Peirce, Holmes and a gold chain – an essay on abductive reasoning

“It has long been an axiom of mine that the little things are infinitely the most important.” – Sir Arthur Conan Doyle (A Case of Identity)

The scientific method is a systematic approach to acquiring and establishing knowledge about how the world works. A scientific investigation typically starts with the formulation of a hypothesis – an educated, evidence-based guess about the mechanism behind the phenomenon being studied – and proceeds by testing how well the hypothesis holds up against experiments designed to disconfirm it.

Although many philosophers have waxed eloquent about the scientific method, very few of them have talked about the process of hypothesis generation. Indeed, most scientists will recognise a good hypothesis when they stumble upon one, but they usually will not be able to say how they came upon it. Hypothesis generation is essentially a creative act that requires a deep familiarity with the phenomenon in question and a spark of intuition. The latter is absolutely essential, a point captured eloquently in the following lines attributed to Einstein:

“…[Man] makes this cosmos and its construction the pivot of his emotional life in order to find in this way the peace and serenity which he cannot find in the narrow whirlpool of personal experience.  The supreme task is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience can reach them…”  – quoted from Zen and The Art of Motorcycle Maintenance by Robert Pirsig.

The American philosopher, Charles Peirce, recognised that hypothesis generation involves a special kind of reasoning, one that enables the investigator to zero in on a small set of relevant facts out of an infinity of possibilities.

Charles Sanders Peirce

As Peirce wrote in one of his papers:

“A given object presents an extraordinary combination of characters of which we should like to have an explanation. That there is any explanation of them is a pure assumption; and if there be, it is [a single] fact which explains them; while there are, perhaps, a million other possible ways of explaining them, if they were not all, unfortunately, false.

A man is found in the streets of New York stabbed in the back. The chief of police might open a directory and put his finger on any name and guess that that is the name of the murderer. How much would such a guess be worth? But the number of names in the directory does not approach the multitude of possible laws of attraction which could have accounted for Kepler’s law of planetary motion and, in advance of verification by predications of perturbations etc., would have accounted for them to perfection. Newton, you will say, assumed that the law would be a simple one. But what was that but piling guess on guess? Surely vastly more phenomena in nature are complex than simple…” – quoted from this paper by Thomas Sebeok.

Peirce coined the term abduction (as opposed to induction or deduction) to refer to the creative act of hypothesis generation.  In the present day, the term is used to the process of justifying hypotheses rather than generating them (see this article for more on the distinction). In the remainder of this piece I will use the term in its Peircean sense.

–x–

Contrary to what is commonly stated, Arthur Conan Doyle’s fictional detective employed abductive rather than deductive methods in his cases.  Consider the following lines, taken from an early paragraph of Sherlock Holmes’ most celebrated exploit, The Adventure of the Speckled Band. We join Holmes in conversation with a lady who has come to him for assistance:

…You have come in by train this morning, I see.”

“You know me, then?”

“No, but I observe the second half of a return ticket in the palm of your left glove. You must have started early, and yet you had a good drive in a dog-cart, along heavy roads, before you reached the station.”

The lady gave a violent start and stared in bewilderment at my companion.

“There is no mystery, my dear madam,” said he, smiling. “The left arm of your jacket is spattered with mud in no less than seven places. The marks are perfectly fresh. There is no vehicle save a dog-cart which throws up mud in that way, and then only when you sit on the left-hand side of the driver.”

“Whatever your reasons may be, you are perfectly correct,” said she. “I started from home before six, reached Leatherhead at twenty past, and came in by the first train to Waterloo…

Notice what Holmes does: he forms hypotheses about what the lady did, based on a selective observation of facts. Nothing is said about why he picks those particular facts – the ticket stub and the freshness / location of mud spatters on the lady’s jacket.  Indeed, as Holmes says in another story, “You know my method. It is founded upon the observation of trifles.”

Abductive reasoning is essentially about recognising which trifles are important.

–x–

I have a gold chain that my mum gave me many years ago.  I’ve worn it for so long that now I barely notice it. The only time I’m consciously aware that I’m wearing the chain is when I finger it around my neck, a (nervous?) habit I have developed over time.

As you might imagine, I’m quite attached to my gold chain. So, when I discovered it was missing a few days ago, my first reaction was near panic,  I felt like a part of me had gone missing.

Since I hardly ever take the chain off, I could not think of any plausible explanation for how I might have lost it. Indeed, the only time I have had to consistently take the chain off is when going in for an X-ray or, on occasion, through airport security.

Where could it have gone?

After mulling over it for a while, the only plausible explanation I could think of is that I had taken it off at airport security when returning from an overseas trip a week earlier, and had somehow forgotten to collect it on the other side.  Realising that it would be near impossible to recover it, I told myself to get used to the idea that it was probably gone for good.

That Sunday, I went for a swim. After doing my laps, I went to the side of the pool for my customary shower. Now, anyone who has taken off a rash vest after a swim will know that it can be a struggle. I suspect this is because water trapped between skin and fabric forms a thin adhesive layer (a manifestation of surface tension perhaps?).  Anyway, I wrestled the garment over my head and it eventually came free with a snap, generating a spray of droplets that gleamed in reflected light.

Later in the day, I was at the movies. For some reason, when coming out of the cinema, I remembered the rash vest and the flash of droplets.  Hmm, I thought, “a gleam of gold….”

…A near forgotten memory: I vaguely recalled a flash of gold while taking of my rash vest in the pool shower some days ago. Was it after my previous swim or the week earlier, I couldn’t be sure. But I distinctly remembered it had bothered me enough to check the floor of the cubicle cursorily. Finding nothing, I had completely forgotten about it and moved on.

Could  it have come off there?

As I thought about it some more, possibility turned to plausibility: I was convinced it was what had happened. Although unlikely I would find it there now,  it was worth a try on the hope that someone had found the chain and turned it in as lost property.

I stopped over at the pool on my way back from the movies and asked at reception.

“A gold chain? Hmm, I think you may be in luck,” he said, “I was doing an inventory of lost property last week and came across a chain. I was wondering why no one had come in to claim something so valuable.”

“You’re kidding,” I said, incredulous. “You mean you have a gold chain?”

“Yeah, and I’m pretty sure it will still be there unless someone else has claimed it,” he replied. “I’ll have a look in the safe. Can you describe it for me?”

I described it down to the brief inscription on the clasp.

“Wait here,” he said, “I’ll be a sec”

It took longer than that but he soon emerged, chain in hand.

I could not believe my eyes; I had given up on ever recovering it. “Thanks, so much” I said fervently, “you won’t believe how much it means to me to have found this.”

“No worries mate,” he said, smiling broadly. “Happy to have helped.”

–x–

Endnote: in case you haven’t read it yet, I recommend you take ten minutes to read Sherlock Holmes’ finest adventure and abductive masterpiece, The Adventure of the Speckled Band.