Statement logic treats "Ava is friendly" as an unbroken block, a single letter $p$. That is fine until an argument depends on what is inside the block. "All dogs are mammals; Rex is a dog; so Rex is a mammal" is valid, but in statement logic it looks like $p$, $q$, so $r$, which is not valid at all. To see why it works we need to look inside simple statements, at the things they are about and what they say of them. This takes up the subject and predicate terms of Categorical Propositions and the simple statements of Simple and Compound Statements.
Key idea
Why it works
Worked examples
Worked example: A simple sentence
- Predicate first, then the name.
Answer: $Fa$
Worked example: With connectives
- "But" is $\land$.
- "Cleo is not tall" is $\neg Tc$.
Answer: $Tb \land \neg Tc$
Worked example: A conditional
- Two simple sentences: $Fa$, $Tb$.
- Join them with $\to$.
Answer: $Fa \to Tb$
Common mistake
| English | Symbols |
|---|---|
| Ava is friendly. | $Fa$ |
| Ava is not friendly. | $\neg Fa$ |
| Both Ava and Ben are tall. | $Ta \land Tb$ |
| Ava is friendly or tall. | $Fa \lor Ta$ |
Some predicates relate two or more things ("Ava likes Ben"); they come later, in Relational Predicates. For now every predicate has one place, filled by one name. Choose letters that help you remember: $D$ for "is a dog", $r$ for Rex, as long as no letter is used for two different things in the same problem.
So far nothing new can be proved: $Fa$ behaves just like a statement letter. The real gain comes in the next lesson, when we can talk about everything or something without naming it, using the quantifiers.