# Alumni Spotlight: Øystein Linnebo

The professor of philosophy at the University of Oslo (UiO) and former CAS Fellow was recently awarded the Fridtjof Nansen award for excellence in science for his work within the fields of philosophy of mathematics and philosophical logic.

We spoke with the professor about approaching philosophical questions with logical-mathematical tools, his current work and his stay at CAS as a fellow.

**Congratulations on being awarded Fridtjof Nansen award for excellence in science!**

**The committee states in its recommendation: ‘Most of Linnebo's works are very technically advanced; they are characterized by exceptionally strong logical-mathematical competence, but also by a deep general philosophical understanding. This rare combination gives him a unique position on the international research front, with frequent citations.’**

**What perspectives and insights can we get from approaching philosophical questions with logical-mathematical tools?**

First of all, let me be clear that the use of such tools is unlikely, all by itself, to answer any big philosophical questions. As Saul Kripke—a famous philosopher with a methodological approach similar to mine—observed, “there is no mathematical substitute for philosophy.” The point is rather that the use of logical-mathematical tools enables us to state philosophical questions and answers with far greater precision than would otherwise have been possible. This helps us avoid confusion and misunderstandings in what is already a terribly difficult subject. It also enables us to formulate arguments for and against various philosophical views in a more precise and rigorous way, which in turn facilitates progress and paves the way for more collaborative work in philosophy.

One example that has occupied me a lot in recent years is the ancient Aristotelian notion of potential infinity. Aristotle claims that the only legitimate form of infinity is that of a process that it is always possible to continue, but impossible to complete. No matter how many times we have divided a line segment, for instance, it is possible to divide it again. But Aristotle denies that the process can be completed, since the segment would then be “divided away into nothing.” To properly express this so-called “potentialist” view of infinity, we need the resources of modal logic—the logic of necessity and possibility—which was developed only a couple of generations ago. Using this logic, I have been able to show, once and for all, that Aristotle’s view is coherent and compatible with ordinary “classical logic,” but also to pinpoint its limitations.

**You have done research within many philosophical fields: metaphysics, logic, philosophy of mathematics and philosophy of language, to mention a few. What are you currently working on?**

Much of my current work grows out of the Aristotelian “potentialist” conception of infinity. Like most mathematicians and philosophers, I believe Aristotle was superseded by the new conception of infinity developed by Georg Cantor, a German mathematician who was also deeply interested in philosophy and theology. But as against the current orthodoxy, I believe there remains a role for an updated version of the Aristotelian ideas. Super roughly: While Cantor is right that there is a vast hierarchy of completed infinite sets and infinite numbers, this hierarchy itself needs to be understood in a broadly Aristotelian manner, that is, as something incompletable or merely potential. This overarching hypothesis gives rise to a large number of more specific projects, ranging from logical-mathematical ones, through metaphysics and the history of philosophy, all the way to some philosophy of religion. In fact, I even envisage applications to adjacent subjects such as formal semantics and formal ontology (a part of artificial intelligence).

It is great fun to be able to engage with so many different fields—all unified by the use of logical-mathematical methods. I also find it very stimulating that much of this work is collaborative.

**Back in 2015/2016 you participated as a fellow in the CAS project ****Disclosing the Fabric of Reality-The Possibility of Metaphysics in the Age of Science.**** What do you remember best from your stay at CAS?**

The stay at CAS offered me a fabulous combination of long stretches of uninterrupted research time and stimulating discussions with likeminded philosophers. At the beginning of the year at CAS, I was growing increasingly nervous about two monographs I had promised to write, one with an extensive draft but a (soft) deadline that was already several years in the past, and another, not even begun but with a (hard) deadline at the end of that year. I decided to attack the latter commitment, which fit quite well with the CAS project. Using the peace of mind offered by CAS, which I hadn’t had for years, I wrote like mad! So I not only made my deadline but also got started on my current project concerning potential infinity, aided by a discussion group that some of us CAS fellows had on the topic. But like most people, I am unable to write all day. The coffee machine and the lunch room always offered stimulating discussions, both in philosophy and beyond. Kant figured centrally in many of these discussions, which gave rise to a number of ideas and projects that I keep thinking about and will probably see the light of day at some point.

**In what way, if any, did your stay at CAS affect your research career?**

The stay at CAS made a huge impact! Without it, I would simply not have been able to finish one of my book projects, which also enabled the other one to be completed another year down the road. That would have been a big blow. I would also have been deprived of some important stimulus for my current project, which I told you about above.

**What advice would you give to future CAS project fellows?**

To value the time at CAS! Most likely, you will never again get an environment as conducive to doing good research, with the mentioned combination of uninterrupted research time and stimulating discussions with experts in one’s own field. And remember to use the garden for discussions, now that spring is on its way!

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