### Logic Primer

Arguments can be looked at in various ways. We can notice their content, what the statements are about. We can also pay attention to their form or structure, how they are set up and the relationships among the various statements. We can try to determine how well the premise statement(s) support the conclusion statement. And we can ask whether the premise statements are true or false. In fact, for a critical interpretation and evaluation of any particular argument we must do all of these.

There are two critical criteria to consider when evaluating an argument:

1. The premises must lead to the conclusion.
2. The premises must be true.
There are formal methods to evaluate the first criterion. The possible worlds method is the most general method. Identifying whether or not the rules for common deductive argument forms (syllogisms, etc.) are followed would be another method of deciding if the premises lead to the conclusion. Many logical fallacies exist and most beginning students find it helpful to stick to one deductive argument form, like conditional syllogisms, in order to be certain that the premises always lead to the conclusion. We will further investigate conditional syllogisms on the next page.

The second criterion is often more difficult to determine since it requires some sort of outside verification. Often the verification will be done by making observations under controlled circumstances (performing experiments) or drawing upon the experience of all human kind (using well-established theories).

Some terminology.

• A deductive argument meets the first criterion, but the process of determining if it is deductive still leaves the second criterion undetermined. That is, the premises lead to the conclusion (without question), but we don't know if the premises are true.

• A valid argument is a deductive argument. Different name, same thing.

• A sound argument must satisfy both criteria. The premises must deductively lead to the conclusion and the premises must be true.

In order for an argument to establish the truthfulness of a conclusion it must be a sound argument, the premises must deductively lead to the conclusion and the premises must be true.