Circular reasoning

“This review site is trustworthy, because the site says its reviews are trustworthy.” The reason offered is the conclusion again.

The conclusion hidden among the premises

Circular reasoning, traditionally called begging the question or petitio principii, uses the conclusion, or something that already depends on it, as one of the reasons for it. The Stanford Encyclopedia of Philosophy quotes an example from the nineteenth-century logician Richard Whately: “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 interest of the Community, that each individual should enjoy a liberty perfectly unlimited, of expressing his sentiments.” The second half says the first half again in longer words. The encyclopedia calls this a disguised repetition that gives no reason for its apparent conclusion.

Short circles are easy to see: “He is the best player because nobody is better.” Longer circles hide better because the steps are spread out. “The rules are fair because the committee approved them. The committee is trustworthy because it only approves fair rules.” Here the fairness of the rules is used, two steps later, to support itself. The Stanford Encyclopedia notes that these more involved versions are what people usually call circular reasoning.

Valid, and still useless

Here is a surprise from the statements course. “p, therefore p” is valid: there is no case in which the premise is true and the conclusion false, because they are the same sentence. So circular arguments are usually valid, and if the premise is true they are even sound. What they cannot do is persuade. Someone who doubts the conclusion will doubt the premise for the same reason. The Stanford Encyclopedia concludes that, since logic in the modern sense is concerned only with what follows from what, begging the question is better described as an epistemic fallacy, a failure to give a reason, than as a logical one.

To check for a circle, take away the conclusion and ask whether the remaining premises would still give anyone a reason to believe it. If a premise only seems true to people who already accept the conclusion, the argument is going round. A good reply asks for support from outside the loop: “What would convince someone who doesn’t already trust the committee?”

A note on wording. In everyday English, “that begs the question” is often used to mean “that raises the question.” In logic the phrase keeps its older meaning: assuming what you set out to prove.