Using logic to get to the truth

What is true, right, and trustworthy? Logic, as a science, is a cornerstone for philosophy, mathematics and computer science. In an interdisciplinary project, logician Graham Leigh will intertwine the three, analyzing similarities and trying to develop methods that work in all fields.

Graham Leigh

PhD, Mathematics

Wallenberg Academy Fellow 2015

University of Gothenburg

Research field:
Logic, in the intersection between mathematics, philosophy, and theoretical computer science

He wants to understand everything. This is Leigh’s own quite simple description of what drives him, and it has been true for as long as he can remember. Already as a school student he chose to study mathematics because “it was obviously the best way to understand science”. When he went on to university he had an intense longing to understand even more, and continued to delve ever deeper into mathematical theories.

“You can’t really go any deeper than logic itself, which is the study of what constitutes a rigorous mathematical proof. In philosophy, logic is a tool for analyzing arguments. In mathematics it is a way of building a solid foundation for the subject. And computer science originally arose out of logic, since logic is needed as a framework to describe the algorithms on which computer science is based. So there are great similarities between the three fields, and I see myself very much not as a philosopher, mathematician or computer scientist, but as a logician.”

“The grant gives me a unique opportunity to do exactly the kind of research I’m most interested in. This project will enable me to delve deep, and see if I can bring out some of the similarities I see within the three scientific fields.”

Understanding how we recognize truth

As a Wallenberg Academy Fellow at the University of Gothenburg, Leigh will be searching for the truth. But not truths in the conversational sense – even though the mathematical and philosophical truths he is studying are related to everyday thinking. He has noticed that we often recognize truth when we see it. A mathematician knows what a correct proof looks like, but precisely what criteria does that evidence then meet?

“I want to see what happens when we formalize these informal perceptions of truth. In my research I will be trying to capture truth in a formal framework, and see how it relates to our intuition.”

His explanation of the work process is simply that at first, it’s all inside his head; then he tries to get it down on paper. He has collected a number of analogous methods from mathematics, philosophy, and computer science, and he is trying to modify them and move them around to see if they can be adapted to the other fields as well.

Little funding for multi-disciplinary research

Leigh began his mathematical studies at the University of Leeds. He came in contact with philosophy, and discovered that there were philosophers who shared his interests.

“They were facing the same problems, but they asked very different questions. And some of those questions needed a mathematician.”

After obtaining his doctorate he moved to Oxford University, to study the formal theories of truth from a mathematical perspective. Oxford has a large computer science department, and when Leigh began looking closer at that field, he found interesting similarities there as well.

But it became increasingly difficult to obtain funding for his research. When he sought money from funding sources focusing on the sciences, they thought his research was too philosophical. When he instead sought funding within the humanities, his research was too mathematical…

He was obliged to put his own research aside for a while. He moved to Vienna to join a research team engaged in computational mathematics. They formulated programming algorithms and proof methods for use in artificial intelligence to automatically verify computer software.

Spending a whole day thinking

“I really like the freedom of research. Even in a project which is very clearly delineated, as the one in Vienna, there are always so many questions to be asked. I enjoy thinking, and I can spend an entire day just trying to understand a problem. If I don’t arrive at any particular conclusion, that’s another day’s work put on file. But you never know when something that seemed pointless suddenly turns out to be relevant.”

As a Wallenberg Academy Fellow, Leigh will be able to build up his own research team, focusing on exactly the things he is most interested in. He calls it a project in three areas of logic – and also quite simply research about logic itself. But he does not know where it will lead.

“There isn’t really a clear ending. It’s all about digging deeper. I’m building an interdisciplinary research team from various fields, but with the same logical underpinnings, and then we’ll see what we find. Perhaps we’ll learn more about computer science, or maybe our focus will be more philosophical. I don’t actually know yet.”

Text Lisa Kirsebom
Translation Maxwell Arding
Photo Magnus Bergström