22 January 2010, VvL Symposium "Lindström's Legacy"

The Dutch Organization for Logic and Philosophy of Science (VvL) would like to invite you to attend a symposium in the honor of Per Lindström, the Swedish logician who has sadly passed away on August 21. Per Lindström's work has had a profound influence on logic, and continues to be of importance in various branches of logic. During the symposium, three distinguished speakers will discuss various aspects of his intellectual legacy.

Below, you will find the program of the symposium and the abstracts of the talks. Everybody is welcome and the program is free.

We hope to see many of you there.

VvL Symposium "Lindström's Legacy"

Friday January 22, 2010, Jaarbeurs Utrecht (Jaarbeursplein, 3521 AL Utrecht)

Program:

[14.15-14.20] Rineke Verbrugge: Introduction
[14.20-15.00] Johan van Benthem: Lindström's Theorem
[15.00-15.30] coffee and tea break
[15.30-16.10] Albert Visser: Lindström's work on metamathematics
[16.10-16.50] Dag Westerstahl: Lindström and generalized quantifiers
[16.50-17.30] Drinks

Abstracts:

>> Flying over the Lands of Logic with Lindström's Theorem
>> Johan van Benthem

Over the 20th century, logicians had developed many systems for analyzing reasoning, from the sciences to the world of natural language. But amidst this diversity, they found that their core system of first-order logic shone especially, with ever further deep mathematical properties being discovered.

In 1969, it took Per Lindström 10 pages in a paper published in the Swedish journal "Theoria" to give us a platform with a breath-taking vista of the whole landscape of logic. I will explain what 'Lindström's Theorem' says, and give a flavour of how it manages to capture what first-order logic is, leading to a study of 'possible logics' in terms of their abstract properties.

I will also discuss limitations of Lindström's high-level approach. In particular, I will discuss some recalcitrant computational logics, the still opaque area of weaker logics below first-order logic, and the rather mysterious probabilistic properties of logical systems.

>> Per Lindström's Metamathemagic
>> Albert Visser

Somewhen during the period 1970-1980, two groups started doing research into the metamathematics of interpretability. There was the Prague group with a.o. Petr Hajek and Viteslav Svejdar. The other group was a singleton group consisting of Per Lindström. The research of both groups focused on degrees of interpretability, but many other interesting results were obtained. Moreover, a wealth of new methods was developed. Of course, there were some differences in emphasis and `flavour' between the two groups.

Typical for Lindström's line of research was a strong focus on extensions of Peano Arithmetic. (This may be viewed as a weakness, but fortunately many of his proofs are easily adapted to a larger class of theories.) He excelled in producing extremely clever proofs. He preferred in his work to stay as close as possible to the hardware level. This preference had the advantage that he did not overlook proofs that did not fit some a priory abstract framework. On the other hand, it made his work sometimes somewhat hard to read, especially in the light of his unwavering adherence to the theorem-proof format.

In my talk I will first explain what this research was all about. I will introduce the notions of interpretation and interpretablity and I will give a bit of information about the degree structures based on them. Rather than try to give an overview of Per Lindström's work, I will then zoom in on one or two specific results. I will try to make the magic and mystery of these results visible. It is not only that the statements of these results are simply amazing, it's also that the methods used to prove them, even if one understands them step-by-step, remain of mystical quality.

>> Quantifiers, quasi-realism, and quasi-descriptivity -- on the philosophy of Per Lindström
>> Dag Westerstahl

Per Lindström did not only give celebrated characterizations of first-order logic and invent clever fixed point constructions for the theory of interpretability. He was also a passionate and serious philosophical thinker. In this talk I take a look at some of these lesser known aspects of his thought.

First, however, I consider one contribution that, curiously, he didn't think of as philosophically relevant at all, although many of us who have eagerly used the concept he introduced found it rich in philosophical, linguistic, and computational content: generalized quantifiers.

Second, for as long as I knew him, Per Lindström was deeply engaged in the philosophy of mathematics. A constant theme was his dislike of (not to say distaste for) epistemic notions of truth. Another was Kreisel's dictum that it is not the existence of mathematical objects but the objectivity of mathematical truth that matters. He was reluctant to publish on these matters, feeling he had not enough of substance to say. When he finally did, however, the resulting 'quasi-realism' turns out to be a viable piece of mathematical philosophy.

Finally, I briefly survey some of his thoughts -- expressed in numerous contributions to the popular Swedish philosophy journal "Filosofisk Tidskrift" -- on some purely philosophical issues that mattered a lot to Per Lindström, such as the freedom of the will, the mind-body problem, utilitarianism, and counterfactuals.