Thinking Lab · 4 lessons

Logical Thinking

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Reason consistently

In one line: Separate whether the reasoning holds from whether you agree with the conclusion.

When you need it

• An argument sounds right and you cannot say why it convinced you.
• Two people are arguing and are not actually contradicting each other.
• You want to check your own case before someone else does.

The common misreading

What people think

A valid argument is a true one.

What is true instead

Validity is about the join between premises and conclusion. A perfectly valid argument from a false premise takes you confidently somewhere untrue.

After this module you can write any argument as premises and a conclusion, and say which of the two ways it could fail.

The key idea

Logic does not tell you what is true. It tells you what follows from what — which is how you find the place where a confident argument quietly breaks.

Start with a hard question

Most people hold a few. Write them both out fully before deciding whether they really conflict.

Name two things you believe that might not be able to be true at the same time.

Answer it before reading the lessons — then again after, and notice what changed.

The lessons

• Premises, conclusions, and the two ways an argument fails — Write the premises and the conclusion on separate lines. Half the problems become visible immediately. (6 min)
• Deductive, inductive and analogical reasoning — Ask which kind of reasoning you are doing. Each has a different failure mode and a different check. (7 min)
• Necessary, sufficient, and common fallacies — Necessary is not sufficient. Much effort goes into satisfying necessary conditions and then stopping. (6 min)
• Enough probability to stop being fooled — A good decision and a good outcome are different things. Judging only outcomes teaches the wrong lesson. (6 min)

Practise it

Short exercises. Under each is what a considered answer tends to contain — not a mark scheme.

Does it follow?

"Every senior engineer here writes tests. Priya writes tests. Priya is a senior engineer." Is the conclusion guaranteed? Explain what the argument actually establishes.

• Tends to contain: The rule runs one way only
• Tends to contain: Others may write tests too
• Tends to contain: What premise would make it valid
• Tends to contain: The difference between necessary and sufficient

Conditional reasoning

"If the launch is late, we miss the quarter." The launch was on time. What, if anything, can you conclude about the quarter?

• Tends to contain: Nothing follows — other things can cause a miss
• Tends to contain: Denying the condition does not deny the result
• Tends to contain: What the statement does let you conclude if the quarter was missed

Pattern and exception

Your last four hires from one university performed well, so you prioritise that university. State the inductive step, its strength, and what would falsify it.

• Tends to contain: Four is a small sample
• Tends to contain: How the four were selected in the first place
• Tends to contain: Nothing is known about candidates never hired
• Tends to contain: What evidence would actually settle it

The three statements

Exactly one of these is true: (1) the file is in the archive, (2) the file is not in the archive, (3) the backup ran. What can you conclude about the backup?

• Tends to contain: 1 and 2 cannot both be false
• Tends to contain: So the single truth is among them
• Tends to contain: Therefore 3 is false
• Tends to contain: Notice the reasoning never needed to know where the file is

Reflect

Where did you find an argument of your own that sounded right but did not actually follow?