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Chapter 3. Truth

In the opening pages of the Sherlock Holmes story Silver Blaze we find Holmes and Watson on the train from Paddington to Exeter. They are on their way to Dartmoor, to investigate the disappearance of the racehorse Silver Blaze and the murder of his trainer John Straker. It is summer 1892, and when we pause to think, the story contains small oddments of information which are quite strange to modern eyes. For instance, everyone smokes — we are told that Holmes spent the previous day pacing back and forth while smoking pipe after pipe of “the strongest black tobacco.”

Holmes and Watson also demonstrate that the late-Victorian gentleman expected to be able to travel with a speed which we would today consider unlikely. In the previous hour or so, they finished their breakfast, took a cab from Baker Street to Paddington Station, bought tickets, bought newspapers and left London on a Great Western Railway train. Installed in their first class compartment they watched the smoke and brick of the city fall behind them, crossed the Thames on Brunel’s magnificent bridge at Maidenhead, and are now well beyond Reading. An hour or so. Impressive.

Holmes finishes reading the newspapers and offers a cigar to Watson. (More tobacco. See what I mean?) Holmes looks at his watch. “We are going well,” he says. “Our present rate is fifty-three and a half miles an hour.” How does he know? Could you do that?

Perhaps your watch has a GPS receiver and tells you your speed, but this is 1892. Holmes’ watch is clockwork, with a gold case and, like all gentlemen, he keeps it in his waistcoat pocket on the end of a gold chain. Of course, Holmes and Watson both know useful little pieces of information about their own era, things that you might not know. For instance, they know that the railway lines have posts every quarter of a mile, near the track. If you put your head close to the window you can see them as they pass by and you can use your watch to time the seconds between them. At your speed it takes 67 seconds to travel a whole mile. Then, since you are a hacker, you know there are 3,600 seconds in an hour and you can do in your head the long division sum 3,600 divided by 67. You get the answer 53½ miles an hour.

Watson is unimpressed. He just says “I have not observed the quarter-mile posts.” He’s telling Holmes that if he had to, he could do the sum too. It’s just schoolboy arithmetic.

But Watson has fallen for Holmes’ gambit. “Nor have I,” says Holmes, about to flaunt his knowledge of arcane trivia. “But the telegraph posts upon this line are sixty yards apart, and the calculation is a simple one.”

Watson is happy to let Holmes have his little victory. It seems very plausible. But when his conclusions are more unexpected or where there is more at stake, Holmes has to work a lot harder to convince Watson. Exactly how does he do it? We will leave Holmes and Watson on the train for now, but we’ll rejoin them later, when they reach the King’s Pyland stables on Dartmoor. In the meantime, I want to explore how the different kinds of logical argument used by Holmes actually work.

Nowadays, in the era of Post-Modernism, there is a popular idea that everything is just opinion and that one person’s opinion is as good as anyone else’s. That nothing is really true. That everything is relative. Holmes and Watson are not Post-Modernists. They are children of the Enlightenment — they believe that there is a truth, and they can find it out and reveal it to others. Their tool for doing this is logical argument.

Logical arguments are very different from moral arguments. To be convincing with a moral argument you need to evoke an unconscious emotional response. With a logical argument on the other hand, you need to get someone to consciously agree on facts, and then to explain to them how these facts lead inevitably, step by step, to your conclusions. As we have seen, the adaptive unconscious is rather good at snap decisions, but tends to jump to conclusions and to be very inflexible in the face of new evidence. Logical arguments are valuable because we can use them to consciously over-ride these unconscious judgements. We can change our minds when we are wrong. This can feel very uncomfortable, but it is better to be uncomfortable and right than to be comfortable and wrong.

Let’s begin with facts, the basic atoms of logical argument. When someone tells you a “fact,” how do you decide if it is true? When we first hear or see something new, it appears that our immediate reaction is to just believe it. Disbelief, if it happens at all, comes at least a moment later. To disbelieve something that we are told, or that we think we saw, takes an effort — psychologists would say that it imposes a “cognitive load.” This effort is harder if we are tired, distracted or under time pressure. note 30

On the other hand, disbelief is easier if the new “fact” contradicts something we already believe to be true. This is because contradiction imposes its own “cognitive load.” It’s very uncomfortable to try to hold two contradictory things in mind at the same time, to hear one thing and believe another or to do one thing and believe another. In the 1950s, psychologist Leon Festinger coined the term “cognitive dissonance” for this effect. We unconsciously act to reduce this uncomfortable feeling, usually by passively ignoring the new thing, sometimes by more actively avoiding or denying it.

