It's the End of Logic As We Know It

In a recent issue of Grazer Philosophische Studien there is an interesting paper by Ian Rumfitt, 'Knowledge by Deduction', vol. 77 (2008), pp. 61-84. The paper deals with the vexed issue of how deductive reasoning can expand our knowledge, but what caught my attention was the last part of the paper. Rumfitt has hinted toward his dislike for multiple conclusion logics in earlier work, but this time he goes all out with a section long argument against it on epistemic grounds.

My intention is not run over the argument here, but just to call attention to a footnote. Rumfitt is considering the idea that multiple conclusion somehow captures the interplay between acceptance and rejection (or assertion and denial). In this context, we get the following footnote:

Something like this case for multiple conclusions is presented in Restall 2005. But he overplays his hand in suggesting that 'Y is a multiple-conclusion consequence of X' can be explained as meaning 'The mental state of accepting all of X and rejecting all of Y would be self-defeating'. The mental state that consists of accepting that there will never be sufficient grounds for accepting or rejecting 'There is a good', while rejecting that very statement, is self-defeating. But 'There is a god' is in no sense a consequence of 'There will never be sufficient grounds for accepting or rejecting "There is a god"'. (p. 80)

Puzzling. I'll have to go back and read Greg's paper again, but I suspect this is a strange way of reading what he's up to.