Chapter Two, Tutorial Three
Semantics and Syntax for SL

A semantics is a definition of meaning for a language. But 'meaning' itself has a number of meanings. Here we fix on a simple idea of meaning: truth conditions.

To understand, say, the meaning of

Sam is riding a horse

is to know under what conditions this statement would be true. That is, one would need to know who Sam is, what riding is, and what a horse is. Then one would know the meaning well enough to understand just when it would be true.

So, we'll give meaning in terms of truth conditions. Let's start with about the easiest case: conjunctions.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Conjunction

So, one way to think about meaning is in terms of truth conditions. We shall apply this idea to molecular sentences of SL (without names). Begin with our simple example

A&B

symbolizing the English "Agnes and Bob will attend law school." Under what conditions is this true? Obviously it's true when and only when both 'A' and 'B' are true. This doesn't sound too interesting yet, but be patient!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Truth Tables

There is one more tool we need for clearer semantics: the truth table. A truth table will just re-express our definition 1.

When P and Q are both true, then P&Q is true. We've already said that, of course.

And...