells his manager, "I finished most of the report." In fact, he finished all of it. Was his sentence false?
basic
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2
Find the promise. "Most" commits Kenji to more than half being finished. More than half was finished, since all of it was.
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3
Find the hint. A listener guesses that some of the report is still undone. Try the cancel test: "I finished most of the report. In fact, I finished all of it." That reads as good news, not a clash.
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4
So "some is still undone" was only a hint. The promise held, and the sentence is true. It undersold Kenji's work, but underselling is not the same as saying something false.
Check your understanding (counts toward your progress)
Which added sentence shows that the first sentence was making a real commitment, not just a hint?
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This added sentence reads as extra information, not a clash. So “not all taken” was only a hint.
Adding “all of them are” fits smoothly after “some,” which shows “some” never promised “not all.”
“Most” after “a few” adds information. It doesn’t clash with anything the first sentence said.
Why
“All of the seats are taken. In fact, one is free” contradicts itself, so “every seat is taken” was a real commitment. In the other pairs, the added sentence only adds information, which shows the cancelled meaning was a hint.
A real commitment can’t be cancelled without contradicting yourself.
Which pair sounds like the speaker taking something back?
A store sign says, “Some items are 50% off.” Every item in the store is 50% off. A shopper says the sign lied. Who is right?
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The sign never mentioned full-price items. That idea came from the shopper, as a hint.
Saying less than you could is not the same as saying something false.
The sign says something is the case, so it passes the reply test and has a truth value.
Why
At least one item is 50% off, so the sign is true. It hinted that not everything was on sale, and that hint was wrong, but a hint is not a promise.
What does “some” commit to? Did that happen?
In careful reading, what does a sentence commit its speaker to?
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A listener’s guess is a hint the listener adds. The stamp doesn’t depend on it.
Private intentions can’t be stamped. Only what the words say can.
How people usually take a sentence often includes hints, like “not all” after “some.”
Why
A commitment is fixed by the words: the conditions under which the sentence is true. Guesses and intentions can mislead, but they don’t change the stamp.
Would the fact-checker look at the words, or at what people guessed?
Practice: Promise or hint? (4 problems · doesn’t affect your progress)
In “Some of the cookies are gone,” which of these is only a hint, not a promise?
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This is exactly what “some” promises. Take it away and the sentence says nothing.
That the sentence is about cookies is plain from its words. It isn’t a guess the listener adds.
Why
“At least one cookie is gone” is the promise. “Not every cookie is gone” is a guess listeners add, and the speaker can cancel it without taking anything back.
Which one could the speaker cancel with “in fact, all of them are”?
Not every cookie is gone.
Which sentence can be followed by “In fact, all of them did” without contradicting itself?
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“None” promises that zero finished. Adding “all of them did” takes that back.
“Only two of the six” promises that four didn’t finish, so “all of them did” contradicts it.
“Not all” promises that at least one didn’t finish. Adding “all of them did” takes that back.
Why
“Some of the runners finished” promises only at least one. “All of them did” adds news without contradicting it. The other three each promise something that “all finished” breaks.
Which sentence only hinted that some runners didn’t finish?
Some of the runners finished.
Sort each pair: does the second sentence cancel a hint or contradict a promise?
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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
Following “some” or “several” with “in fact, all” only adds news. Following “all” or “nobody” with an exception takes back what was said.
Correct answer
Also accepted:
Why
Does the speaker seem to be adding news or taking something back?
A review says, “Some diners loved the soup.” Every diner loved it. The chef says the review undersold the soup. Is the review false?
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That was a hint, and hints don’t decide the stamp. The words only promise at least one diner loved it.
Saying less than the full truth is not the same as saying something false.
Why
At least one diner loved the soup, so the review is true. The chef has a fair complaint about the hint, but not about the truth value.
What does the review commit to? Did that happen?
No. It is true but says less than it could.
Some, all, none, and only
For each of these words, there is one question that cuts through everything: what would the fact-checker need to find to stamp the sentence FALSE?
