Circular reasoning

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Circular reasoning is a form of proof by assertion, often used by Christians and Evangelicals in which one uses a conclusion of an argument as a premise to that same argument (The Bible is true because it is the Word of God, it is the Word of God because it says so in the Bible) , that is, ending where it began. This is also known as petitio principii or begging the question.

It is considered invalid and therefore is not permitted by the rules of formal logic.

An analysis

The simplest argument is a single inference, as per the Law of Detachment:

• If P, then Q.
• P.
• Therefore, Q.

The Law of the Syllogism uses Detachment to establish an intermediate conclusion between the original premise and the eventual conclusion. Thus:

• If P, then Q.
• If Q, then R.
• Therefore, if P, then R.
• P.
• Therefore, Q and R.

Contraposition uses Detachment in reverse to show that a thing is not true:

• If P, then Q.
• Not Q.
• Therefore, not P.

All these proofs start with a proposition already verified or denied.

This is the classic structure of circular reasoning, that is an abuse of the Law of the Syllogism:

• If P, then Q.
• If Q, then R.
• If R, then P.
• P.
• Therefore, Q.
• Therefore, R.
• Therefore, P.

Each of these three conditional statements would be valid by itself. Together, they create a flawed argument, because P now depends on itself to be true. The line of reasoning ends where it began, and is thus a circle. The only difference between this and proof by assertion is that the latter attempts to use a single conditional statement--"if P, then P"--while circular reasoning uses at least two, and typically three or more, syllogisms.

Circular arguments can be very difficult to detect. Circular arguments found in the professional literature, or in propaganda, typically use five or six (or more) syllogisms.

Every logical system must begin with a set of generally accepted assumptions called postulates or axioms (from the Greek αξιος or axios worthy or deserving). Similarly, any set of definitions must start with a set of fundamental terms that need no definition. An axiom is usually a fundamental property of nature upon which all agree. Persons attempting to show that something is a fundamental property of nature when it is not, or a value of that property that is contrary to fact, typically use circular reasoning to make such an attempt.

Examples

• Christians use circular logic to defend the Bible. They argue that the Bible is true because it is the Word of God, that it is the Word of God because it says so, and that we can rely on it because it is true. Almost all religions worldwide use this sort of reasoning in order to assert their individual beliefs' validity.

See also

• No true Scotsman, a specific example of circular reasoning