Vicious Circle

VICIOUS CIRCLE – BEGGING THE QUESTION
PETITIO PRINCIPII

1. The Terms

Vicious circle, begging the question
The two expressions are equivalent. The expression vicious circle emphasizes the cognitive and textual, semantic aspects of the phenomenon, while begging the question emphasizes the dialectical interactional character of the same concept.
The speaker “begs the question”, that is, asks that what is « in question » (the disputed conclusion itself) be granted, as an argument or principle.

Petitio principii
The Latin expression petitio principii is used as the equivalent of begging the question.
In classical Latin, petitio means “request”, and principium means “beginning” (Gaffiot [1934], Petitio; Principium). A petitio principii is literally a “request” of the “principle”. Tricot considers that the expression “petition of the principle” is “vicious”. He notes that “what we ask to be granted is not a principle but the conclusion to be proved” (Note 2 on Aristotle, Top., VIII, 13, 162a30, p. 359).

2. Vicious Circle

In the Aristotelian system of fallacies, a vicious circle is a fallacy independent of language, see fallacies-2. It is a process of reasoning that attempts to prove a conclusion, by using that conclusion as an argument for the conclusion itself. Hence the image of the circle. Its logical schematic form is:

A, since, so, because… A.

There are different ways « to beg a question » (Aristotle, Top., VIII, 13).

2.1 Repetition

In ordinary discourse, the compound statements « A because A » can be regarded as begging the question from a logical point of view:

S1 — Mom, why do I have I to make my bed every morning?
S2 — You have to because you have to. It is so because it is not otherwise.

But despite its format, this is not a vicious circle. The answer is not an invalid justification but a rejection of any justification, as evidenced by the associated mood, despair or exasperation.

2.2 Reformulation

In many cases, there is a vicious circle because the conclusion is a reformulation of the argument:

I like milk because it’s good.

Fortunately, I like milk, because if I didn’t like it, I wouldn’t drink it, and that would be a shame 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 of 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 smart, he will solve the problem.

The predicate “can solve problems” is a defining feature of “is smart”. The misleading inference is actually a reformulation.
Nevertheless, reformulations are interesting in that they are never strictly synonymous with their basis. They introduce a semantic shift that can be productive. Begging the question is deceptive only in so far as it is strictly the same term that is repeated, see orientation.

Goethe claims that, in any argumentation, the argument is only a variation of the conclusion; from this, 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 only 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[1].

2.3 Ad Hoc General Laws

 The Topics point out the frequent case in which one assumes in the form of a general law what is in question in a particular case (ibid.):

Politicians are liars / corrupt. So, this politician is a liar / corrupt.

This is a common form of argumentation. The speaker postulates an ad hoc principle, in order to apply it to the case at hand.
Such cases can also be analyzed as  poorly constructed definitions: “being corrupt” is taken to be an essential characteristic of politicians, whereas it is only an accidental characteristic, see definition; accident.

2.4 Mutual Presupposition

Not all vicious circles are reformulations. One objection to the idea of ​​a miracle for example, is that it creates a vicious circle. Miracles are supposed to justify the doctrine, to prove that it is true and holy, but a fact is only recognized as a miracle by the doctrine it is supposed to prove. It is a form of resistance to refutation:

S11 — This miraculous fact proves the existence of God.
S21 — But only those who believe in the existence of God recognize this fact as a miracle.

S2 might add that S1 does not recognize other equally surprising facts; to which the latter might reply:

S12 — These other facts are miracles performed by the devil to deceive people.

2.5 Equal Uncertainty

The term diallel is used by skeptics, with a meaning identical to “vicious circle”:

And the diallel mode occurs when that which ought to make the case for the matter in question requires the support of that very matter. Therefore, 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, which no longer focuses on a semantic equivalence or an epistemic relation, but on the very definition of argumentation as a technique for reducing the uncertainty of a claim by linking it to a less doubtful statement, the argument, see argumentation-1. Skeptics will therefore try 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 purports to explain.

[1] 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 collected these maxims during all his life.