Thinking clearly: logic and common fallacies

What you'll learn: What an argument is in the logical sense, how to find its premises and conclusion, and how to rewrite a messy real-world claim so you can judge it.

A leaflet through the door

Jo Mensah is a nurse who lives on Mill Lane in Kesterby, a small town with one primary school, one high street and, this autumn, one big argument. The town council has proposed closing Mill Lane to through traffic for a six-week trial, because drivers use it as a shortcut past the school gates. Jo's nine-year-old son, Kofi, walks that way every morning.

On Monday a leaflet lands on her doormat from a group calling itself Keep Kesterby Moving. It says:

Closing Mill Lane will push hundreds of cars onto Station Road. Station Road is already jammed at school time. So the closure will make traffic worse, not better. Don't let the council wreck our town.

On Tuesday, the residents' group chat is full of people who either agree loudly or call the leaflet nonsense. Jo wants to do something rarer: work out whether it is actually a good argument. Over this course we will follow her as she does that, all the way to the council meeting where the decision is made.

What "argument" means here

In everyday speech an argument is a row. In logic, an argument is a set of statements where some of them (the premises) are offered as reasons to believe another one (the conclusion). It is not about raised voices. It is about support.

A useful way to picture it is a table. The conclusion is the tabletop: the thing you are being asked to accept. The premises are the legs holding it up. If a leg is rotten (a premise is false) or a leg is not actually touching the tabletop (a premise is true but irrelevant), the table will not hold your weight, however solid it looks from across the room.

Not everything persuasive is an argument. "Don't let the council wreck our town" is a slogan: it gives no reason. "Station Road is jammed" on its own is just a claim. It only becomes part of an argument when it is used to support something else.

Finding the conclusion first

The quickest way into any argument is to ask: what is this trying to get me to believe or do? That is the conclusion. Certain words often signal it, and others signal premises.

These are clues, not rules. People often put the conclusion first ("The closure is a mistake. It will push cars onto Station Road...") or leave the signal words out altogether. In the leaflet, the word "So" points straight at the conclusion: the closure will make traffic worse.

Rewriting the argument in standard form

Logicians lay arguments out in standard form: numbered premises, a line, then the conclusion. Jo does this on the back of the leaflet:

1. Closing Mill Lane will push hundreds of cars onto Station Road.
2. Station Road is already jammed at school time.
3. Therefore, the closure will make traffic worse.

Writing it out forces two useful questions. First, is each premise true? Second, if they were all true, would the conclusion follow?

She immediately notices a gap. The conclusion talks about "traffic" in general, but the premises only talk about Station Road. Traffic could get worse on Station Road and better on Mill Lane. So the leaflet relies on a premise it never states, something like "Traffic being worse on Station Road means traffic is worse overall." Unstated premises like this are called hidden assumptions, and finding them is one of the most useful habits in this whole course. The argument might still be right, but now Jo knows exactly what she would need to check.

Separating arguments from everything around them

Real persuasion arrives wrapped in other things: emotion, examples, jokes, insults, repetition. None of these is automatically bad. A vivid story about a child nearly hit by a car on Mill Lane is moving and may be true. But Jo asks of every piece: is this a premise, the conclusion, or decoration?

In the leaflet, "Don't let the council wreck our town" is decoration with a strong emotional charge. The word "wreck" assumes the conclusion rather than supporting it. Spotting that is not cynical; it simply lets you set the decoration aside and look at the legs of the table.

A second argument, for balance

The council's own notice argues the other side:

1. Around 1,900 vehicles a day use Mill Lane, many as a shortcut.
2. The school entrance is on Mill Lane, and many children walk to it.
3. Fewer vehicles near a school entrance means fewer chances of a child being hit.
4. Therefore, closing Mill Lane to through traffic will make the school run safer.

Jo applies the same treatment. The conclusion is about safety, not traffic overall, so it is a different claim from the leaflet's, and both could be true at once: the closure could make Mill Lane safer and Station Road busier. Much of the heat in the group chat comes from people answering a conclusion nobody actually made.

Recap

• In logic, an argument is premises offered as reasons for a conclusion.
• Find the conclusion first by asking what you are being asked to believe or do.
• Signal words like "so" and "because" help, but are not always there.
• Standard form (numbered premises, then the conclusion) exposes hidden assumptions.
• Separate premises from decoration such as slogans and loaded words.
• Two arguments with different conclusions can both be right.

