Frege, the Proliferation of Force, and Non-cognitivism

TLDR: In this article, Dummett and Geach use appearance in the antecedent of a conditional as a test to rule out various proposals to construe words or phrases as force signs, including a noncognitivist construal of 'wrong' as expressing condemnation.

Abstract: But these two inferences could not proceed on the same principle if we'... had to recognize a special way of judging for the negative case'. In inference (i), assertoric force attaches to the first premise as a whole and to the second premise as a whole, and the thought expressed in the second premise coincides with the thought expressed in the antecedent of the first premise. 1 If we were to recognize denying as a special kind of judging, in inference (2) assertoric force would still attach to the-,first premise as a whole, while in the second premise the negation sign would be absorbed into the act of denying. Thus the thought expressed in the second premise would no longer coincide with that in the antecedent of the first premise, so that 'the inference ... cannot be performed in the same way'.2 In 'Compound Thoughts' Frege makes several further remarks that lead Michael Dummett to claim that it is Frege's doctrine that force'... cannot significantly occur within a clause which is a constituent of a complex sentence, but can attach only to a complete sentence as a whole', a doctrine which, if true, would provide '... a powerful new method for detecting spurious claims to have identified a new kind of force'.3 Peter Geach in particular has put the doctrine to this use: in 'Assertion', he uses appearance in the antecedent of a conditional as a test to rule out various proposals to construe words or phrases as force signs, including a noncognitivist construal of 'wrong' as expressing condemnation. Geach's argument starts out parallel to Frege's in 'Negation': he claims that 'it's true that . . .' and 'wrong' cannot carry force because modus ponens goes through in the usual way from the premises 'If it's true that p, then q' and 'If gambling is wrong, then inviting people to gamble is wrong', which involve neither asserting that p nor condemning gambling. Geach goes on