Logic is the study of the structure and principles of reasoning. The main tool used in philosophical reasoning is argument. Logic is concerned with the formal aspect of argument rather than the content, i.e. how an argument is shaped, or structured, rather than what it is about. It is useful "in distinguishing the rational from the irrational, the sane from the insane".
What argument is not is bickering and fighting, rather, it is a technical term for how a set of statements relate such that one statement follows from the others. The statements that are the premises are the reasons that aim to support the statement that is the conclusion.
All arguments have an issue, or question, that the argument hopes to settle (if everyone agreed there wouldn't be an issue, and therefore nothing to argue about). In an argument the reasons are generally accepted, or assumed for argument's sake, and the conclusion has to be discovered (e.g., If a squiggum is a mammal and a mammal is an animal, then we can conclude without any doubt that a squiggum is an animal.), whereas an explanation is sort of an upside-down argument since the conclusion is generally accepted (e.g. the space shuttle crashed) and the reasons have to be discovered (that the O-rings failed).
There are two main kinds of arguments: deductive and inductive. In a deductive argument the arguer claims that it is impossible for the conclusion to be false when all the premises are true (as in the squiggum example above). In an inductive argument the arguer claims it is improbable that the conclusion is false when all the premises are true (e.g. the sun has risen every day that I know of, so it probably will rise again tomorrow).
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