Beginner's Guide to Logic

重要なポイント

• Before judging any argument, find its conclusion, write down the premise it quietly depends on, and try to imagine the premises true and the conclusion false.
• Validity is about form and truth is about facts, so check both: a valid argument built on one false premise can still mislead you.
• An if-then claim runs one way: its contrapositive says the same thing, but its converse and inverse are new claims that need their own evidence.
• One clear exception is enough to sink an 'all' claim, and 'not all passed' means at least one failed, not that everyone did.
• Test arguments you agree with as hard as ones you dislike, because liking a conclusion is a common reason people wave a bad argument through.

このbitの内容

1. What logic studies and what it cannot

   Logic is the study of when a conclusion follows from the reasons given for it. It does not ask whether each reason is true; that is a job for evidence, measurement and experience.

2. The working vocabulary of arguments

   An argument is a set of statements in which some, the premises, are offered as reasons for another, the conclusion. The step from one to the other is the inference.

3. Your first three moves with any argument

   Every argument you meet, from a sales pitch to a family debate, yields to the same three moves. First, find the conclusion by asking what you are being asked to accept; it is often buried in the middle or left unsaid.

4. Conditionals, where careful people still slip

   An if-then statement links a condition to a consequence, and it runs in one direction only. If a parcel is marked express, it carries a red sticker, means express is enough to guarantee red; red is required on every express parcel but may appear on others too.

5. All, some, none: the small words that decide

   Quantifiers, the words all, some and none, carry more weight than their size suggests. To show that 'all the invoices were paid' is false, you need only one unpaid invoice; you do not need to show that none were paid.

6. Beginner mistakes and a self-check routine

   Three mistakes catch almost every beginner, and they get subtler as you improve. The first is belief bias: judging an argument by whether you like its conclusion.