1. “Vicious circle”, “begging the question”, “petitio principii”
Petitio principii — In classical Latin, petitio means “request”, and principium “beginning” (Gaffiot , Petitio; Principium). A petitio principii is literally a “request” of the “principles”. Tricot considers that the rendition as “petition of principle” is “vicious”. He notes that “what we ask to grant is not a principle but the conclusion to be proved” (note 2 to Aristotle, Top., VIII, 13, 162a30, p. 359).
The two expressions vicious circle and begging the question are equivalent. The expression vicious circle stresses the cognitive and textual, semantic aspects of the phenomenon, while begging the question emphasizes the dialectical interactional character of the same concept.
The speaker is “begging the question”, that is asking that what is « in question » (the disputed conclusion itself) be granted, as an argument or principle.
The Latin expression petitio principii is used as an equivalent of begging the question.
2. Vicious circle
In the Aristotelian system of fallacies, a vicious circle is a fallacy independent of language, S. Fallacies (2). It is a process of reasoning which seeks to prove a conclusion, by giving as an argument this conclusion itself. Hence the image of the circle. Its schematic form is:
A, since, so, because A.
There are different ways in which to beg a question (Aristotle, Top., VIII, 13).
In ordinary discourse, compound statements “A because A” might be considered as begging the question from a logical point of view:
S1 — Mum, why do I have I to make my bed every morning?
S2 — You have to do it because you have to do it. It’s like that because it’s not otherwise
Nonetheless, despite its format, this is not a vicious circle. The answer is not an invalid justification but a refusal of justification, as testified by the associated mood, exasperation.
In common cases, there is a vicious circle where the conclusion is a paraphrastic reformulation of the argument:
I like milk because it’s good.
Fortunately I like milk, because if I did not like it I would not drink it, and it would be a pity because it’s so good.
When the very result to be demonstrated is postulated, “this is easily detected when put in so many words; but it is more apt to escape detection in the case of different terms, or a term and an expression, that mean the same thing” (Aristotle, Top, VIII, 13).
In the theory of Argumentation within Language, the concept of orientation@ introduces a bias which is not so different from mere petitio principii. The statement
Peter is clever, he will solve the problem.
The above example has a misleading deductive appearance, because the predicate “can solve problems” is in fact included in the definition of “is clever”. The misleading inference is actually a reformulation. Reformulations are interesting insofar as they are never strictly synonymous with their basis. Instead, they introduce a semantic shift, which can be productive. Begging the question is deceitful only in so far as it is strictly the same term that is repeated, S. Orientation.
Goethe claims that, in any argumentation, the argument is only a variation of the conclusion; hence it follows that argumentative rationality is simply vain rationalization:
§50 It is always better for us to say straight out what we think without wanting to prove much; for all the proofs we put forward are really just variations on our own opinions, and people who are otherwise minded listen neither to one nor to the other.
Johann Wolfgang von Goethe. Maxims and Reflections.
2.3 Ad hoc general laws
The Topics point out the frequent case in which one assumes in the form of universal law what is in question in a particular case (ibid.):
Politicians are liars / corrupt. So this politician is a liar / corrupt
This is a most common kind of argumentation. The speaker postulates a one shot, ad hoc principle, in order to apply it to the case at hand. Such cases can also be analyzed as ill-constructed definitions: “being corrupt” is considered an essential characteristic of politicians, whereas it is only an accidental characteristic, S. Definition, Accident.
2.4 Mutual presupposition
Not all vicious circles are reformulations. An objection to the idea of a miracle for example, is that it establishes a vicious circle. Miracles are said to justify the doctrine, to prove that it is true and holy, but a fact is recognized as a miracle only by the doctrine it is supposed to prove. It is a form of resistance to refutation:
S1_1 — This miraculous fact proves the existence of God.
S2_1 — But only those who believe in the existence of God recognize this fact as a miracle
S2 may add that S1 does not recognize other equally surprising facts; to which the latter might reply that:
S1_2 — These other facts are miracles operated by the devil to deceive people.
2.5 Equal uncertainty
The term diallel is used by the Skeptics, with a meaning identical to “vicious circle”:
And the circularity mode occurs when what ought to make the case for the matter in question has need of support from that very matter; whence, being unable to assume either in order to establish the other, we suspend judgment about both. (Sextus Empiricus, Outlines of Pyrrhonism, I, 15, 169)
This definition introduces a new concept of the vicious circle that no longer focuses on a semantic equivalence or an epistemic relation, but on the very definition of argumentation as a technique to reduce the uncertainty of a claim by connecting it to a less doubtful statement, the argument. S. Argumentation. Skeptics will therefore endeavor to show that the argument is systematically no more obvious than the conclusion. In this sense, Skeptics are the first deconstructionists.
3. Circularity in explanation
Circularity is welcome in definitions, but not in demonstrations or explanations. An explanation is circular, if the explanans is at least as obscure as the phenomenon it claims to account for.
 Johann Wolfgang von Goethe. Maxims and Reflections. Trans. by E. Stopp. London: Penguin Books, 1998. Quoted after https://issuu.com/bouvard6/docs/goethe_-___maxims_and_reflections__ No pag. Goethe gathered these maxims during all his life.