What you'll learn: The difference between a valid argument and a sound one, how to test validity with a counterexample, and why a valid argument can still have a false conclusion.

Two separate questions

Last time, Jo put the Keep Kesterby Moving leaflet and the council's notice into standard form. She ended with two questions for each argument: are the premises true, and if they were, would the conclusion follow? Logic gives those two questions names, and keeping them apart is the single most useful skill in this course.

An argument is valid when the conclusion follows from the premises: if every premise were true, the conclusion would have to be true. Validity is about the connection, not about whether anything is actually true.

An argument is sound when it is valid and all of its premises really are true. A sound argument's conclusion must be true.

A recipe and its ingredients

Think of a perfect recipe made with off milk. The method can be flawless, and if you follow it with good ingredients you are guaranteed a good cake. But no recipe can rescue bad ingredients. Validity is the recipe: it guarantees that true premises lead to a true conclusion. Soundness is the recipe plus good ingredients.

That gives four combinations, and every one of them happens in real life.

Notice that only one cell guarantees anything. A true conclusion can come out of a bad argument, and a false conclusion can come out of a valid one.

Valid but unsound

Here is a valid argument Jo overhears at the school gate:

1. Every road closure in history has caused gridlock.
2. Closing Mill Lane is a road closure.
3. Therefore, closing Mill Lane will cause gridlock.

The structure is perfect: if both premises were true, the conclusion would follow. But premise 1 is false (plenty of closures cause little disruption, and some reduce traffic overall as drivers change routes or times). So the argument is valid but unsound, and it tells us nothing about Mill Lane.

This matters because valid arguments feel convincing. The click of a conclusion following neatly can make you forget to check whether the starting points were true.

Invalid, even with true premises

Now a different one, from the group chat:

1. If the closure makes the school run safer, the head teacher will support it.
2. The head teacher supports it.
3. Therefore, the closure will make the school run safer.

Both premises might be true. But the conclusion does not follow: the head teacher might support the closure for other reasons, such as cleaner air or parents' requests, even if safety does not improve. The argument is invalid. Its conclusion could still be true; this argument just does not show it. (This particular broken shape has a name, affirming the consequent, and it is the star of lesson 4.)

Testing validity with a counterexample

How do you tell whether a conclusion follows? The most practical test is to try to imagine a situation where every premise is true but the conclusion is false. If you can describe one that is even possible, the argument is invalid.

Jo tries this on the leaflet from lesson 1:

1. Closing Mill Lane will push hundreds of cars onto Station Road.
2. Station Road is already jammed at school time.
3. Therefore, the closure will make traffic worse.

Can she picture the premises true and the conclusion false? Yes, easily. Station Road gets busier, but Mill Lane becomes nearly empty, some parents switch to walking, and total travel time across town stays about the same. Both premises hold, the conclusion fails. So the leaflet's argument, as written, is invalid.

That does not mean the leaflet is wrong about traffic. It means the reasons given are not enough. To make it valid, the authors would need to add the hidden assumption Jo spotted last time ("worse on Station Road means worse overall") and then defend that.

Imagining a counterexample is not a trick for winning; it is a way of finding what an argument still needs. Jo now has a precise question to ask the leaflet's authors, instead of a vague feeling that something is off.

The council's argument under the same test

Fairness means applying the same test to the side you lean towards. Jo, a nurse with a child at the school, is inclined to like the closure. The council's argument was:

1. Around 1,900 vehicles a day use Mill Lane, many as a shortcut.
2. The school entrance is on Mill Lane, and many children walk to it.
3. Fewer vehicles near a school entrance means fewer chances of a child being hit.
4. Therefore, closing Mill Lane to through traffic will make the school run safer.

Can the premises be true and the conclusion false? Possibly: if traffic diverted onto Station Road, and many children cross Station Road too, the school run as a whole might not get safer. So strictly, this is also invalid without an extra premise such as "the diverted traffic will not create equal danger elsewhere on the children's routes." That premise is checkable, and it becomes a question Jo wants the trial data to answer.

Recap

• Valid means the conclusion would have to be true if the premises were true.
• Sound means valid with premises that are actually true.
• A valid argument can have a false conclusion; an invalid one can have a true conclusion.
• Test validity by imagining the premises true and the conclusion false.
• A failed test shows which premise is missing, not that the conclusion is wrong.
• Apply the same tests to arguments you like.