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.

17 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?

    • hi Tim,

      The draft with the quote

      “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.”

      has been published last week in the open access journal ‘Roars Transactions, a Journal on Research Policy and Evaluation’ at

      The publication of this paper (‘Is partial behaviour a plausible explanation for the unavailability of the ICMJE disclosure form of an author in a BMJ journal?’) shows, at least towards my opinion, that one can indeed use circular arguments in a scientific debate / dialogue with parties / people who do not respond.

  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.

      • But it’s still a logical fallacy. Even in the example you used! If A then B, and if B then A is incorrect. If A = B, then B = A is correct, but those two are different. “Then” implies that the two, A and B, are distinct, which automatically concludes with a fallacy. For example, what you said. If the bible is true, then god exists. This is true, however, the claim that if god exists then the bible is true is incorrect because god existing is not the only statement of the bible. The teo A and B are distinct, and thus are not equal. If god is real, but he’s actually the left nipple of some fat sweaty nerd, then the bible would be incorrect, even though god is real. However, I suppose you could say, A then B, so B then Partially A, but I’d hardly consider that a convincing arguement. Its still circular, and its not really an arguement if you say “if.” That’s like me saying, “well god is real because if the bible is true then god is real so god is real.” In fact, that’s even worse than the original! All you did was add an “if” to the mix! But I would be happy if you could correct me. Is there something that I am missing?

  6. Yes this would be a form of circular logic but a lesser faction and not entirely circular. Due to the stress of If does leave the cascade of the argument a more open ability to being possibly true because the If hasn’t been proven. Case in point the If would have to be changed to either a variable of C let’s say or a When. For the purpose of explanation, If A Is actually true then A would undoubtedly be true and by all rights of logic this stands to hold, but that isn’t circular by this measure. If A is true and you can prove A is true then the denying A would be falsehood because you have already provide proof of A to start with. Hence, no further analysis would be needed. However, if A is true then B is true is where the divergence happens.
    If A doesn’t prove B is true then A proving B doesn’t matter anyway. An assumption is being made through the then section of the argumentative set. Which is why this would even would be considered circular logic to begin with because after the first assumption is made present the the second assumption Follows.

    I agree that valid circular arguments can be made, but technically here you are pregranting an out with and through the If statement. Now if you change If to a When position its harder to escape the fallacy. Hence, let’s change the set up to When A and while still granting the assumption of Then B. In the assumption that: When A is true then B follows and if B is true then A follows.

    Here we arrive at an issue with the assumption status of then B being true. Which is again is why most circular logic is invalid because the Then mode has no direct proof profile, so the then proof file of B then A is also set up to be possibly false as well.

    In reality this second point is actually even less possible for a valid rational analyst because the first assumption was never proven to begin. Through these two assumptions in combination you have created the middle third assumption variable between the two first assumptions: When A is true then (assumption) B is true, then (assumption) that if B is true then (assumption) A is true. Hence, the assumption of Then with lack of proof is a large portion of the problem with circular logic in addition to the When verse If status. In using If as a possiblity not as an If and only If status negates circular reasoning.

    In using When instead of If the argument would be most certainly circular at this point, but not necessarily valid. The circular argument isn’t valid unless you can prove that what makes A true is B and what makes B true is A. Here’s why, A is granted as being true through already established proof once the If changes to When and in that moment you don’t need B to prove A’s validity anyway. Which puts us right back to A is true When A is true, but why is A true? An outside variable must be established for the When previous to A.

    However, in choosing to follow the circular logic terms first given: A is true because of B, that is after the If A then B sequence. Now this can actually hold up iff you provide proof and take away the (assumption) of the Then standings while inserting a variable for When when in exchanging it for If. However, A would be true merely because of A either way in that regard because of C and changing If into When. The B varient or any other variable can of course still exist in this cycle, but wouldn’t really matter. Therefore, A is a circular logic theory that is still invalid by itself until you use a extra outside variable during the When exchange for If. Otherwise, A is still self defined. A is true because of A doesn’t hold in an argumentative process. That no different than saying When or If A is A then A is A. Obviously A is A, but what makes A would be C.

    It must be that , A is true because of C and when A then B and when B then A, but it would start with C. When there is a C then it’s not totally circular in theory because the line still has a start an stop point. Which is why you can’t start with just If or When because you must have an actual market place holder which becomes the outside C variant and turns If into When (C).

