Logic: A Very Short Introduction

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Most people like to think of themselves as logical. Telling someone ‘You are not being logical’ is normally a form of criticism. To be illogical is to be confused, muddled, irrational. But what is logic? In Lewis Carroll’s Through the Looking Glass, Alice meets the logic-chopping pair Tweedledum and Tweedledee. When Alice is lost for words, they go onto the attack: 

What Tweedledee is doing — at least, in Carroll’s parody — is reasoning. And that, as he says, is what logic is about.

We all reason. We try to figure out what is so, reasoning on the basis of what we already know. We try to persuade others that something is so by giving them reasons. Logic is the study of what counts as a good reason for what, and why. You have to understand this claim in a certain way, though. Here are two bits of reasoning — logicians call them inferences:

1. Rome is the capital of Italy, and this plane lands in Rome; so the plane lands in Italy.

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