by Bruce Thompson.
My friend and mentor R. B. Angell—Brad to those of us who knew him—always kept a mousetrap beside his computer. It was primed and ready to snap at any moment.
“Do you have a problem with mice?” I asked him on one of my visits to his house.
“No,” he replied, a little puzzled that I would ask such a question
“Then, why the mousetrap?” He laughed as he realized what I was referring to.
“The mousetrap is to remind me that there really are causal relations. ‘If I touch the trigger, then it will snap’.”
Brad and I had met at a philosophy conference about a year before. We were logicians, working in the same (very narrow) field of logic. Specifically, we were what could be called “logical realists,” although the technical term is “connexivists.” We had never met prior to running into each other at that conference. However, we knew of each other’s work because he had politely rejected a paper of mine for publication—and I had agreed that he was right to do so. At the time, I was a recent Ph.D. graduate working at my first real job; he was a distinguished scholar, and my paper was full of the errors one might expect from a rank beginner. After he rejected my paper, I avidly researched his work, and come to the conclusion that he was perhaps the most brilliant and important logician of the 20th Century. I have not since wavered in that opinion. Meeting him was, for me, like meeting Aristotle.
We talked for what seemed to us like barely ten minutes. His wife, Imogene, stood beside him, smiling at the pleasure her husband felt in talking to someone who knew and understood his work. I looked at my watch and realized that we had been talking for over an hour. I was mortified that we had been so inconsiderate as to talk so long, leaving his poor wife surely bored to tears. She reassured me that, while she had not understood a word we said, she was delighted that her husband had met a kindred soul.
Brad taught at Wayne State University in Detroit. He invited me to teach an introductory logic course (as a visiting instructor) during the summer semester. At the time, I was living in Erie, Pennsylvania. My classes at Wayne State met on Tuesday and Thursday afternoons. My weekly schedule was to drive from Erie to Detroit on Tuesday morning, and arrive in time for my afternoon class. I would then go to Brad’s house, where he had a guest bedroom. I would spend Tuesday and Wednesday nights with Brad and Imogene. On Thursday, I would meet my class again—and then drive home to Erie.
Wednesday was the height of my week: Brad and I would spend the whole day going over our current work in connexive logic, debating which principles were foundational axioms, which were derivable theorems, and how one could go about proving “logical completeness” for connexive systems.
It was on one such Wednesday that I noticed his mousetrap.
Connexive logic is an attempt to formalize a logic in which real causal “connexions” are recognized. We believe that a statement such as “If the moon is made of green cheese, then it is raining,” is false, since there is little connection between the chemical composition of the moon and the current weather. Most people who are not trained in formal logic agree with us; so, it may surprise you to learn that the standard logic, upon which all computer science is based, holds that this statement is true! Since the moon is not made of green cheese, the “if…then…” proposition is true by default. Under Boolean logic, any “if…then…” statement is true merely because its antecedent is false (or its consequent true), and for no other reason. Underlying causes (if any) are irrelevant. Of course, this has profound implications for artificial intelligence research. How can we expect a computer to think like a human being, when human beings understand and reason about real causal connections, while computers do not, and cannot?
I asked Brad, “Do you ever touch the trigger on the mousetrap?”
“Never!” he replied. “The mousetrap is there to remind me that the statement ‘If I touch the trigger, then it will snap’, is true whether I touch the trigger or not.”
Humans make decisions believing that choices have real outcomes. We avoid certain actions because we know what the consequences of those actions would be—even if those actions are never taken. Causality is not a truth-table. Yet, every connexivist has moments in which the quest for a non-Boolean logic seems futile. Perhaps the Booleans were right after all. When Brad had such moments, he would see his mousetrap and wonder how badly it would hurt to stick his finger just … Brad was using the mousetrap to stay grounded, to resist the temptation to give up, to remind himself not to be seduced by the easy convenience of Boolean truth tables.
Brad Angell died in 2010, not long after completing his work, The A-Logic, which he had been working on during the summer I spent with him. I doubt that his work will have much influence on modern logicians. It is too far outside the mainstream of modern logic—which is to say, it is utterly brilliant, and therefore unlikely to be appreciated. My own work has been far more conservative. I have tried to hew closely to the expectations of modern logicians in the hope that my work would someday be understood and appreciated—which is to say, my work is not especially brilliant. But, remembering Brad’s mousetrap, I have not given up.
The mentor-protégé relationship is something special in academic circles. It is hard to describe. Is it like a father-son relationship? Not really. Brad and I knew each other for barely a whole year; but, it was one of the most influential years of my life. I can say this: if I had not known Brad and Imogene, then my life would have been quite a bit different and infinitely poorer. There is a real causal connection between their lives and mine.