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Wikipedia defines "begging the question" as

To "beg the question" is to put forward an argument whose validity requires that its own conclusion is true.

I assume this is something Aristotle's term logic does not permit. Wikipedia quotes Hugh Tredennick's translation of *Prior Analytics* II xvi 64b28–65a26:

...If, however, the relation of B to C is such that they are identical, or that they are clearly convertible, or that one applies to the other, then he is begging the point at issue.... [B]egging the question is proving what is not self-evident by means of itself...

I assume this means one cannot have the following in Aristotle's term logic:

Premise 1: All B is C. Premise 2: All B is C. Conclusion: All B is C.

However, using the proof checker associated with *forall x: Calgary Remix* I can construct a valid argument in truth-functional logic using "reiteration" (page 123-4) by repeating a line I already have.

This is derived from conjunction introduction using two identical conjuncts and then using conjunction elimination to get one of those identical conjuncts. (page 136)

Could this reiteration rule, or permitting conjunction introduction to use two identical conjuncts, be considered begging the question?

Edit 10/6/2018: I was reading Frederic Fitch's *Symbolic Logic: An Introduction* and noticed that I could have simplified the proof I gave above using reiteration by doing the following (page 26):

5.13.There is nothing that excludes a formal proof from possessing only a single item. The following single-item proof is a hypothetical proof ofpon the hypothesisp. It is a proof ofpin the sense thatpis the last (and only) item of the proof.

This is how it looks in Klement's proof checker:

References

Fitch, F. B. (1953). Symbolic Logic; an Introduction.

Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/

Wikipedia, "Begging the question" https://en.wikipedia.org/wiki/Begging_the_question

I find that an odd definition. Why would the argument’s

validityrequire thetruthof the conclusion? In fact, your P ⸫ P is a counter-example: that’s valid, even if P is false. Also, isn’t ‘beg the question’ a notion frominformal logic / critical thinking / rhetoric (or whatever you want to call it), whereas reiteration is a rule offormallogic. (Also, it’s aproofrule, not a model-theoretic thing, which makes the appeal to (the semantic notion of) truth even stranger.) – MarkOxford – 2018-08-12T19:13:24.370@MarkOxford Maybe there's a better definition of "begging the question"? The informal fallacy of begging the question doesn't imply that the conclusion of the argument is true or false only that the way to reach that conclusion is questionable. That would be the case for any logical fallacy, at least as I see them. – Frank Hubeny – 2018-08-12T19:22:22.277

I do not think your argument scheme with three identical lines falls under any of the syllogism figures. But Aristotle's syllogistic was not fully formalized, if it was and he wanted to use the same sentence more than once in an argument he'd need a repetition rule. "Begging the question" is a circularity charge against a possibly valid argument when its conclusion is already contained in the premises. – Conifold – 2018-08-12T19:27:28.757

Instead of just ‘beg the question’, I wonder whether we should say ‘beg the question

against X’. E.g., the person who rejects p will also reject p&q; so p&q ⸫ p begs the question againstthem– but that tells us little about the formal validity of that argument. @conifold speaks of conclusions that are ‘already contained in the premises’. That’s no doubt the gist of begging the question, but note that this is a fairly vague notion. Consider: p, p->q ⸫ q. Is q ‘contained in’ the premise? – MarkOxford – 2018-08-12T19:31:43.403More formally, if φ⊧ψ, but φ and ψ have no sentence letters in common, then either φ is a contradiction or ψ is a tautology. So, unless you’re arguing from a contradiction or for a tautology, the conclusion is always ‘contained in’ the premises, at least in part. I think my point is that it's potentially misleading to use an informal notion like 'beg the question' and then apply it to formal logic. – MarkOxford – 2018-08-12T19:50:00.073

@MarkOxford There are formalizations of "contained" going back as far as Peirce. In modern terms conclusion is "contained" in the premises if it is derivable using monadic predicate calculus ("syllogistic") only, for example, similar notions are used to distinguish "trivial" and "non-trivial" proofs by Hintikka and others. I also noticed that "begging against" is typically used with a meaning distinct from circularity, namely arguing from premises or presuppositions that the opponent is known to reject. – Conifold – 2018-08-12T20:06:16.397

@Conifold Interesting. So, is the conclusion Rab contained in Pab&(Pab->Rab)? (I ask because you say

monadicFOL, which these sentences aren’t.) – MarkOxford – 2018-08-12T20:17:31.937@MarkOxford This inference is purely propositional despite the presence of dyadic predicates, so yes. Hintikka's extension is that one does not need to introduce new quantified variables in the course of the proof, see Hintikka'80. It was objected that some purely propositional proofs are intuitively "non-trivial" while they come out as trivial by Hintikka's lights. I think Jago came up with a more sophisticated version recently.

– Conifold – 2018-08-12T20:43:42.323@Conifold I made up the bogus syllogism to suggest it was not something Aristotle would have accepted to my knowledge. – Frank Hubeny – 2018-08-13T00:32:24.207