[Math Lair] Logic

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Logic is the study of reasoning, proof, thinking, or inference. Logic enables us 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, knowledge of logic can improve our ability to make decisions, help us argue for our beliefs logically, and help us analyze the arguments of others.

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:

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

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:

Traditionally, there are two types of arguments: A deductive argument provides conclusive proof of its conclusions. In an inductive argument, 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 can be helpful to investigate propositional 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. Formal fallacies involve errors in the form or structure of the argument, while informal fallacies involve other errors.

See also recreational logic.