“Beyond the obvious facts that he has at some time done manual labour, that he takes snuff, that he is a Freemason, that he has been in China, and that he has done a considerable amount of writing lately, I can deduce nothing else.”

― Arthur Conan Doyle, The Red Headed League

The great detective was wrong. Or, to be fair, Arthur Conan Doyle was wrong.

Sherlock Holmes is known for a few things: his deerstalker cap, his various addictions, his saying “Elementary, my dear Watson” (which actually never appeared in this form in the Conan Doyle stories), and his superhuman deductive skills.

Scratch that.

Sherlock Holmes did not practice deduction.

A deduction is a logical process by which one reaches a conclusion which is absolutely certain in the face of a set of facts. It starts from the general and moves to the particular.

Here is a classic deduction:

1. All men are mortal (a fact);

2. Arthur Conan Doyle is a man (a fact);

3. Therefore, Arthur Conan Doyle is mortal (the deduction).

There can be no other conclusion. What we know is not that some men are mortal. Conan Doyle is not sometimes a man. Because all men are mortal, and because Doyle is a man, he has to be mortal. This is a deduction.

In the story “The Red Headed League”, Holmes reasons that his visitor has been to China because of the way in which the scales of his fish tattoo have been stained pink, a technique he has observed is limited to the Chinese. Moreover, a Chinese coin dangles from the man’s watch-chain.

That the man visited China is certainly one explanation for these observations but by no means the only one. Another (and some might claim even likelier) explanation is that the man never left London. His tattoo was made by a Chinese immigrant who learned his trade in China, and the man bought the coin at a foreign market.

What Holmes is known for is to take observations and derive from them the most likely explanation, but never the only explanation. This process can be referred to as inductive reasoning.

Let’s say I am a zoologist who has travelled the world for the past 30 years. I have personally observed 8386 swans. They have all been white. I might induce that all swans are white. This is by no means the only possibility. There could be a few black swans hiding somewhere in Belgium. However, after having witnessed 8386 swans, all of them white, I may be tempted to state that the most probable conclusion is that swans only come in one colour.

(There exists a third form of logical reasoning termed “abductive reasoning”. Some people accept that it is a form of inductive reasoning; others claim it is not. I’m afraid I could not find a clear distinction between the two and will thus stick to the deduction/induction dichotomy. If you are a philosopher or artificial intelligence scientist, please chime in in the comments section)

I bring up the distinction between a deduction and an induction for a purpose much more educational than to simply “tsk” in Arthur Conan Doyle’s general direction. Deductions and inductions play a big role in our exploration of the world around us. They are methods of scientific inquiry.

We can go back to the first half of the 19^th century to see the inductive model of reasoning playing a considerable role in our understanding of biodiversity. And we owe it all to a very observant man by the name of Charles Darwin.

Prior to Darwin’s contribution, Europeans were being told by their clergy that biological life was immutable, a model known as the “fixity of species”. This worldview was neither deduced nor induced, but rather clumsily interpreted from the passages of a revered book written by Iron-Age scribes recording a long oral tradition. One might say they were justified in their belief because the book was a Good Book. Tim Minchin might have something to say about that.

Charles Darwin joined the HMS Beagle in 1831 on its five-year trip to chart the coast of South America. It was on this voyage that Darwin made numerous geological and biological observations which would play a role in his inductive construction of the theory of evolution.

He ponders in his seminal book On the Origin of Species that, on the Galapagos Archipelago, situated 973 kilometers from South America, “almost every product of the land and water bears the unmistakeable stamp of the American continent”¹. His observations lead him to question the established model: are we supposed to believe that these 25 distinct land bird species endemic to the Galapagos yet frighteningly similar to their American brethren were created there? He further writes:

“The naturalist, looking at the inhabitants of these volcanic islands in the Pacific, distant several hundred miles from the continent, yet feels that he is standing on American land. Why should this be so? why should the species which are supposed to have been created in the Galapagos Archipelago, and nowhere else, bear so plain a stamp of affinity to those created in America?”¹

These and related observations led Darwin to induce a model by which species were not fixed but rather evolved, and that those species best fit for their environment were more likely to survive and pass on their fit genetic material. Darwin took a collection of observations and induced from them the most likely model that would explain them.