Some. "Some students passed the quiz." To stamp it FALSE, the fact-checker needs to find that zero students passed. If even one passed, it's TRUE. That includes the case where every single student passed. So in this course "some" just means "at least one."
All. "All the lockers on this floor are locked." To stamp it FALSE, you need to find one unlocked locker on this floor. One is enough.
None. "None of the lights are on." To stamp it FALSE, you need one light that is on.
Only. "Only members may use the pool." To stamp it FALSE, you need a swimmer who isn't a member. Notice what does not break the sign: a member who didn't get to swim. "Only" talks about who is allowed. It doesn't promise that everyone on the list gets in.
Now the strangest one. A sign on an empty lot says "All trespassers will be fined." Nobody has ever trespassed there. Is the sign false? To stamp it FALSE, you'd need a trespasser who wasn't fined. There isn't one. Nothing breaks the sign, so it isn't false. And a statement always gets one of the two stamps. So it's TRUE, even though no trespassers exist. That feels odd, but it matches how rules work. A rule about trespassers still stands on a day when nobody trespasses. So "all" never promised that trespassers exist. It only said what happens to each one there is.
Four quantity words do most of the work. For each, the useful question is what would make the sentence false.
| Sentence | Commits to | False exactly when |
|---|---|---|
| Some A are B | at least one A is B | no A is B |
| All A are B | every A there is, is B | at least one A is not B |
| No A are B | not even one A is B | at least one A is B |
| Only A are B | anything that is B is an A | something is B without being A |
Three consequences follow, and each one clashes with a common habit.
First, "some" means at least one. "Some students passed" is true if one passed, if half passed, and if all passed. It is false only if none did.
Second, "all" makes no promise that anything of the kind exists. Read "All A are B" as "if anything is an A, it is a B." "All passengers who miss the ferry get a refund" is not false on a day when nobody misses the ferry. Being false would require a passenger who missed it and got no refund, and there is none. Since a statement must be true or false, it is true. Everyday speech often assumes the A's exist, but that is a hint from the setting, not a commitment of the word "all."
Third, "only" reverses the direction of "all." "Only members may use the pool" says every swimmer is a member. It does not say every member may swim. A member might still be turned away for another reason, and the sign would not be broken.
A related trap: "Not all the flights were late" commits only to at least one flight not being late. That flight might have been on time, early, or canceled. The sentence hints that some were late, but it does not promise that.
Does the claim survive?
The claim is “Some of the team’s players scored.” Sort each match report: does it make the claim true or false?
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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
Does it promise that something exists?
Sort each sentence: does it commit the speaker to at least one such thing existing, 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
“Some” when it is really all
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1basic
A teacher says, "Some students passed the quiz." In fact, all 24 passed. Is the teacher's sentence true or false?
basic
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2
Ask what would make it false: no student passing. Here all 24 passed, so that didn't happen.
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3
Check what "some" commits to: at least one student passed. At least one did; in fact 24 did.
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4
The sentence is true. The listener may have guessed "not all," but that was a hint the teacher never promised. Replacing "some" with "at least one" makes this easy to see.
Worked example
A rule with nobody to apply it to
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1common trap
A sign on an empty lot reads, "All trespassers will be fined." In the sign's whole history, nobody has trespassed. Is the sign's statement true?
common trap
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2
Rewrite it the careful way: "If anyone trespasses here, that person will be fined." This version makes no claim that trespassers exist.
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3
Ask what would make it false: a trespasser who was not fined. There have been no trespassers at all, so there is no such person.
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4
Nothing makes it false, and a statement must be one or the other. So it is true. The habit to resist is thinking "all" promises there are some. It only says what happens to each one there is.
Worked example
Reading “only” in the right direction
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1variation
A pool sign says, "Only members may use the pool." Jordan is a member but was turned away because the pool was full. Morgan, who is not a member, swam anyway. Which of these, if either, goes against the sign?
variation
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2
Rewrite the sign in the "all" direction it really has: "Everyone who uses the pool is a member." It talks about swimmers, not about members.
