 # Logic

Logic is the study of reasoning. Logic investigates the level of correctness of the reasoning found in arguments. An argument is a group of statements of which one (the conclusion) is claimed to follow from the others (the premises). A statement is a sentence that is either true or false. Premises are statements that contain information intended to provide support or reasons to believe a conclusion. The conclusion is the statement that is claimed to follow from the premises. In order to help recognize arguments, we rely on premise indicator words and phrases, and conclusion indicator words and phrases.

There are two types of argument: deductive and inductive. A deductive argument is one in which it is claimed that the conclusion follows necessarily from the premises. In other words, it is claimed that under the assumption that the premises are true it is impossible for the conclusion to be false. An inductive argument is one in which it is claimed that the premises make the conclusion probable. In other words, it is claimed that, under the assumption that the premises are true, it is improbable for the conclusion to be false.

When we evaluate deductive arguments, we use the following concepts: valid, invalid, sound, and unsound. A valid argument is one where, assuming the premises are true, it is impossible for the conclusion to be false. In other words, the conclusion follows necessarily from the premises. An invalid argument is one where, assuming the premises are true, it is possible for the conclusion to be false. In other words, a deductive argument in which the conclusion does not follow necessarily from the premises is an invalid argument. When logical analysis shows that a deductive argument is valid, and when the premise are all true, then the argument is sound. If a deductive argument is invalid, or if at least one of the premises is false, then the argument is unsound.

When we evaluate inductive arguments, we use the following concepts: strong, weak, cogent, and uncogent. A strong inductive argument is one such that if the premises are assumed to be true, then the conclusion is probably true. In other words, if the premises are assumed to be true, then it is improbable that the conclusion is false. A weak inductive argument is one such that if the premises are assumed to be true, then the conclusion is not probably true. An inductive argument is cogent when the argument is strong and the premises are true. An inductive argument is uncogent if either or both of the following conditions hold: the argument is weak, or the argument has at least one false premise.

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