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.
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.