T2.1: 2 of 7
Now, don't worry if symbolization seems foreign at first. We will introduce the methods for translating from English to SL slowly over the course of three chapters! Now, we just need to get familiar with the connectives, the symbols that are the glue of compound sentences.
We've already been introduced to two connectives: '&' and '>'. The first of these, ampersand, is found on your keyboard; it's usually the shifted-7. It's a common abbreviation for "and"; so SL is in conformity with this standard usage.
However, there are a number of different ways to say "and". There is the long winded way:
1. Agnes will go to law school and Bob will go to law school.
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". In SL, we symbolize 1 as 'A&B'. It too we call a conjunction, with conjuncts 'A' and 'B'.
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".)
So, 2 can be symbolized as:
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.
But first, click on the antecedent of the following: