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# What Is Deductive Logic?

Doctors may need to use deductive logic when treating a patient.
A deductive argument can be either valid or invalid.
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• Written By: Angie Bates
• Edited By: John Allen
2003-2015
Conjecture Corporation
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Most often used in philosophy, deductive logic is one of two classifications for logical arguments. Unlike inductive logic, deductive logic begins with presumably true premises and then makes a deduction from those premises. Both deductive and inductive logic are only used in arguments.

Inductive logic begins with facts that are known to be true, such as statistics, and aims to explain the reason behind those statistics in a logical, reasonable manner. Deductive logic, on the other hand, begins with a set of premises and deduces a logical conclusion from those premises. Premises are statements that may or may not be true, but for the purpose of the argument are taken as fact.

Deductive logic is concerned with the structure of the argument more than the argument's content. In a deductive argument, one states that premise A and premise B are true, and therefore, conclusion C is also true. Outside of philosophy, geometry proofs are a type of deductive logic. In fact, the structure can be seen clearly using simple numbers. For example, assuming A equals 1 and B equals 2, then C must equal 3.

A deductive argument can be either valid or invalid. Since deductive arguments are based on the assumption that the premises are true, an argument can be valid without being true. For example, the argument, "All gray-haired women are grandmothers. Betty is a gray-haired woman. Therefore, Betty must be a grandmother," is valid but is false.

If the premises are true then the conclusion that Betty is a grandmother is also true. The first premise, however, is not true. All gray-haired women are not necessarily grandmothers, so Betty is not necessarily a grandmother. If an argument is valid but untrue, then a premise in that argument is false.

Invalid arguments occur when the conclusion does not follow logically from the premises. The following is an example of an invalid argument: "Layla is always hungry after she dances. Layla is hungry. Therefore, Layla has been dancing."

Dancing is only one thing of many that results in hunger. Layla could be hungry because she has been dancing, but she could be hungry simply because she had not eaten all day. Although the premises are true, the conclusion does not follow logically from the premises and, therefore, is invalid.

Both deductive and inductive logic are only used in arguments. Arguments are things that are debatable or can be disagreed with. Descriptions or simple opinion are not arguments and, therefore, neither form of logic can be used. For example, saying, "My favorite ice cream is butter pecan," is just an opinion and so cannot be argued.