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Truth theories in focus for new professor of logic

News: Sep 20, 2013

Ali Ayanat. Photo: Thomas Melin.Hello Ali Enayat, new professor of logic at the University of Gothenburg. What is your research about?

‘Broadly speaking, my research area falls within the discipline of Mathematical Logic. Mathematical Logic is the young, vibrant offspring of two ancient parents: Philosophy and Mathematics; it employs the powerful methodology of Mathematics to probe the scope and limits of abstract, symbolic reasoning. The birth of Mathematical Logic as an established academic subject dates back to the early 1900’s, with the appearance of Russell and Whitehead’s monumental Principia Mathematica in Cambridge University. Shortly thereafter, the field’s center of gravity shifted to University of Göttingen, around the central figure of David Hilbert, one of the greatest mathematicians of the twentieth century. By now, Mathematical Logic is recognized as a major field of study throughout the world, and research in the subject is conducted in various academic departments (including Philosophy, Mathematics, Computer Science, and Linguistics), as well as many software firms.’

‘My own research concerns a range of logical systems, often known as “foundational systems”. These include ZF – Zermelo-Fraenkel theory of sets – and PA – Peano’s axioms for number theory. The distinctive feature of foundational systems is that they provide a precise, unified conceptual framework for the entirety of modern Mathematics and Computer Science, in a manner very similar to the sort of foundation that Molecular Biology offers to Life Sciences.’

Can you give us some examples of your work?

‘One of my recent projects has been in collaboration with Albert Visser from Utrecht University. It involves “axiomatic truth theories”, a subject that has been of great interest to both logicians and philosophers because the notion of truth, even in the exact sciences, is fraught with all sorts of philosophical difficulties that are often only resolvable with the help of tools from Mathematical Logic. We began our work four years ago with the aim of writing a paper on a specific aspect of the subject, but our initial work brought new uncharted vistas into view, and has led to a number of fascinating developments. By now the volume of our technical results demands a monograph-length exposition.’

‘Another topic that I have been working on is “interpretation between theories”. Roughly speaking, this involves the extent to which one theory – couched in precise mathematical language – might be translated into another one. For example, in the early days of Quantum Mechanics, Heisenberg and Schrödinger came up with radically different theories to explicate the nature of matter; the former used Matrix Mechanics, while the latter used Wave Mechanics. But some time later the legendary von Neumann – who was also an expert in Mathematical Logic – was able to show that each of the two theories can be translated into the other one using a rather sophisticated mathematical toolkit. This showed that the two theories were really two sides of the same coin.’

What can society learn from your research?

‘My research work is highly abstract and esoteric and its impact on society is quite different from the research activities of say a sociologist or an engineer. However, at a deeper level, the impact of research work on Mathematical Logic on society is enormous since we live in the age of automation, surrounded by machines and gadgets whose very essence, capabilities, and limitations, can only be understood with the help of the abstract language and esoteric techniques of Mathematical Logic.’

‘But even more generally, Mathematical Logic offers a conceptual framework that can be applied to many diverse settings beyond the technological ones. To brag a bit, one of my closest friends from my graduate school days in the U.S. is Sergio Fajardo, a Colombian mathematical logician who returned to his country and eventually managed to be elected as the mayor of the city of Medellin, and is currently the Governor of the state of Antioquia. He has often claimed (both in his speeches and essays) that he has been able to dramatically reduce the rate of the crime in his city, reverse trends of poverty, and successfully deal with many other social problems through the use of the methodology of axiomatic thinking that is the hallmark of Mathematical Logic.’

After 25 years in the US you have chosen to continue your work in Gothenburg, why?

‘Firstly, my position in Gothenburg offers a more extensive set of scholarly opportunities because most of my research colleagues are based in Europe. Secondly, the Swedish standards for quality of life and concern for our fellow human beings are far closer to my ideals than those that I experienced in the U.S.’

‘By the way, I was a faculty member at American University (Washington, D.C) for 26 years, and previous to that I had worked for three years as a faculty member in Illinois and California, so the correct number of my years of full-time academic work in the US is 29.’

You are the second professor of logic at the University of Gothenburg, what are your main duties as a professor?

‘The first professor of Logic at the University of Gothenburg was Per Lindström, who I never had the pleasure of meeting. However, already when I was a graduate student in the University of Wisconsin in the early 1980s, I knew about his legendary accomplishments and never imagined I would be his successor one day. With that introduction, let me say that my main responsibilities fall into the following categories: my own research, supervision of Ph.D. students, curriculum and program development, graduate-level teaching, grant acquisition to support graduate students, postdoctoral researchers, and visiting faculty; and finally the organization of local and international conferences.’

+46 (0)31 786 10 68, +46 (0)766 18 10 68

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