A contemporary of Darwin’s, Alfred Russel Wallace, stumbled upon the same world-changing idea using a different process, that of deductive reasoning. As he began his career as a naturalist, Wallace had already embraced the idea that species were not fixed and set about to collect evidence to support this hypothesis. It seems Wallace had been particularly open-minded to the heretical claims of a few scientists, including Darwin’s grandfather, Erasmus Darwin, that species changed in response to their environment and that these changes would be passed on to their offspring. Wallace designed his trips to test the hypothesis that closely related species would be found in proximity.

When his observations seemed to confirm his hypothesis, Wallace set about to seek validation of the soundness of his argument and sent a manuscript detailing his findings to a trusted colleague. His manuscript was entitled “On the Tendency of Varieties to Depart Indefinitely from the Original Type”. His colleague was Charles Darwin.

In the end, Darwin and Wallace’s findings were read out at the Linnean Society of London in 1858. A year later, Darwin’s seminal book, On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life, would be published. It would seem that both roads lead to Rome: the inductive model and the deductive model led two separate men to the same discovery.

This equivalency did not result in both models being equally preferred. Science historian Naomi Oreskes relates that, in the early 20^th century, “American scientists preferred the inductive method, being more democratic and anti-authoritarian”². This tradition was inherited from earlier advocates of scientific research, people like Galileo Galilei, Nicolaus Copernicus, and Isaac Newton. In fact, Newton was strongly against a deductive method of scientific inquiry, writing in Principia,

“For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses […] have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.”³

Oreskes goes on to describe how the leap from massive data sets to crisp explanation was eventually criticized as illogical, even unscientific. How did one go about formulating a model to explain a thousand observations? The deductive model of science, with its logical framework of directed evidence gathering, began to take hold of the scientific community and continues, to this day, to be perceived as the scientific method of choice.

To recap, this hypothetico-deductive model begins with a hypothesis which needs to be validated. There are implications to this hypothesis being correct, implications which can be tested. If the earth is a sphere, then some stars seen in the north will not be visible in the south. Tests are carried out, either as designed experiments or specific observations, and scientists are forced to either maintain their hypothesis for now, or reject it and try to find a better hypothesis which can explain older observations and those of the current experiment. This model is based on a logical deduction: if the general hypothesis is true, then it must necessarily follow that a particular fact will be observed. There is no probability, only an absolute.

By contrast, the inductive process of science consists of scientists going out into the world, making observations and, eventually, trying to come up with a probable model that does the best job at explaining the maximum number of observations.

However, I would argue that the choice between inductive and deductive science is a false dichotomy. It implies that only one model is right and that the two do not overlap. The reality seems closer to the ancient Ouroboros symbol of a snake eating its own tail. Inductive science informs deductive science, which frequently falls back into induction. Hypotheses generally do not arise ex nihilo; they are the product of real-world observations. This is induction. They must then be tested to ensure that every implication of the hypothesis holds true. This is deduction. If experiments disprove the hypothesis, many scientists will go back to observing the world around them to help them formulate a better hypothesis.

In scientific disciplines in which deduction reigns supreme, inductive science can be a tough sell to granting agencies. Moreover, graduate students confronted with non-hypothesis-driven research projects relying on inductive reasoning—projects known in laboratories as “fishing expeditions”—can easily feel they are out to fend for themselves with no end in sight. How does one defend one’s research project when all it consists of is generating data and seeing if anything interesting pops up?

Still, there ought to be room for both types of approaches in science. Deductive science can be easier to fund and more appropriate for short- and medium-term student projects. Inductive science, with its lengthy observational phase and riskier outcomes, should perhaps be left to permanent staffers and principal investigators. Inductive science is not inferior to its younger sibling; after all, it worked quite well for both Darwin and Holmes.

 

(Feature picture by Isriya Paireepairit)

 

1. Darwin, Charles. On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life. Kindle edition produced by Sue Asscher based on the first edition.

2. Oreskes, Naomi. (2012, November). Building scientific knowledge: the story of plate tectonics. Howard Hughes Medical Institute Holiday Lectures on Science – Changing Planet: Past, Present, Future. Lecture conducted from the Howard Hughes Medical Institute, Chevy Chase, MD.

3. Cohen, Bernard, and Anne Whitman, trans. Philosophiae Naturalis Principia Mathematica, General Scholium by Isaac Newton. University of California Press, 1999.