Prof Roumen Anguelov, Head of the Department of Mathematics and Applied Mathematics at the University of Pretoria, cordially invites you to a public lecture, titled 'Self-reference and the limits of logical deduction and algorithmic solvability', by established visiting scholar Prof Valentin Goranko, who visits the University of Pretoria under the Visiting Professor Programme.

 

In this lecture, Prof Goranko will explore 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, of which the most well-known is the ancient liar's paradox, exemplified by the sentence, 'This sentence is false'.

 

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. Self-reference, applied to computer programs, provides the simplest examples of algorithmically unsolvable problems, the most famous of which is Turing's Halting problem. Moreover, when applied in sufficiently expressive logical languages,

where arithmetic of natural numbers can be formalised, self-reference can be used to produce formal statements that claim their unprovability, which is the core idea of the proof of Gödel's celebrated incompleteness theorems. 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.

 

 

 

 

Brief biographical sketch: 

 

Prof Goranko is a professor of logic at Stockholm University. He received his PhD in mathematics from Sofia University (Bulgaria) in 1989 and has more than 30 years of experience teaching and conducting research in departments of Mathematics, Computer Science and Philosophy at universities in Bulgaria, South Africa, Denmark, and Sweden. Prof Goranko's main research interests are in theory and application of logic to computer science, mathematics, artificial intelligence and philosophy. He has published more than 100 research articles, as well as the recent books 'Logic and discrete mathematics', 'Logic as a tool' and 'Temporal logics in Computer Science'. 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.