T4 p2

You just chose L>(A&B) to symbolize 3. This made it clear that 3 is an "if...then..." sentence. The grouping clarifies meaning.

We build our compound sentences from atomic sentences (like 'A') connectives (like '&') and parentheses. For clarity, everytime we connect two sentences together with a connective, we add parentheses. Exception: We allow ourselves to drop outside parentheses. This will never make the meaning unclear.

The language we have developed so far, a language without names, provides a logic that is often called "sentence logic" or just "SL".

We'll continue to think about connectives and compound sentences. But we can also symbolize the names that occur in these sentences. Let's see how that will work before continuing on with compound sentences.

Sometimes (like on the last page) we symbolize a whole sentence (like "Agnes will go to law school") with a single symbol. But at other times we'll want to break an English sentence up to analyze it.

Here's a new way to look at symbolism: We'll use lower case letters as names of our symbolic languge to stand for objects. So, we might take 'a' as a name of Agnes. In such a case, we will say that 'a' refers to Agnes. And we'll use upper case letters as predicates to stand for properties. So, we could use 'W' to stand for "will go to law school". Then,

Yes, it's a little backward from the English. But you'll get used to it! Oh, and this, 'Wa' counts as a knew sort of atomic sentence. Let's see what we can build with it.

There are a number of different ways to say "and". There is the long winded way:

Or we could write "Agnes and Bob will attend law school" or "Both will attend law school". And these are just the beginning. These three sentences are different ways of explicitly saying two statements are both true. We will call all such sentences conjunctions. The two components, both said to be true, we call the conjuncts.

So, 1 above is a conjunction. Its two conjuncts are "Agnes will go to law school" and "Bob will go to law school". Before we had names in our symbolic language, we would symbolize 1 simply as 'A&B'. But now (taking 'b' as a name for Bob, we can symbolize 1 as

There are also a number of ways of expressing "if ... then..." statements in English. For example, we could write,

2. If Agnes will go to law school, then she will be miserable for the first year.

Or we could phrase the same exact idea in this way: "Agnes will be miserable her first year if she goes to law school". (But notice that it means something different to say "if she's miserable next year, then she is in law school".)

If she goes to law school, then she'll be miserable.

means the same as

She'll be miserable if she goes to law school.

These two are stylistic variants: their "if" clauses (aka, antecedents) simply go in different spots. But

If she'll be miserable, then she goes to law school.

has a different "if" clause and means something different.

All such "if...then..." statements we will call "conditionals". The "if" clause we call the "antecedent", the clause following "then" is called the "consequent". So, in 2, the antecedent is "Agnes will go to law school" and the consequent is "she will be miserable for the first year". In 'A>M', 'A' and 'M' are antecedent and consequent respectively.

Whew! There is quite a bit of logic terminology to learn. But we will get much of it out of the way in a hurry and get down to the real substance of logic. We have only three connectives to go to finish this introduction to SL.