Circular arguments

Circular arguments are perfectly valid

You have likely heard the claim that circular arguments are wrong or incoherent. In this short post I will outline why this is not the case. Circular arguments are perfectly fine; in fact, they can be quite convincing!

Lets start with perhaps the most famous bad example of a circular argument:

God exists because the bible says so, and the bible is true because God exists.

It is clear that this is circular, as each statement depends on the other to be true. It’s also a bad argument from a logical standpoint, as logical arguments tend to be formulated in “if A than B”, and this formulation is missing here. This emphasizes the other weak aspect of this argumentation: both claims have a rather low prior probability.

Lets see what happens when we rephrase the above argument to the following:

If the the bible is true God exists, and, if God exists the bible is true.

While both claims still have the same very low probability, it is now a more coherent – albeit circular – line of reasoning. Is there anything wrong with these arguments because they are circular? No. The circularity does not reduce the validity of these arguments in any way. That is, there is nothing inherently wrong with circular argument, although this does not mean that all circular arguments are valid and/or sound.

Lets examine this a little further by stripping this argumentation type to its most abstract form:

If A then B. If B then A

It should be more clear now that this line of reasoning is perfectly valid. Each individual statement is perfectly valid, and the combination of the two are also valid. In fact, if B stands for something with a non-zero prior probability than the inclusion of the second argument increases the probability that A is true. This is why these types of circular arguments are not only completely valid, they can be convincing as well – if used properly.

The real problem is in how circular arguments are used. That is, most informal uses of circular arguments will look like this:

If the the bible is true God exists, and if God exists the bible is true. Therefor: the bible is true and God exists.

Of course this is not sound. Likewise, just because ‘if A then B’ and ‘if B then A’ are perfectly valid, they do not lead to the sound conclusion that A and/or B are true. Simply because a line of reasoning is logically valid, they can merely be vacuously valid, such as the following statement:

If [something impossible/false] is true, then [insert any claim]

The above statement is technically correct (the best kind of correct!), it is also utterly meaningless as the antecedent is false. No logician will stop you from making this claim, but no rational person will update his believes in any way after hearing it. The validity of an argument is only the first step to consider: you also need to consider the probability of the antecedents (e.g., the probability that the bible is true). In the case of circular arguments you also need to especially wary that they are often used incoherently.

To recap.

It is perfectly valid to state:

If A then B. If B then A.

In fact, the above is more informative and stronger than just claiming either, and can thus be used to convince someone who already holds either A or B to be true (or false). In and by itself this line of reasoning should not lead us to consider A and B to be true, just like how just “If A then B” by itself doesn’t lead us to believe that B is true.

It is perfectly invalid to state:

If A then B. If B then A. Therefor: A and B.

10 thoughts on “Circular arguments are perfectly valid

  1. I think this mostly comes down to the definition of a circular argument. “If A then B; if B then A” doesn’t seem circular to me; it has two “handles” as entry points, kind of like a maze with two entry points. “God exists because the bible says so, and the bible is true because God exists” is a sealed unit with no way in, kind of like a round city wall with no doors.

    • Correct me if I’m wrong, but “God exists because the bible says so” is equivalent to “B because A” which is equivalent to “if A then B”.

      There are presumably other type of circular arguments as well – I didn’t claim that all of those are correct. However, it is a fallacy to state that an argument is bad *because* it contains circularity. “God exists because the bible says so, and the bible is true because God exists” is bad not because it is circular, but because both premises have a very low prior probability. It’s value in a discussion depends on how much you value the premises, but this is true for any line of reasoning.

      • >>“B because A”
        >>which is equivalent to
        >>“if A then B”.
        I don’t think that holds. The first assumes A. The second is conditional on A.

        I wish I’d paid more attention in the very few logic classes that I took, then I could be more confident about this and say it was Zarg’s Conjecture or something.

  2. Nice post! Although I wouldn’t say your example is exactly circular. Let me explain.

    “If A then B & if B then A” is equivalent to “A if and only if B” which is just a characterization (an equivalence). They are both true or both false (as you mentioned).

    It’s of course just a matter of definition, but I would require at least three statements in my informal definition 🙂

    A => B
    B => C
    C => A

    Which is “more circular” (of course, they are quivalent as before!).

    • Technically, the shortest form of a circular argument requires only one statement: A, therefor A.
      I don’t think having more statements (2 in my example, 3 in yours) makes it more circular. The reason I chose an argument with two statements is because it aligns with commonly known arguments like the god/bible thing.

  3. I agree with Juan. I think you’re just talking about equivalence between A and B, A and B being necessary and sufficient for each other, A B, A iff B, etc. It’s not even an argument, let alone a circular one, because no statement is deduced from any other statement. It’s simply the claim that A B.

    • The blog stripped away my double-headed-arrow symbol (probably because it contains closed < brackets and so looks like HTML). So FYI those two instances of "A B" are supposed to read "A ⇔ B" (hopefully this latter symbol works).

  4. hi Tim, I am frequently communicating about a variety of issues which are related to the efforts to retract a fraudulent study on the breeding biology of the Basra Reed Warbler, see and for backgrounds, with researchers who do not communicate with me because they do not communicate with me.

    I have therefore recently started to communicate with these researchers, and with their allies, through the framework of ‘tacit approval wihtin a fixed period of time’ (for example within 3 working days). These researchers do not communicate with me because they do not communicate with me and they therefore also do not respond on my proposal to communicate with them within the framework of tacit approval within a fixed period of time. These researchers do not communicate with me and thus also not rebut / reject my statement that communicating with them through the framework of tacit approval within a fixed period of time is common practice within their field of research (in this case publication ethics).

    I hold the opinion that it is legitimate to communicate with these researchers through this framework, and in particular after receiving auto-replies (receiving auto-replies implies towards my opinion that these researchers have received my email in good order).

    It has turned out that communicating with such researchers though the concept of ‘tacit approval within a fixed period of time’ is a very successful strategy in enlarging the list of people and organisations who support the (main) conclusions of

    So what’s your view about this method of communicating with researchers who do not communicate because they do not communicate, and/or using the outcome of such discussions for articles? Copy/pasted from a draft:

    “This non-response is towards my opinion the strongest argument that my view about partial behaviour by BMJ is founded. I have thus no proof that the unavailability of the form can indeed be attributed to partial behaviour by BMJ. BMJ has, on the other hand, not rebutted that partial behaviour is the real motive for the decision that the form is unavailable. BMJ states on its website that they ‘encourage open debate, comment and criticism’. This statement indicates that BMJ has no objections against the publication of this article.”

    Is this some sort of argueing with circular arguments?

  5. Correct me if I’m wrong, but did you just use a circular argument to prove circular arguments are true? Maybe I’m looking too deep into this.

    • I didn’t say circular arguments are true – there is very important distinction between whether a line of argumentation is *logically consistent* (valid) and whether it (the antecedents and/or the conclusion) are *true*. The whole bible/god example is in false in the sense that the antecedents are false, but the A->B and B->A is logically consistent.
      If you think that modus ponens is valid, then these types of circular arguments are as well.

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