An Introduction to Formal Logic
Completion requirements
Supplement what you just read by reading the first chapter of this book. As you read, you will see the careful human thought that is required to create the logical constructs required to get the computer to do anything worthwhile. Section 1.6 begins the process of creating a formal syntax, or language, from human statements. In this course, we use the formal language Java to translate human statements into something that can be translated into the 1's and 0's the computer works with, the settings of the computer's electronic switches.
Summary of logical notions
- An argument is (deductively) valid if it is impossible for the premises to be true and the conclusion false; it is invalid otherwise.
- A tautology is a sentence that must be true, as a matter of logic.
- A contradiction is a sentence that must be false, as a matter of logic.
- A contingent sentence is neither a tautology nor a contradiction.
- Two sentences are logically equivalent if they necessarily have the same truth value.
- A set of sentences is consistent if it is logically possible for all the members of the set to be true at the same time; it is inconsistent otherwise.