Feb. 19, 2021

Dr. Richard Zach wins a 25th anniversary prize from the Association of Symbolic Logic

A paper published during his PhD program is recognized 20 years later for its contributions to the discipline
Man with glasses in grey suit with arms crossed
Dr. Richard Zach

The Association for Symbolic Logic is celebrating a quarter century of The Bulletin of Symbolic Logic journal with a BSL 25th Anniversary Prize. A distinguished panel of judges have awarded the prize to Dr. Richard Zach, professor in the Department of Philosophy at the University of Calgary, for his paper “Completeness Before Post: Bernays, Hilbert, and the Development of Propositional Logic.”

We asked Dr. Zach about the prize and having his paper recognized for its contribution to the discipline.

What does it mean to you to win this 25th Anniversary Prize?

It's nice to see that it stands the test of time and is still read after 20 years.

The prize is described as being awarded to papers that have “helped students get started, allowed researchers to see connections between different areas of research, and let all of us see some of the history of [symbolic logic].” How do you think your paper fulfilled this?

My paper tells the story of propositional logic: how a handful of mathematicians and philosophers became interested in formal logic at the turn of the 20th century, who influenced their work, why they asked the questions they did, and how they answered the questions they asked.

The story for predicate logic is more well-known. It was Kurt Gödel who proved the completeness theorem in 1929. Although he provided a solution, he did not have to come up with this question. For propositional logic, there was no precedent: not only did Bernays and Hilbert have to prove completeness, they first had to invent the idea of completeness. I think this is an aspect of the history of science that is sometimes overlooked: it is often not the celebrated results that are interesting, but the preparatory work of coming up with the right definitions and questions.

It is called "Completeness before Post" because Emil Post is (or was) usually credited as being the person who first proved the completeness theorem for propositional logic. I showed that Paul Bernays had gotten there a few years earlier (and independently), but never published the result. 

Where were you in your academic career when you wrote this paper? Was it an especially significant or memorable publication for you?

I was in the middle of my PhD program at the University of California. This was my first publication that wasn't a purely technical logic paper, and it became the first chapter of my dissertation. The source materials I used were unpublished (at least, at the time): notebooks, correspondence, and lecture notes. It took a lot of research to unearth all the details, and I spent weeks in archives in Germany and Switzerland to collect all the bits and pieces.

Have you gone on to further research this particular topic, or did it inspire subsequent publications?

The second chapter of my dissertation was essentially a sequel: in about 1918, Bernays and Hilbert had worked on propositional logic, and then Hilbert introduced his proof theoretic programme in 1920. I addressed what happened in the early years of proof theory. The same people played lead roles, but there were some new characters and plot lines.  Since then, I’ve continued to publish on the history of logic in the 1920s and 1930s in particular. Some papers have focused on the same group of people, but I’ve branched out, too.