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3
Morgan used the pool and is not a member. That is the very case the sign rules out, so Morgan's swim goes against it.
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4
Jordan did not swim. The sign never promised that every member gets in. It only limits who may. So Jordan being turned away does not go against the sign at all.
Check your understanding (counts toward your progress)
All 24 students passed the quiz. Is “Some students passed the quiz” true?
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“Not all” is a hint listeners add. The sentence never says it. Try adding “in fact, all of them did”: nothing clashes.
A statement always gets a stamp. An odd word choice can mislead, but it doesn’t remove the stamp.
Why
“Some students passed” commits only to at least one student passing. With 24 passing, that is met, so the sentence is true.
Replace “some” with “at least one” and read it again.
“Only members may use the pool.” Which of these would go against the sign?
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The sign limits who may swim. It never promised that every member gets in.
A member swimming is exactly what the sign allows.
An empty pool has no swimmer who isn’t a member, so nothing breaks the sign.
Why
“Only members may use the pool” means everyone who swims is a member. The one thing that goes against it is a swimmer who isn’t a member.
Turn it around: “Everyone who uses the pool is a …”
What would make “None of the lights are on” false?
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Every light on would do it, but you need far less. A single light on is already enough.
That is the situation the sentence describes, so it would make the sentence true.
A broken light is off. That fits the sentence rather than breaking it.
Why
“None” rules out every case, so one exception breaks it. A single light that is on makes the sentence false.
How many lit lights does it take to break “none”?
“Not all the flights were late.” What does this sentence commit to?
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“Some were late” is a hint riding along. The sentence stays true even if every flight was on time.
That goes too far. The sentence allows for some late flights; it only rules out all of them being late.
Nothing here counts the flights. One flight that wasn’t late, among fifty, is enough.
Why
“Not all were late” is true exactly when “all were late” is false, which needs just one flight that wasn’t late: on time, early, or canceled. It hints that some were late but doesn’t promise it.
What single case would make “all the flights were late” fail?
Practice: Some, all, none, and only (5 problems · doesn’t affect your progress)
What does “some” commit to in careful reading?
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“Not all” is a hint listeners often add, but the word never promises it.
“Some” doesn’t count past one. A single case is enough.
“Some” sets no upper limit, so it stays true even when all qualify.
Why
“Some” means at least one. It stays true with one, with many, and with all.
What is the smallest number that makes a “some” sentence true?
At least one
Every apple in the bag is bruised. Is “Some apples in the bag are bruised” true?
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“All” would be more informative, but a less informative sentence can still be true.
That the rest are fine is a hint, not a promise. The sentence never says it.
Why
With every apple bruised, at least one is bruised, so the sentence is true.
Replace “some” with “at least one.”
Yes. At least one apple is bruised.
“All refunds are processed within five days.” The store has never issued a refund. Is the sentence false?
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Talking about each refund there is doesn’t claim there are any. With none, nothing breaks the rule.
“All” only says what happens to each refund. It never promised refunds exist.
Why
Nothing breaks the sentence, so it isn’t false. An “all” sentence makes no promise that anything of the kind exists.
Rewrite it: “If a refund is issued, it is processed within five days.”
No. It would take a slow refund to make it false.
“Only seniors may leave campus at lunch.” Which case goes against it?
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The rule limits who may leave. A senior staying is fine.
Nobody leaving means nobody broke the limit.
Seniors are exactly who the rule allows.
Why
The rule says everyone who leaves is a senior. A sophomore leaving is the one case that breaks it.
Turn it around: everyone who leaves at lunch is a …
A sophomore leaves campus at lunch.
Which pair says the same thing?
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The first limits who votes; the second grants every member a vote. A member barred from voting breaks only the second.
If every guest left early, the first is true and the second is false. They can come apart.
