Clark Nøren Glymour
Alumni University Professor
1. Why were you initially drawn to formal methods?
A bit of biography then.
My family history is a story of educational mobility: my grandfather went to school with Einstein, I went to school with Evel Knievel. I spent my high school years in Butte, Montana, then a hard but joyful mining town high in the Rocky Mountains, since laid desolate by corporate America and not long from now to be uninhabitable from the same cause. There were few books of interest—the city library owned only one “philosophical” book, Schopenhauer’s Essays, and I swear there was no work of logic in the entire county--yet my father kept a small but serious library, including Darwin’s Origin of Species, and Spinoza’s Ethics which was, I suppose the first source of my interest in formal methods in philosophy.
The summer of my 155h year, still suffering from adolescent religious angst and fascinated with the prospect of proofs about God, I decided to work through The Ethics, lemma by lemma. Pencil in hand and pad in lap, I spent summer days under a tree overlooking the tracks of the Butte, Anaconda and Pacific Railroad, which carried copper ore from Butte’s mines past my house to the smelter in Anaconda, 28 miles away, while I tried to reconstruct demonstrations about the Deity’s lack of parts. I could make no sense of Spinoza’s purported deductions; the meaning of each term seemed to morph and meander in the course of each argument. I had completed a year of plane geometry taught more or less from Euclid, and since the Ethics was obviously in imitation, I hit upon the following strategy: for each of Spinoza’s terms, I would try substituting a geometrical term, and see if Spinoza’s purported deductions became valid proofs in geometry. Faint hope, which I soon gave up for another tack. Since Spinoza’s terminology seemed to me so slippery, I would substitute throughout a letter for each occurrence of a term, distinct letters for distinct terms, and see if the resulting reasoning seemed sound. It never did. I gave it up, and for the next 25 years I thought the experience showed a defect of my intellect, until I read George Boole’s attempt, in The Laws of Thought, to provide logical reconstructions of the same arguments, with results similar to my own. The following summer break from Butte Public High School I read Darwin, who made me an atheist ever after, and removed any motivation for trying further with Spinoza.
I was never good at mathematics in school, and not much interested in it. I matriculated at the University of Montana in 1960, where I immediately (and secretly, since my father opposed it) began studying philosophy, almost exclusively, even withdrawing from an introductory mathematics course in my first year. My private concern was with a single question--what are the limits of knowledge—but I enjoyed courses on every topic except Sartre, whom I thought was cute rather than profound, and Heidegger, whose work was badly taught by a Polish disciple, Zygmunt Adamczewski, as a scripture rather than a hypothesis. (Adamczewski had avoided execution in the Katyn Forest only because he was too young to have the officer’s pins he, as a Polish aristocrat, would have received at age 18. Nonetheless, he literally worshiped Heidegger, the man who sought to be Hitler’s Minister of Education, and was deeply wounded when Heidegger broke a promise to let Adamczewski publish his English translation of Sein und Zeit.)
The result was that within two years I had completed all of the requirements of a major in philosophy except a course in logic. At the end of my second year, the University dismissed me because I refused to take part in military exercises, which were then required in many American colleges and universities. At the University of New Mexico, to which I transferred with the intention of continuing a course of philosophical study, I found the members of the Philosophy Department intolerably foolish, and so determined that I would take no more philosophy beyond the required logic course, and instead spend my remaining two undergraduate years qualifying for a second major in another subject. I picked chemistry because it was a natural science, and because, by taking a number of courses by examination, I could complete the requirements in my remaining four semesters, something I could not do in physics. Biology did not interest me at the time, and in Montana I had found the two courses I had taken in psychology to oscillate between banality and unintelligibility.
I took the introductory courses in chemistry, and organic chemistry as well, by examination, which was allowed at the University, and so saved considerable time. That would not do, however, for physical chemistry and quantum mechanics, both of which were required. There I was handicapped because I knew no more mathematics than high school geometry and algebra, absolutely nothing of calculus and differential equations. I managed nonetheless to obtain a better than average grade in both courses by a kind of ruse: in doing assignments, I teamed with a graduate student who could integrate and differentiate and understood the strange idea of logarithms, but who seemed baffled by problems stated in words. I learned more mathematics from doing problems with him than from the calculus courses in which I was enrolled at the same time.
I graduated in chemistry and philosophy, although the University thought the combination so improbable that my diploma read “English and Philosophy,” and I enrolled as a graduate student in chemistry, all philosophy departments to which I had applied being unwilling to grant me that status. The summer between I spent climbing in the Tetons with my best friend, Bruce Boettner. I took along a single philosophical book, Stephen Toulmin’s Philosophy of Science, which, having carried it to the exclusion of other reading in a full pack up a high mountain, I found so vapid that in disgust I threw it into a deep cavern. So there is another source: I came to formal philosophy in disappointment at the alternative. More accurately, by now I was disappointed in philosophy from all sides.
