The Meaning of Tonk

Abstract

The present article follows on a line of research proposed by Ripley in his 2015 article ‘Anything goes’, where he proposes a conception of logical consequence bearing the peculiar characteristic of discarding the cut rule entirely, and transitivity with it. This is, of course, a bold step to take, given transitivity’s usefulness. It still bears some fruitful advantages for an inferential theory of meaning nonetheless, as it allows entrance into the inferential realm of meaning to many previously problematic entities -such as connectives like Prior’s infamous tonk. As the title of Ripley’s article suggests, it seems that in this interpretation of the turnstile (almost) anything goes. But how exactly does it go, we may ask ourselves. And indeed, this shall be the question we will try to sketch an answer for presently. What exactly could the meaning of tonk be in a framework which accounts for it, i.e. Ripley’s? We believe Ripley’s intuition to be mainly right, and that connectives like tonk do indeed possess a meaning, so we will try to delve deeper into what the meaning of these faulty connectives could be about. We will also briefly consider a side issue, which has to do with the fact that, even if everything goes, it does not seem to be the case that everything goes in the same way. Indeed, thanks to the many responses to Prior’s article numerous differences have been spotted between regular, ‘healthy’ connectives like conjunction and problematic ones like tonk.