

Introduction to Logic

Tools for Thought


Consider the interpersonal relations of a small sorority. There are just four members  Abby, Bess, Cody, and Dana.

As it turns out, there are quite a few possibilities. Given four girls, there are sixteen possible instances of the likes relation  Abby likes Abby, Abby likes Bess, Abby likes Cody, Abby likes Dana, Bess likes Abby, and so forth. Each of these sixteen can be either true or false; there are 2^{16} (65,536) combinations of these truefalse possibilities; and so there are 2^{16} possible worlds.

Let's assume that we do not know the girls ourselves but we have informants who are willing to tell us about them. Each informant knows a little about the likes and dislikes of the girls, but no one knows everything.

This is where Logic comes in. By writing logical sentences, each informant can express exactly what he or she knows  no more, no less. For our part, we can use the sentences we have been told to draw conclusions that are logically entailed by those sentences. And we can use logical proofs to explain our conclusions to others. In the next three sections, we consider each of these elements in turn.
Observations 
⇓ 
Conclusions 
⇓ 
Explanations 

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