Screens keep children awake→Children need sleep to learn→So: schools should ban phones
Picture a post. Screens keep children awake. Children need sleep to learn. So schools should ban phones. Three sentences. Two of them are reasons, and the third is the claim the reasons are meant to hold up. That shape, reasons joined to a claim, is called an argument.
Are the reasons true?
++
Do they reach the claim?
An argument has two things to check, and they are different. Are the reasons true? And do the reasons reach the claim? A reason can be true and still not reach. It rained today, so the bus will be late: the rain is real, and it does not get you to the bus.
All fish live in water→A shark is a fish→So: sharks live in water
All fish live in water. A shark is a fish. So sharks live in water. Do the reasons reach the claim?
No. Some sharks might live somewhere else.
Not yet. If a shark lived out of water, then either it is not a fish or not all fish live in water, and one of the reasons would be false. With both reasons true, the claim cannot fail.
Only partly. Reasons never fully reach a claim.
Not yet. Some do. This one leaves no gap at all; the trouble with most arguments is that they are not shaped like this one.
Yes. If both reasons are true, the claim has to be true.
Right. There is no way for both reasons to hold and the claim to fail. That is what reaching means: the reasons leave the claim nowhere else to go.
Reasons trueyes
vsvs
Claim must followno, only might
The second check in plain words: if every reason were true, would the claim have to be true, or only might be? Screens keep children awake and sleep matters. Both can be true, and a ban can still be the wrong fix: phones at home, or a cheaper rule. The reasons point at the claim. They do not reach it.
Each is a short argument. Do its reasons reach the claim, do true reasons fall short, or is a reason itself false?
One card at a time. Tap the pile it belongs to.
Card 1 of 6
Ice is frozen water. This cube is ice. So this cube is frozen water.
It rained today. So it will rain tomorrow.
Bats are birds. Birds lay eggs. So bats lay eggs.
Everyone I asked liked the film. So everyone likes the film.
Whales breathe air. Whales live in the sea. So some sea animals breathe air.
The Moon is made of cheese. Cheese is food. So the Moon is food.
Ice is frozen water. This cube is ice. So this cube is frozen water. → Reaches
Not yet. Reaches. Both reasons true, and with both true there is nowhere else for the claim to go.
It rained today. So it will rain tomorrow. → Falls short
Not yet. Falls short. The rain is real, and tomorrow is a different day; the reason points at the claim without getting there.
Bats are birds. Birds lay eggs. So bats lay eggs. → A reason is false
Not yet. A reason is false. Bats are not birds. The shape is fine; the first reason is not true, so the chain starts broken.
Everyone I asked liked the film. So everyone likes the film. → Falls short
Not yet. Falls short. The people asked are a sample, lesson 5, and a small one; everyone else was not asked.
Whales breathe air. Whales live in the sea. So some sea animals breathe air. → Reaches
Not yet. Reaches. Two true reasons, and a claim that cannot fail if they hold.
The Moon is made of cheese. Cheese is food. So the Moon is food. → A reason is false
Not yet. A reason is false. The shape reaches, which is the point: a perfect shape carries a false reason straight to a false claim.
2Reaches
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2Falls short
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2A reason is false
Right. Two reach, two fall short, and two have a false reason. The last two show why the checks are separate: a shape with no gap in it will carry a lie as faithfully as a truth.
1 link90 in 100
3 links73 in 100
6 links53 in 100
Each link 9 in 10 sure, computed.
Now the long argument. Most real claims rest on a chain: this, and then this, and then this. Say each link is 9 in 10 sure, and the links are separate. One link: 90 in 100. Three links: about 73. Six links: about 53. Each link you add takes a tenth off what is left.
Move the control through the number of links in the chain. Each link is 9 in 10 sure on its own, and the links are taken as separate. Computed.
The whole chain holds90 in 100
Each link alone90 in 100
Links in the chain: 1
One link, 9 in 10 sure. The whole chain is 90 in 100.
The whole chain holds81 in 100
Each link alone90 in 100
Links in the chain: 2
2 links, each 9 in 10 sure on its own. For all 2 to hold at once: about 81 in 100. Every link you add takes a tenth off what is left.
The whole chain holds73 in 100
Each link alone90 in 100
Links in the chain: 3
3 links, each 9 in 10 sure on its own. For all 3 to hold at once: about 73 in 100. Every link you add takes a tenth off what is left.
The whole chain holds59 in 100
Each link alone90 in 100
Links in the chain: 5
5 links, each 9 in 10 sure on its own. For all 5 to hold at once: about 59 in 100. Every link you add takes a tenth off what is left.
The whole chain holds43 in 100
Each link alone90 in 100
Links in the chain: 8
8 links, each 9 in 10 sure on its own. For all 8 to hold at once: about 43 in 100. Every link you add takes a tenth off what is left.
The whole chain holds35 in 100
Each link alone90 in 100
Links in the chain: 10
10 links, each 9 in 10 sure on its own. For all 10 to hold at once: about 35 in 100. Every link you add takes a tenth off what is left.
A story needs five things to all be true, each 9 in 10 sure. How sure is the story?
About 9 in 10. Every link is 9 in 10.
Not yet. Nine in ten is each link on its own. The story needs all five to hold at once, and a tenth comes off for every link added.
About 6 in 10.
Right. Nine tenths, five times over, is about 59 in 100. Each link felt nearly certain, and the chain they make together is barely better than a coin.
About 5 in 100. Five links at 9 in 10 each makes 45.
Not yet. Multiplying the chances is right, but 0.9 times itself five times is 0.59, not 0.05. The chain is weakened by each link, not demolished.
Move the control.
each 9 in 10Ten links
↓→
about 35 in 100The whole story
This is why a long, clever story is weaker than it sounds. Every and then is a link. A story with ten and-thens, each nine in ten sure, holds about one time in three. Each link can sound certain on its own. The story is weak because there are ten of them.
Thing 1: 9 in 10→Thing 2: 9 in 10→Thing 3: 9 in 10
A plan needs three things to go right, each 9 in 10 sure and separate. Out of 100 tries, about how many times does the whole plan work?
in 100
Nine tenths of nine tenths of nine tenths.
Right. About 73. Ninety of a hundred pass the first thing, 81 the second, 73 the third. A plan of three near-certain steps fails about one time in four.
Strictone link
vsvs
Strict, unfair, dislikes youthree links
Which is more likely about a new teacher: that they are strict, or that they are strict and unfair and dislike your class?
Strict. Every and adds a link, and every link takes something off.
Right. Strict and unfair and dislikes you is three things that all have to be true, so it can never be more likely than strict alone. It sounds more likely because it sounds like a person.
They are the same. Strict teachers are usually all three.
Not yet. Usually is not always, and the three-part claim needs all three. The moment one of the three fails, the whole claim fails, and strict on its own is still standing.
Strict and unfair and dislikes your class. It sounds more like a real teacher.
Not yet. It sounds more real because it is more detailed, and every detail is a link. Three links at 9 in 10 each leaves 73; one link leaves 90. The detailed story is the weaker one.
Lesson complete
A true reason can still fall short of its claim. Every link added to a chain makes the chain weaker.