Arresting circles in formal dialogues

The study of the informal fallacies has an importance acknowledged by its place in both ancient and contemporary logic texts. Unfortunately, their study produces what Hamblin [3] has called the Standard Treatment. bereft of theory, laden with dogma and hoary illustrations appropriated from Aristotle, a corpus that often seems more to perpetrate the fallacies than to explicate them. Recently, however, a few writers have been seeking for some basic theoretical understanding of what these fallacies are, and we hope here to add something to this effort with some remarks about the petitio principii. Notwithstanding invitations occasioned by ambiguities which lurk in the title of this paper, our aim is not to report on dialogical circles we have known and loved, but rather to say something about how they may be stopped. It is of some interest to determine the extent to which circular reasoning can be studied by means of three distinct kinds of system. They are: (i) Systems of doxastic-epistemic logic such as may be found in the work of Kripke [6] ? Hintikka [4]. and Wu [ 131 ; (ii) systems of formal dialectic or formal dialogues as represented by Hamblin [3 1 and Lorenzen [7] ; and (iii) such non-intensional, non-game-theoretic standard approaches as are afforded by first-order logic. De Morgan [2], pp. 254ff., presents the first systematic case for an approach to the petitio in the style of (iii), and a note of Hoffman [S] pursues a similar method. De Morgm's Thesis, as we shall call it, is that every genuine instance of the petitio is reducible to the case in which a conclusion is identical to some premiss or conjunctive part of a premiss. The trouble with this, however, is that examples abound of clearly circular arguments in the form of the disjunctive syllogism, yet in which the conclusion is not identical to any premiss or conjunctive part thereof. It is ventured in Sanford [8] and in Woods and Walton [ 111 that De Morgan's treatment is inadequate to the petitio, and in Woods and