Disimplicature

Speranza

Self-reference has played a prominent role in the development of metamathematics, starting with Goedel’s first incompleteness theorem. 

Given the nature of this and other results in the area, the informal understanding of self-reference in arithmetic has sufficed so far. 

Recently, however, it has been argued that for other related issues in metamathematics and philosophical logic (Grice's topic -- the Bartlett dictionary has Grice as a "British logician"! -- a precise notion of self-reference and, more generally, reference is actually required. 

These notions have been so far elusive and are surrounded by an aura of scepticism that has kept most philosophers away. 

As Griceians, we may suggest we shouldn’t give up all hope. 

First, we may introduce the anti-Grice to these issues. 

Second, we may discuss the conditions a good notion of reference in arithmetic must satisfy. 

Accordingly, we may introduce adequate notions of reference for the language of first-order arithmetic, which we may show to be fruitful for addressing the aforementioned issues in metamathematics.

Grice thought that Austin's translation of Frege on arithmetic was, however, 'boring' -- "as is Blackwells!"