I had by this time, 1964, learned some calculus, some differential equations (a course I had to take twice, engaged the first time round principally in courting a young woman), and I had learned to program in Fortran— then practiced by producing quantities of punch cards, an exercise I very much disliked. I concentrated in inorganic chemistry, aiming to synthesize a molybdenum sandwich compound—a precursor of Buckeyballs. This required endless nights in the laboratory while chemicals gurgled away in racks of glass tubes, a setting made romantic by association with film images of the laboratories of mad chemists, which mine much resembled, but unproductive of molybdenum sandwiches. I was a lousy lab chemist. In those laboratory nights I turned to reading mathematics, mostly topology and differential geometry, and again to reading philosophy, this time Reichenbach’s The Direction of Time, which I found fascinating.
It was not long before I was once more about to be dismissed from university, this time for instructing undergraduates in the theories of Paracelsus. I was put in charge of an undergraduate chemistry laboratory supervising 20 or so undergraduates in a course of experiments none of which required more than half an hour to complete, but for each of which 3 hours had been allotted. The harridan who had dominion over laboratory instruction refused to allow me to release the students when they had completed their experiments, and so I had to keep them entertained for more than 2 hours each week, first by playing poker, and then, feeling that poker was inappropriate, giving the students lectures on the history of chemistry. In an excess of seriousness, I decided that if students received two hours of instruction each week on the history of chemistry, they should be tested on the content. That was my downfall. The chairman of the chemistry department came across a copy of one of my little examinations, as it happened on Paracelsus, and thinking I was teaching the students that modern chemistry turns on the sulfureous principle, and the like, decided to fire me. I calmed him a bit, but it became clear that I had no future there. I applied to Indiana in History and Philosophy of Science, and my beloved teacher at Montana, Cynthia Schuster, prevailed on her old friend, Wesley Salmon, to admit me.
At Indiana I learned modern algebra and some serious logic from a mathematician, Andrew Adler, and did chemical physics as a minor subject, where I learned three things perhaps more important than chemistry. I struggled through the graduate statistical mechanics course, full of long calculations that invariably tripped me up, only to receive the highest mark in the course because of the final exam—an essay test. I learned this: mistakes of calculation are easier to remedy than mistakes of conception. In my graduate quantum theory course, the professor labored to produce a clumsy theorem (I don’t remember what) of the form “if p then q.” The contrapositive was more intuitive and I said so, only to hear the professor adamantly deny the truth of the contrapositive formulation, and when presented with the general logical principle, deny that too. I learned, as had better minds before me, Boole’s and Frege’s included, that logic is not about people. The man gave a final examination with no time limit, full of problems each of which could be solved by a calculation requiring hours or in a moment by one or another trick. Some poor students labored over it for two days without sleep. I learned that cleverness is no excuse for cruelty.
My doctoral thesis was on logical empiricist accounts of scientific theories, and except for one little piece, it was not mathematics. It did leave me with a problem I have never solved: Consider the theory of infinity in the identity relation alone, in a first order language with identity having another binary predicate. With Adler’s help, I proved there is no logically weakest, consistent, finitely axiomatizable extension of the theory. Which raises the general question: when, if ever, does a recursively but not finitely axiomatizable theory have a logically weakest finitely axiomatizable conservative extension in extra predicates?
From Indiana I went to Princeton, where Richard Grandy and Dana Scott helped me to prove some things about equivalent theories, and I obtained an amusing result on indistinguishable space-time models of general relativity, which helped me to win tenure. I spent several years trying to work out a formal theory of confirmation, vaguely inspired by Carnap and by my then colleague, Carl Hempel, and wrote a book about it, only to realize in the end that I could not make the formalism work because the project itself was ill-conceived: I had not answered, and worse had not asked, what confirmation has to do with finding the truth. That reflection, and conversations with Scott Weinstein, led me to an interest in formal learning theory, which Hilary Putnam had introduced fifteen years before and the philosophical community had largely ignored, and, regrettably, still does. I had at that point, thirty eight years of age, discovered nothing I thought of any real value, and in the bleakness of my self-imposed exile in Oklahoma thought my ambition to make a real intellectual contribution was lost. I wanted to contribute more in a life than the high brow book reports and whiggish histories of science that I found increasingly passed for philosophy of science, and that still do. Yet in the course of writing the book that disappointed me, I came across a statistical and social science literature on causal inference, where hypotheses were justified by statistical constraints on observed variables, and by 1980 or so I asked myself a question: what are the class of causal hypotheses, under what assumptions relating causation and probability, that can account for any specified set of probability constraints on observed variables? I never answered that question just as posed, but the fruits of the effort it prompted in collaboration with my then students, Peter Spirtes, Richard Scheines, and Kevin Kelly, did finally make me a kind of formal philosopher.