    When C Then A and Then B, and Then When B then A. This is technically the only truly valid circular argument one could make. Problem is people don’t start with the outside varient and use the status of Then by way of assumptions. Whereby, When C then A and then A (remember any other variable doesn’t matter because it all comes back to A eventually) by in large isn’t circular at all because of the outermost varient of C.

    In closing, yes you can make circular logic arguments, but the If mode here is the place that in fact produces something that isn’t actually circular at all. The If which must be changed to (When) and it is circular at this moment but not valid. When the When status is utilizes and the varient C is used as the outside value before the circular argument has ever been made, and by providing proof that A does in fact lead back to A just not outside the A the argument the circular logic navigation through B and back to A can be valid, but for productivity of simplicity it doesn’t matter. All it does is account for the extra variables that keep perpetuating A, but it’s really C that began the process of the proof file. However, we often don’t know what C varient is. Hence, why we resort to false circular logic and can’t escape it.

  7. What do you mean by probability? Are you referring to the probability of the intended conclusion from the circular reasoning of God/Bible & Bible/God? If your basis for low probability of the truthfulness of this conclusion on presuppositions outside of the circle of reasoning then that is fallacious…because the only way to know if the probability is low is to examine within itself, and that can only be done by examining the Bible thoroughly yourself. I give the probability of this particular circular reasoning a 1 or definite probability because I see the 100% truthfullness of it from within the circle itself. If you aren’t well informed as to the content of anything, then you’re in no place to establish probabilities as to the validity of the content. The “if” is not necessary from within the circle, but only from without where the truthfulness of the conclusion is still not evident. For instance, if I say “the sky is blue, therefore the oceans are blue and the oceans are blue because the sky is blue”. If you choose not to ever look at the sky or the ocean then whatever probability you place on this claim is nonsensical. Likewise, making conclusions about the probability of truth of God and the Bible in this reasoning without looking at/to the Bible or God is nonsensical as well.

  8. Oh boy. Where do I start. First off, “If A then B and If B then A” is not an argument. It’s a conjunction. An argument must have premises and a conclusion. Assuming the argument you’re making is “If A then B” Therefore “If B then A”, that is an invalid argument. Return to your example about god’s existence. “If the Bible is true then god exists.” If one assumes that conditional, AND the fact that the bible is true, It MUST follow that god exists. However, if one assumes that conditional AND the premise that god exists, it does NOT follow that “The Bible is True” must be true. It is possible for both statements to be true, and the statement “The Bible is True” to be false. That is a common logical fallacy called “Affirming the Consequent.” You could however by Modus Tollendo Tollens conclude that The Bible is NOT true if god does NOT exist.

    Now, as to the original question.Incorrect. Circular Reasoning is ALWAYS valid. Deductively, In all cases a Premise ‘P’is true, The same premise is True. Now, your conclusion, ‘P’ rests on the Assumption that ‘P’ is true. In a debate the conflicting party does not share that assumption. In order to PROVE the Assumption ‘P’ in the context of a debate, you’ll need to use assumptions that are shared with the people you’re debating with. The criteria for soundness is that the argument is BOTH valid, and the premises are in fact true. Your premise in this case is ‘P’, and assuming it is true does not mean ‘P’ is true. You must first derive ‘P’ from facts already known to be true. Thus, there’s nothing invalid about circular reasoning, but nothing can be said about the soundness of certain circular arguments because more information is needed to determine whether the premises are in fact true.

  9. I wouldn’t say it’s circular but more illogical and definitely not a valid argument. If God exist it wouldn’t exactly make the bible true, it would simply means their is truth to it. I guess the argument that follows would probably be circular

  10. Jude is correct, the example in your argument has an error, but your conclusion is still true: circular arguments are not invalid because they are circular.

    They are at best just weak arguments because neither the premises nor the conclusion have any evidence which isn’t already presupposed by the argument…Or rather, it is simply “begging the question”, as is said modernly.

    A better example of circular reasoning is:
    “A is true because B is true; B is true because A is true.”

    I think this might’ve been mentioned already. To put it more simply:

    A because B.
    B because A.

    This is very circular, but it doesn’t make either A (the conclusion) or B (the premise) false. It just makes it a weak argument. You’d have to independently provide proof or evidence of either A or B to strengthen this argument.

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