One on-time train makes the first true, but the second needs every train on time.
Why
“No students were absent” and “Not even one student was absent” fail in exactly the same case: one absent student. Every other pair can come apart in some case.
For each pair, look for a case that makes one sentence true and the other false.
“No students were absent” and “Not even one student was absent”
What "or" allows
"Or" is a small word with two possible jobs, and people slide between them without noticing.
Here's the first job. A job ad says, "Applicants need a degree or two years of experience." Sam has a degree and two years of experience. Does Sam qualify? Of course. Having both is not a problem; it's more than enough. When "or" works like this, it's called an inclusive or. The claim is true as long as at least one part holds, and having both counts. The only way to break it is to have neither.
Now the second job. A restaurant says, "Your meal comes with soup or salad, but not both." Here "or" means one of the two, and only one. That is called an exclusive or. Having both breaks it, and so does having neither.
Which job does "or" do when a sentence doesn't say? In this course, the first one. We read "or" as inclusive unless the sentence spells out "but not both" or something that means the same thing. The fact-checker stamps "A or B" TRUE whenever at least one part holds.
Why not just guess from the setting? Because the setting can mislead. A menu that says "soup or salad" probably means not both. But that limit comes from the restaurant, not from the word. When a limit matters, good writing states it. And the word "either" doesn't change anything. "Either Kai or Lena will drive" is still true if they take turns.
An "or" statement joins two parts: "A or B." There are two ways to read it.
- Read as an inclusive or, "A or B" is true when at least one part is true. That includes the case where both are true. It is false only when both parts are false.
- Read as an exclusive or, it is true when one part is true and the other is false. It is false when both are true, and also when both are false.
Careful reading uses the inclusive reading by default. It switches to the exclusive reading only when the sentence itself rules out both: "but not both," "one or the other, not both," "exactly one of." The word "either" alone does not do this. "Either Kai or Lena will drive" is still true if they share the driving.
Sometimes the two parts can't both be true anyway: "The light is on or it is off." Then the two readings give the same stamp in every case, and nothing depends on the choice.
Menus and offers are the classic source of confusion. "The meal comes with soup or salad" is usually meant to exclude getting both, and a diner who takes both may be charged. That limit comes from the restaurant's policy and the setting, not from the word "or." A carefully written menu that wants the limit says "soup or salad, not both."
Who meets the requirement?
A posting says: “Applicants must speak French or Spanish.” Sort each applicant: meets the requirement or doesn’t.
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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
Having both parts
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1typical
A job ad reads, "Applicants need a degree or two years of experience." Sam has a degree and three years of experience. Does Sam meet the stated requirement?
typical
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2
Look for words that rule out both parts, such as "but not both." There are none, so read the "or" inclusively.
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3
An inclusive "or" is met when at least one part holds. Sam has a degree, so the first part holds. The second part holds too.
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4
Both parts holding still meets an inclusive "or." Sam qualifies. The only applicant who fails is one with neither a degree nor two years.
Worked example
Spotting an exclusive “or”
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1recognition
Which of these sentences uses an exclusive "or": "You can pay by cash or card," "Pick a free drink or a free dessert, not both," or "The door is open or it is closed"?
recognition
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2
"You can pay by cash or card" has no words ruling out both. It is inclusive. A store that let you split a bill across both would not break it.
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3
"Pick a free drink or a free dessert, not both" says "not both" out loud. That is an exclusive "or": one treat, never two.
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4
"The door is open or it is closed" can't have both parts true at once. The two readings agree in every case, so there is nothing to decide. Only the drink-or-dessert offer is exclusive in what it says.
Check your understanding (counts toward your progress)
A menu says, “The meal comes with soup or salad.” A diner gets both and is charged extra. Where does the “not both” limit come from?
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That is the mix-up this section warns about. “Or” on its own is read inclusively; the limit comes from somewhere else.
“The meal” names one meal. It says nothing about how many sides come with it.
