Does the Traditional Treatment of Enthymemes Rest on a Mistake?

Argumentation 12 (1):15-37 (1998)
Abstract
In many actual arguments, the conclusion seems intuitively to follow from the premisses, even though we cannot show that it follows logically. The traditional approach to evaluating such arguments is to suppose that they have an unstated premiss whose explicit addition will produce an argument where the conclusion does follow logically. But there are good reasons for doubting that people so frequently leave the premisses of their arguments unstated. The inclination to suppose that they do stems from the belief that the only way in which an argument's conclusion can follow definitely from its premisses is to follow logically. I argue that this belief is mistaken. I propose a revision of the current generic conception of logical consequence, and its variant specifications, to avoid the paradoxes of strict implication. The revised conception can then be naturally extended to include also what we might call 'enthymematic consequence'. This concept is a kind of consequence, whose properties merit investigation
Keywords enthymeme  unstated premiss  consequence  logical consequence  enthy-mematic consequence
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Tomis Kapitan (1982). On the Concept of Material Consequence. History and Philosophy of Logic 3 (2):193-211.
Gilbert Plumer (2000). The Paradoxical Associated Conditional of Enthymemes. In Christopher W. Tindale, Hans V. Hansen & Elmar Sveda (eds.), Argumentation at the Century's Turn [CD-ROM]. Ontario Society for the Study of Argumentation.
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