You can find HERE the full version of “Alice and the 5th Logical Notion”

This paper has ben published in a special issue of Studia Humana  (Volume 9, Issue 3/4, 2020, pp. 19—36), edited by Andrew Schumann, dedicated to Jan Woleński's 80th birthday, and also in the book Judgements and Truth - Essays in Honour of Jan Wolenski.

In 2020, Andrew Schumann asked me to contribute to  a special issue of Studia Humana dedicated to Jan Woleński. 

My orginal idea was to write a paper on squaring the 4 logical notions put forward by Lindenbaum and Tarski. On the one hand I had been working on the square of opposition since many years, on the other hand I always thought this idea of logical notions very interesting and since a while I had the idea to the check the application ot the theory of the square of opposition to the theory of logical notions.   

It seemed to me a good topic for a paper dedicated to Wolski, because Lindenbaum/Tarski is a famous pair of the school of Polish logic of which he is a great specialist, and because he also had been working on the square of opposition. 

In the outcome of this investigation, there is a square of the four logical notions (section 5 of the paper), but this is not the central point. The central point is a mystery related to a notion that I called a variety, arguing that it makes sense to consider it as a 5th logical notion (section 6). In the last part  of the paper (section 7). I present an enigma related to this 5th logical notion.   

When the paper was finished I sent it to about 200 colleagues and friends all over the world to ask them if they knew the solution to the enigma.   

Here a list of people who sent me useful comments to improve the paper: Arnon Avron, John Corcoran, Brad Dowden, Mike Dunn, Melvin Fitting, Rodrigo Freire, David Fuenmayor, Katarzyna Gan-Krzywoszynska, Val Goranko, Brice Halimi, Lloyd Humberstone, Srećko Kovač, Décio Krause, Arnold Koslow, Laurent Lafforgue, Dominique Luzeaux, David Makinson, David W.Miller, Daniele Mundici, Francesco Paoli, Daniel Parrochia, Rohit Parikh, Anca Pascu, Arnaud Plagnol, Robert Purdy, Stephen Read, Christophe Rey, Pascale Roure, Jean Sallantin, Sergey Sudoplatov, Alasdair Urquhart, Ioannis Vandoulakis, Denis Vernant, Jorge Petrucio Viana.