Prof Valentin Goranko, a professor of logic at Stockholm University in Sweden, was co-hosted by the Department of Computer Science and the Department of Mathematics and Applied Mathematics at the University of Pretoria (UP) under the Visiting Professor Programme. The purpose of this programme is to bring established scholars from abroad to UP, where they add value to the University with respect to research excellence, postgraduate supervision and academic mentoring, while contributing to the academic offering through their specialist knowledge and scholarly expertise. The friendships and collaborative partnerships that come about as a result of the programme also strengthen networks of international collaboration and partnerships between participating institutions through shared activities such as the development of research, funding applications, projects and publications.

As part of his visit Prof Goranko delivered a public lecture titled 'Self-reference and the limits of logical deduction and algorithmic solvability' on Thursday, 9 February 2017, during which he explored how most logical paradoxes are based on self-reference — a phenomenon where an entity (a person, sentence, picture, computer programme etc) refers to itself and can thus create absurd situations. The most well-known of these is the ancient liar's paradox, exemplified by the statement, 'This sentence is false,' which is paradoxical in that, if the statement is true it must be false, and if it is false it must be true.

Prof Goranko explained that the idea of self-reference can be formally applied in logic and mathematics, thus leading to various foundational problems, such as Russell's paradox and many others. He discussed how self-reference, when applied to computer programs, provides the simplest examples of algorithmically unsolvable problems, the most famous of which is Turing's halting problem, which demonstrates that there can be no general procedure to decide if a self-contained computer program will eventually halt. He continued that moreover, when applied in a sufficiently expressive logical language, where the arithmetic of natural numbers can be formalised, self-reference can be used to produce formal statements that claim their unprovability. Prof Goranko said that these results outline the fundamental limitations of the method of logical deduction for acquiring mathematical knowledge and of the algorithmic approach for solving logical and mathematical problems.

Prof Goranko received his PhD in mathematics from Sofia University in Bulgaria in 1989 and has more than 30 years' experience teaching and conducting research in departments of Mathematics, Computer Science and Philosophy at universities in Bulgaria, South Africa, Denmark and Sweden. His main research interests are in the theory and application of logic to computer science, mathematics, artificial intelligence and philosophy. He currently serves as president of the Association for Logic, Language and Information (FoLLI); editor-in-chief of the Springer LNCS FoLLI book series; and a member of several other editorial boards and steering bodies of professional organisations.

From left to right: Prof Stefan Gruner (Associate Professor in the Department of Computer Science), Dr Ruaan Kellerman (Lecturer in the Department of Mathematics and Applied Mathematics) , Prof Valentin Goranko (Visiting Professor from Stockholm University, Sweden), Prof Stephanie Burton (Vice Principal: Research and Postgraduate Education) and Prof Roumen Anguelov (Head of Department of Mathematics and Applied Mathematics)