In their classic book on relevant logic, Alan R. Anderson and Nuel D. Belnap briefly discuss the transitivity of entailment:

Any criterion according to which entailment is not transitive is ipso facto wrong. It seems in fact incredible that anyone should admit that B follows from A, and that C follows from A, but feel that some further argument was required to establish that A entails C. What better argument (…) could one want? ¹ (¹⁹⁷⁵, p. 154)

It would not be too surprising to find such a quick dismissal in the words of classical logicians. But Anderson and Belnap’s goal is to set the pillars upon which to conduct a rigorous study of relevant logic, which was seen at the time (and it is also probably seen today) as one of the main rivals of classical logic.

At any rate, quick dismissals such as this one are—fortunately—harder to find nowadays. Non-transitive consequence relations are no longer seen as “ipso facto wrong” and many logicians and philosophers have acknowledged non-transitivism as a viable position in the context of a number of discussions.

Without a doubt, one of the main reasons for this—if not the main reason—are Dave Ripley’s writings on the topic. Ripley has forcefully argued that the non-transitive approach is not only interesting from a technical point of view, but also that it is compelling as an account of meaning and as a solution to a number of long-standing puzzles.

On July 31, 2017, a symposium on Ripley’s forthcoming book ^Uncut was held in Buenos Aires. ² Ripley presented the main ideas in the book and there were comments by some of the participants. After the symposium, many of us agreed that it would be a good idea to put together a volume to reflect some of the interesting discussions that took place there.

Uncut is fundamentally a book about the paradoxes of truth, the paradoxes of vagueness and meaning. One of its novelties is that it offers a unified account of both types of paradoxes in which they are understood as challenges to our intuitive conception of meaning. Paradoxes are dangerous because they pose a threat to the standard way of interpreting the vocabulary involved in the statements that generate them. Ripley’s suggestion, in a nutshell, is that we can deal with the paradoxes while maintaining the intuitive account of meaning if we endorse a non-transitive consequence relation.

The book contains (but it is not restricted to) many of the ideas that Ripley (sometimes on his own, sometimes with his coauthors) has been developing for the last decade or so. The impact and influence that these ideas have had since their appearance is enormous. ³ The pieces put together in the present volume touch on some of these ideas while at the same time exploring some aspects of non-transitivism that have not been discussed in the literature so far. The volume contains a précis of Uncut written by its author; then there are six short comments by Eduardo Barrio & Federico Pailos, Jonathan Dittrich, Thomas M. Ferguson, Rohan French, Paula Teijeiro and Damian Szmuc; lastly, we can find Ripley’s responses.

I hope that readers of this journal will find the contents of the volume as interesting as I did.