Logic

Logic is the science of reasoning, proof, thinking, or inference. With logic, we are able to determine whether a given piece of reasoning is valid or invalid. One doesn't need to study logic in order to reason correctly. Most of us already use the rules of logic when making decisions in our lives, even though we may not know it. However, some knowledge of logic can be quite helpful when analyzing an argument.

The basic building block of a logical argument is a proposition. A proposition is a statement that is either true or false, but not both. For example, the following statements are propositions:

• All men are mortal.
• This book is difficult to read and expensive.
• Some cows are blue.

The following statements are not propositions, since we cannot say that they are either true or false:

• Come here right now!
• Is it raining outside?
• This statement is false. (See my paradoxes page for more about this statement).

An argument consists of a series of propositions connected in a manner to establish some other proposition. An argument consists of three steps: First, the propositions necessary for the argument (called premises) are stated. Next, the premises are used to infer other propositions. Finally, the proposition that was originally set out to be established is affirmed on the bases of the premises and inferences. This is the conclusion of the argument. Here is a simple example:

• All men are mortal. (premise)
• Socrates is a man. (premise)
• Therefore Socrates is mortal. (inference and conclusion)

Traditionally, there are two types of arguments: A deductive argument is one that provides conclusive proof of its conclusions. An inductive argument is one where the premises provide evidence for the conclusion, but do not conclusively establish it. Deductive arguments can be either valid or invalid. A valid argument is one that is well-formed. If the premises of a valid argument are all true, then the conclusion will be true. However, if the premises are false, then the conclusion may or may not be true.

To delve further into logic, it is often helpful to use the propositional calculus (also known as symbolic logic).

A fallacy is used to refer to an argument that is technically incorrect, even though it may seem to be valid. There are two types of fallacies: formal and informal. These names have nothing to do with how well-dressed they are; formal fallacies involve errors in the form or structure of the argument, while informal fallacies involve other errors.