“But that’s no coincidence, I think,” I interrupted. I was trying to link the results that I had presented at the seminar with what I was now hearing and find where they fitted in the large figure that Seldom was now drawing for me.
“No, of course not. My hypothesis is that it is profoundly linked to the aesthetic that has been promulgated down the ages and has been, essentially, unchanging. There is no Kantian forcing, but an aesthetic of simplicity and elegance which also guides the formulation of conjectures; mathematicians believe that the beauty of a theorem requires certain divine proportions between the simplicity of the axioms at the starting point, and the simplicity of the thesis at the point of arrival. The awkward, tricky part has always been the path between the two-the proof. And as long as that aesthetic is maintained there is no reason for indeterminable propositions to appear ‘naturally’.”
The waiter returned with a pot of coffee and filled our cups. Seldom remained silent for a time, as if he was unsure whether I’d followed what he was saying, or was perhaps a little embarrassed at having talked so much.
“What I was most struck by,” I said, “the results that I presented in Buenos Aires, were in fact the corollaries that you published a little later on philosophical systems.”
“Actually, that was much easier,” said Seldom. “It’s the more or less obvious extension of Godel’s Incompleteness Theorem: any philosophical system which starts from first principles will necessarily have a limited scope. Believe me, it was much easier piercing through all the philosophical systems than through that single thought matrix to which mathematicians have always clung. Because all philosophical systems are simply too ambitious. Basically, it’s all a question of balance: tell me how much you want to know and I’ll tell you with how much certainty you’ll be able to state it. Butt at the end, when I’d finished and I looked back after thirty years, it seemed that that first idea that Marx’s sentence had suggested to me hadn’t been so misguided after all. It had ended up, as the Germans would say, both eliminated from and included in the theorem. Indeed, a cat doesn’t simply assess a mouse, it assesses it as a prospective meal. But the cat doesn’t assess all animals as prospective meals, only mice. Similarly, historically, mathematical reasoning has been guided by a criterion, but that criterion is, deep down, an aesthetic. I found this to be an interesting and unexpected substitution with regard to necessity and a priori Kantians. A condition that is less rigid and possibly more elusive, but which also-as my theorem had shown-was substantial enough to be able, still, to say something and make waves. As you see,” he said, almost apologetically, “it isn’t easy to be free of such an aesthetic: we mathematicians always like to feel that we’re saying something that is meaningful.
“However that may be, I have devoted myself ever since to studying what I privately call the aesthetic of reasoning in other spheres. I began, as always, with what seemed like the simplest model, or at least the closest: the logic of criminal investigations. I found the parallels with Godel’s theorem very striking. In every crime there is undoubtedly a notion of truth, a single true explanation among all the possible explanations. On the other hand, there are also material clues, facts that are incontrovertible or at least, as Descartes would say, beyond reasonable doubt: these would be the axioms. But then we’re already in familiar territory. What is a criminal investigation if not our old game of thinking up conjectures, possible explanations that fit the facts, and attempting to prove them correct? I began systematically reading about real-life murders, I went through public prosecutors’ reports for judges, I studied the method of assessing evidence and of structuring a sentence or an acquittal in a court of law. Just as when I was a teenager, I read hundreds and hundreds of crime novels. Gradually I began to find a multitude of interesting little differences, an aesthetic inherent in criminal investigations. And errors, too. I mean theoretical errors in criminology, which were potentially much more interesting.”
“What kind of errors?”
“The first, and most obvious, is attaching too much importance to physical evidence. Just think of what’s happening now in this investigation. If you recall, Inspector Petersen sent one of his officers to retrieve the note I received. Here once again the same insurmountable gap opens up, between that which is true and that which is provable. I saw the note, and that’s the part of the truth that the police can’t get to. My statement isn’t much use as far as police procedure goes; it doesn’t carry the same weight as the little piece of paper itself. Now, the officer, Wilkie, completed his task as conscientiously as he could. He questioned Brent and got him to go over what he knew several times. Brent clearly remembered seeing a piece of paper folded in two at the bottom of my wastepaper basket, but it hadn’t occurred to him to read it. Brent remembered too that I’d asked him if there was any way of retrieving the paper, and he told Wilkie what he told me: that he’d tipped the contents of the basket into an almost full refuse bag, which he’d put out soon after. By the time Wilkie arrived at Merton, the refuse lorry had been and gone almost half an hour earlier. When Petersen called me yesterday to ask me to describe the handwriting to their artist, I could tell that he was very disappointed at not finding the note. He’s considered to be the best police inspector we’ve had in years. I’ve had a look at the complete notes to several of his cases. He’s thorough, meticulous, implacable. But he’s still an inspector. I mean, he was trained in accordance with police procedure: you can predict the way his mind is going to work. Unfortunately, people like him follow the principle of Ockham’s Razor: as long as there’s no physical evidence to the contrary they always prefer a simple hypothesis to a more complicated one. That’s the second error. Not just because reality tends to be naturally complicated but mainly because, if the murderer really is intelligent and has prepared the crime carefully, he’ll leave a simple explanation for all to see, a smokescreen, like a conjuror leaving the stage. But in the stingy logic of the economy of hypothesis a different reasoning prevails: why assume something strange and out of the ordinary, such as a murderer with intellectual pretensions, if they have more immediate explanations to hand? I could almost physically feel Petersen step back and re-examine his hypotheses. I think he would have started suspecting me, if he hadn’t already checked that I was teaching between one and three that afternoon. I expect they checked out your statement too.”
“Yes. I was in the Bodleian Library when it happened. They went to enquire about me there yesterday. Luckily, the librarian remembered me because of my accent.”
“So you were consulting books at the time of the murder?” Seldom raised his eyebrows sardonically. “For once, knowledge really is freedom.”
“Do you think Petersen will pounce on Beth now? She was terrified yesterday after they questioned her. She thinks the inspector is after her.”
Seldom thought for a moment.
“No, I think Petersen is cleverer than that. But consider the dangers of Ockham’s Razor. Suppose for a moment that the murderer, wherever he is, decides that he doesn’t have a taste for murder after all, or that the business with the blood and the police getting involved have ruined his fun; suppose that, for some reason, he decides to disappear from the scene. I think Petersen would then go after Beth. I know he questioned her again this morning, but this may simply have been a diversionary tactic, or a way of provoking the murderer, acting as if they don’t know about him, as if this were an ordinary case, a murder in the family, as the newspaper suggested.”