5. Circular Arguments
From Common Fallacies in "Clear Thinking" by E W Jepson

A Circular Argument is still another form of begging the question, although it is usually considered separately.

Arguing in a circle is first using a premiss to prove a conclusion, and then using the conclusion to prove the premiss; in other words, it is an attempt to prove two statements reciprocally from each other.

You quote, we will say, as evidence in support of some point you are making, certain statements which appear only in F 's Diary. Later on in the argument, when your opponent expresses his doubt as to the authenticity of F 's Diary or its trustworthiness as a source of evidence, you say, perhaps not in these words, that it must be reliable and authentic because it contains the information you have already quoted. Then you are arguing in a circle; your argument boils down to this:

These facts are true because they are in F 's Diary.
F 's Diary is true because it contains these facts.

The symbolic form of such an argument could be put thus:

If A, then B: if B, then C: if C, then A.

Let me draw on Alice in Wonderland for an amusing example of this fallacy.

In that direction," the Cat said, " lives a Hatter and in that direction lives a March Hare. . . . They're both mad."
"But I don't want to go among mad people," Alice remarked.
"Oh, you can't help that," said the Cat: "we're all mad here. I'm mad. You're mad."
"How do you know I'm mad?" said Alice.
"You must be," said the Cat, "or you wouldn't have come here."
Alice didn't think that proved it at all.

When the circular argument is expressed in simple and unmistakable language, with the intervening discussion omitted, it is easy enough to detect, and you might justly say that no one in his senses would ever be deceived. But when the two halves of the circle are widely separated, and the disputant uses his terms loosely and vaguely, then the argument has a plausibility about it that may deceive a hearer who is not alert.