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I was wondering if circular reasoning is always a problem I was thinking about something like this if A then B, And If B then A.

Premise. A is true

Conclusion. B is true.

All this shows is that B logically follows from A being true, Why is this form of circular reasoning logically wrong? it seems like an inductive argument to me.

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    This is not circular reasoning, this is proving that A and B are logically equivalent. It may well be informative when the equivalence is non-obvious. Circular reasoning would, literally, be "if A and B then A", or, informally, when A is replaced in the premise by some A' transparently equivalent to it. Even then it is not logically wrong, just substantively uninformative, and hence an informal fallacy.
    – Conifold
    Commented Mar 16, 2023 at 23:22
  • @Conifold Thanks I understand I'm going to leave this up for a few more people to answer although yeah that makes that sounds correct to me.
    – Firebirdofnercy
    Commented Mar 16, 2023 at 23:27

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This is not a circular argument, it's an if and only if statement.

There's nothing formally wrong with circular arguments. A therefore A is always true. They just don't prove anything, since they're logically identical to the premise by itself. If I am purple, then I am purple. I am not, in fact, purple. If I am purple, then I am purple, therefore you should believe that I am purple is a garden variety non-sequitur.

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Quite the opposite. Circular reasoning is always correct, it is just useless.

“If A then A” is absolutely true. It just doesn’t tell you anything about A. Now what will happen that someone tries to prove A. They start a reasonable proof, then sneak in the completely unproven statement A, then end up with A. It may not be directly, because that would be too obvious. Sometimes it is very well hidden that a proof is circular.

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