Circular logic

Circular reasoning (Latin: circulus in probando, "circle in proving"; also known as 'circular logic') is a logical fallacy in which one begins arguing in the wrong end of a premise that indicates some regularity and tries to move either a)in the opposite direction, from an assumption or observation that verifies a consequent, what in medicine is essentially a mere symptom, or, which logically is the same, b)from negating an antecedent, from negating one cause of a symptom that can have many causes, for example in the move from the regularity-premise "if x, then y"; and one ends up 'completing the circle', so to speak (Soerfjord 2013, PhD thesis HKU). Version a) has the formal label "Affirming the Consequent", and b) the label "Denying the Antecedent" - both deductively invalid. They are essentially the same fallacy (Soerfjord 2013; PhD thesis HKU), which is the assumption of a limitation that is not expressed by the premise itself, the premise "if x, then y", also expressed "x implicates y". In other words they both rest on the false assumption that "if x, then y" has a logical meaning that includes the assumption 'if y, then x', which is to say the assumption that it means "x is logically equivalent to y". The fallacy in natural language can be as follows: a)"All Chinese drink green tea, so if you see a man drinking green tea, then you know he's from China" or reasoning b), from the implicit idea that 'all Chinese drink green tea', by saying "That man isn't from China, so he doesn't drink green tea". They are both circular reasoning; the first, a), 'affirms the consequent' of the assumed regularity 'if Chinese, then a drinker of green tea'; the second, b), 'denies the antecedent' of the assumed regularity. The fallacy lies in the conclusion of some logical necessity in the move from that 'affirmation' of a consequent or 'denial' of an antecedent to the exemplified conclusion in either case (Soerfjord 2013, PhD thesis HKU).

Circular reasoning is often of the form: "A is true because B is true; B is true because A is true." Circularity can be difficult to detect if it involves a longer chain of propositions. Academic Douglas Walton used the following example of a fallacious circular argument:

He notes that, although the argument is deductively valid, it cannot prove that Wellington is in New Zealand because it contains no evidence that is distinct from the conclusion. The context – that of an argument – means that the proposition does not meet the requirement of proving the statement; thus, it is a fallacy. He proposes that the context of a dialogue determines whether a circular argument is fallacious: if it forms part of an argument, then it is. Citing Cederblom and Paulsen 1986:109, Hugh G. Gauch observes that non-logical facts can be difficult to capture formally:

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