Price and Rumfitt on Rejective Negation and Classical Logic

Abstract

We are, according to Humberstone (2000), in the midst of a revival-a revival of rejective negation.1 An account of negation, the revivalists tell us, should be given in terms of a speech act of rejection-a speech act that is 'on all fours' with the speech act of assertion. It seems to me that rejective negation does have many of the virtues claimed for it. But there is a need to temper the enthusiasm of the revivalists. One touted virtue is that rejective negation undermines Dummettian suspicions of classical logic. Price (1983, 1990) and Rumfitt (2000) offer arguments to this conclusion. In my paper, I shall attempt to show that Price's and Rumfitt's arguments fail. Rumfitt introduces the helpful label 'bilateral theory of sense' to refer a theory according to which the sense of a logical connective is fixed not only by inferences concerning assertions but also inferences concerning rejections. To specify a bilateral theory of sense, he uses signed sentences: '-' is used as the rejection-sign;'+' is used as the assertion-sign. For example, a classicist might specify the sense of negation using the following four rules of inference:2