A restaurant can set a limit. The point is only that the limit comes from policy, not from the word “or.”
Why
The menu probably means one side, but that comes from the restaurant’s policy and the setting. A menu that wants the limit stated should say “soup or salad, not both.”
If the menu wanted the limit in its words, what would it add?
When is “The package will come by truck or by drone,” read inclusively, false?
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Using both is allowed under an inclusive “or.” Only an exclusive “or” is broken by both parts holding.
Coming by truck makes the first part true, which is all an inclusive “or” needs.
Coming by drone makes the second part true, so the sentence holds.
Why
An inclusive “or” is false only when both parts are false. If the package comes by neither truck nor drone, the sentence fails; any other case keeps it true.
An inclusive “or” needs just one part to hold.
Sort each sentence by how careful reading takes its “or.”
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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 shirt sentence says “not both” and the presenter sentence says “exactly one,” so those two are exclusive. The rest have no such words, so both parts holding is allowed. “Either” by itself doesn’t change that.
Correct answer
Also accepted:
Why
Only words like “but not both” or “exactly one” switch off the default.
A posting says, “Applicants must speak French or Spanish.” Sort each applicant.
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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
With no “but not both,” speaking at least one of the two languages meets the requirement, and speaking both still counts. Only Kwame, who speaks neither, fails it.
Correct answer
Also accepted:
Why
What is the only way to fail an inclusive “or”?
Practice: What “or” allows (5 problems · doesn’t affect your progress)
Without “but not both,” how does careful reading take “or”?
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The exclusive reading is used only when a sentence rules out both.
“Or” never needs both parts. One part holding is enough.
Why
The default is the inclusive or. It is false only when both parts fail.
The default is the reading that allows both.
Inclusively: at least one part holds, maybe both.
“Visitors must show a student ID or a library card.” Aiko shows both. Did she meet the rule?
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Nothing in the rule says “not both.” Showing both is more than enough.
The words settle it. No extra permission is needed.
Why
Read inclusively, the rule needs at least one of the two. Aiko showed both, which meets it.
Does the rule say “but not both”?
Yes. Both still meets an inclusive “or.”
The rule is “Players must be under 14 or have a coach’s approval.” Sort each player.
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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
Zoe meets the age part, Sam meets the approval part, and Ari meets both, which still counts. Bo has neither, the only way to break an inclusive “or.”
Correct answer
Also accepted:
Why
Only one player has neither part.
“Either Kai or Lena will drive to the game.” They split the drive. Is the sentence true?
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Only words like “but not both” switch to the exclusive reading. “Either” doesn’t.
Each of them drove part of the way, so each part of the sentence holds.
Why
Both parts are true, and nothing in the sentence rules that out. Read inclusively, the sentence is true.
Did the sentence say “not both”?
Yes. “Either” alone doesn’t rule out both.
Which sentence is false when both of its parts are true?
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With no “not both,” paying with both fits this sentence.
“Either” doesn’t exclude both. Heater and fan both on still makes it true.
Bringing both still meets this. Nothing rules it out.
Why
The refund sentence says “but not both,” so it is exclusive, and both parts holding makes it false. The others are inclusive.
Only an exclusive “or” is broken by both parts holding.
You get a refund or a replacement, but not both.
Where this shows up later in the course
Where this goes next
This course
Chapter 4 studies patterns of reasoning built on "or." Every one of them assumes the inclusive reading taught here. Chapter 8 is built entirely on "all," "some," and "no." Its section 8.4 returns to the empty-lot sign. Whether "all" promises that anything exists decides which of the old textbook rules still work. Chapter 9 gives "or" its own symbol, and that symbol always means the inclusive "or." Chapter 10 shows how to write the exclusive version when a sentence really means it.
Outside the course, the same care pays off in fine print. "Some customers saw savings of 40%" promises that at least one did. It says nothing about you. "Only orders over 50 ship free" does not promise that every order over 50 ships free. It only says smaller orders don't.