The most important concepts to understand in Formal Logic is the concept of validity. All logic students should memorize and come to understand these three different (but related) ways of defining validity:
- In a valid argument, the premises imply the conclusion
- In a valid argument, if the premises are true, then the conclusion must be true.
- If an argument has true premises and a false conclusion, then it is invalid.
The first one is the shortest, and thus the easiest to memorize, and it also review the concept of implication that was covered in relationships between statements.
The second one is the easiest to understand.
The third is the most practical, in terms of the tools that will be developed for analyzing the validity of arguments, not only Introductory Logic, but also Intermediate. These tools include counterexamples, rules of validity, formal and informal fallacies, longer and shorter truth tables, and truth trees.
The other major concept that must be understood is this one:
Validity depends on the form of the argument, not the truth value of the statements.
The most common misunderstandings to correct are these:
Error 1. An argument is valid if the premises and the the conclusion are true.
Error 2. An argument with a false conclusion is invalid.
If a student understands and remembers these, he has learned the most important practical concept of formal logic.