Abstract
Traditionally, logicians construed fallacies as mistakes in inference, as things that looked like good (i.e., deductively valid) arguments but were not. Two fallacies stood out like a sore thumb on this view of fallacies: the fallacy of many questions (because it does not even look like a good argument, or any kind of argument) and the fallacy of petitio principii (because it looks like and is a good argument). The latter is the concern of this paper. One possible response is to say that the tradition is right about the concept of fallacy but wrong about its extension: petitio principii is not a fallacy. If the only proper ways to criticize an argument are to say that it is invalid or that it is unsound, and petitio principii is not criticisable on either of these counts, then calling it a fallacy is tantamount to saying we should prefer invalid or unsound arguments Robinson (Analysis, 31(4): 114 ,1971). I will present a third way to logically criticize arguments and show that fallacious instances of petitio principii are so criticisable while other instances of petitio principii are non-fallacious; hence, this fallacy is not a reductio of the Standard Treatment. It is not my intention in this paper to come out on the side of any of the competing theories—the Standard Treatment, the dialectical theories, and the epistemic theories—as general theories of fallacy. I show only that petitio principii can be handled by something closely resembling the Standard Treatment in so far as that, on entirely logistical principles, there can be made a distinction such that circular arguments form at best a degenerate kind of argument. Circular arguments look like good arguments but are not, not because they are deductively invalid (which they are not) but because they do not deserve to be called arguments at all.
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Notes
In Hamblin’s game the questioner and the answerer each have their own commitments, while van Eemeren and Grootendorst (1987, 288) appeal instead to the commitments that they share in common. It makes little difference to the illustration.
Sinnott-Armstrong (1999, 175) calls these arguments strongly circular. Note that orthographic identity on its own does not guarantee the identity of propositions expressed, because of the possibility of ambiguous terms etc.
Walton (2005, 87) gives Whateley’s example: “To allow every man an unbounded freedom of speech must always be, on the whole, advantageous to the State; for it is highly conducive to the interests of the community, that each individual should enjoy a liberty perfectly unlimited, of expressing his sentiments.” Unbounded freedom of speech and unlimited liberty of expressing his sentiments express the same thing, as do (perhaps less plausibly) the advantage of the State and the interests of the community, so the premise and conclusion are equivalent.
Woods and Walton (1975) give three definitions for dependence circularity:(CD) The conclusion entails some premises-conjunct.(CDE) In order to know that some premiss-conjunct is true, a must know that the conclusion is true.(CM) There is some premiss-conjunct that can be known to be true only by inference from the conclusion. I will be arguing later that (CDE) and (CM) can only be satisfied if the conclusion is atomic. Otherwise, there will always be another source of evidence that is independent of the conclusion, even if this evidence is not objectively good evidence. Horoscopes are not fallacies—they are just ill-supported by the balance of evidence.
Some things cannot be demonstrated because they are self-evident, which is to say they can be proved through themselves. So, pragmatically speaking, begging the question could be seen as presenting as self-evident something that is not. But this relies on a problematic notion of self-evidence.
Equally for the disjuncts of a disjunction, and other logical formulae that may be seen as conditionals in disguise, e.g., the negation of a conjunction.Frege shows some indications of giving this distinction its due, hence my use of his assertion-sign “├” as an indicator of a context whose contents are asserted. Now we could write for a conjunction ├(├p∧├q) to show that the conjunction is asserted and each conjunct is also asserted. A disjunction would be written as ├(p∨q). This suggests further that what the ∨-operator takes as its operands are not propositions but, as Mill (1882, 70) suggests without elaborating, names of propositions.
This suggests another why by which we might try to get around Woods and Walton (1975) problem of indefensibility with regard to the disjunctive syllogism—we do not have inconsistent attitudes towards p, but an attitude towards p and an attitude towards “p”. When the rule of inference is applied but not before, the true disjunct is disquoted.The assertion-sign fell into disuse following criticisms of Wittgenstein in the Tractatus Logico-Philosophicus, and in one sense he was right: truth-valued logic is only concerned with truth and not with unassertedness. All of the rules for the logical operators preserve truth, so if truth is all we are concerned about, we need not make any distinction. One might consider asserted and unasserted as uninterpreted symbols in the metalogic that, in truth-valued logic, are given the same interpretation, thus collapsing the distinction, yet the distinction remains at the most basic syntactical level of the argument-form; it is not dependent on considerations of truth or informativeness, although it can be used to capture a notion of informativeness in a suitably interpreted epistemic logic.
We may unproblematically continue to speak of valid pseudo-arguments, for example, defining validity at the semantic level as the truth of the premises necessitating the truth of the conclusion, or one of the many variations thereof.
This is basically the thought, remarked elsewhere, that p∧q├ p is circular if the arguer believes the conjunction because he believes p, but not if he believes the conjunction because he believes q. I say that it actually depends on the quantificational complexity of p and q but does not depend on the actual route the arguer takes to his belief. If he gives the argument p∧q├ p when his evidence is for p rather than q, then he has acted inappropriately in providing redundant argumentation, but has not committed a fallacy.
Ritola (2003), in trying to find a way between the relativism of Sanford’s approach and the counter-intuitiveness of Biro’s verdict, introduces a knowledge-base into which new propositions can be added when they can be shown to follow from propositions that are already in the knowledge-base. Evaluation of the argument is relative to this knowledge-base but not to the beliefs of the arguer. If a proposition is in question, you beg the question if you try to insert it without showing that it follows from propositions already in the knowledge-base, or if you use it as a premise to try to insert some other proposition. This way does not seem to allow for arguer justification either.
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Botting, D. Can ‘Big’ Questions be Begged?. Argumentation 25, 23–36 (2011). https://doi.org/10.1007/s10503-010-9196-1
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DOI: https://doi.org/10.1007/s10503-010-9196-1