This effect is essentially the same as what more recent psychologists have called “confirmation bias.” People tend to seek out new information confirming what they already believe and they avoid information which contradicts it. Whatever we call this effect, it means that we are apt to ignore inconvenient facts if we don’t deliberately stop to consider them.

“Facts” that we tentatively accept become more and more believable as we hear them again and again, even when they come repeatedly from the same source. This is because our adaptive unconscious seems to use a rule of thumb that when something is easy to recall, then it must be true. Psychologists call this the “availability heuristic.” So events described in vivid detail seem more plausible, the risks of gruesome accidents seem more likely. And bizarrely, denials can make something seem more believable, because the idea being denied is made more memorable by the denial, while the “not” in the denial fades out after a few days. So if you say, “This man is not a thief,” after a few days, people will tend to remember the opposite. note 31

With conscious effort, we can examine apparent facts more closely and decide rationally whether to accept them or not. The first step of course is to use your conscious mind and not just leave the job to your adaptive unconscious. Stop and think! When you look at it more carefully, you will often find that the “fact” you are being handed isn’t actually a fact at all. Perhaps it is really just an opinion, a rumour, a speculation or a lie.

If we think that a “fact” may be true, but we are not sure, we tend to rely on the respectability or authority of whoever gives it to us. Holmes tells Watson that the telegraph posts on the Great Western Railway are 60 yards apart. Now, Holmes often keeps information to himself, but he doesn’t often lie to Watson directly, particularly about such trivial matters. Watson is happy to take this information on trust. If more was at stake, Watson might want to check how Holmes came to know it — does he have a plausible story? Can he show some document that confirms it? What would be enough to prove it in a court of law? If Watson wanted to be really sure, he might decide to take a tape-measure, walk the line and measure the spacing for himself.

If we can’t go back and measure something for ourselves, if we have to rely on reports from witnesses, then we need to appreciate just how unreliable witnesses can be, and the sort of mistakes they tend to make. People are surprisingly poor at seeing what really happened and even worse at remembering it. Of course, they can do much better if they are prepared and paying attention, especially if they are experts with a lot of experience in what they are watching. But otherwise people are quite easy to fool. We tend to see things and remember things that didn’t quite happen.

We can fool ourselves quite innocently and we can also be fooled deliberately by other people. Neuroscientist Michael Gazzaniga recounts an especially impressive example, a trick performed by stage magician Harry Blackstone:

Even other stage magicians couldn’t work out how he did it. (It was all distraction: while Blackstone and the beautiful assistant were keeping the audience’s attention with the sheet exchange, a second assistant simply walked on stage with the donkey, placed the hat on it and walked off again. Even though everyone in the audience saw the second assistant with the donkey, they didn’t notice him at the time or remember him later. He was too uninteresting. Blackstone then simply turned and threw a sheet over the hat and the donkey. When he whipped the sheet and hat away, there was the donkey! The fact that the trick was called “Out of Your Hat” was a further piece of misdirection.)

In recent years, psychologists have demonstrated scientifically what stage magicians always knew: we only consciously notice the things that we unconsciously consider salient. If you are an expert in what you are seeing, you unconsciously notice more details, so you have a better chance at registering what really happened, but even experts can be deceived. Even other stage magicians couldn’t work out Blackstone’s trick. If you are not an expert and you are not prepared, you can be deceived even by events that you might think would be transparently clear. You can easily miss a fight by the side of the road. You can even miss someone standing in full view wearing a gorilla costume. (Both of these mistakes have been demonstrated in modern experiments.) note 33

Since we miss so much of what happens around us, it’s unsurprising that witnesses to an event tell different stories about what they saw. Even worse, people’s adaptive unconscious actually fills in the details that are missing. People can be absolutely convinced that the details they have invented are quite real. Gazzaniga describes an experiment by psychologist Michael Miller:

The detail that people recall seems convincing to us, and it’s more than convincing to them — it’s what they remember. But it can still be false. Perhaps even more disturbingly, recent research by neuroscientist Karim Nader suggests that the old theory of “memory reconsolidation” may be correct after all. In this theory, memories are not fixed things, like images on a film, but very fluid and changeable. Like unpacking and repacking a suitcase, every time we recall something, we re-remember it afterwards, and it’s not necessarily the same as it was before. note 35

It’s certainly the case that questions from others can prompt memories of things that didn’t really happen, and that these memories can become more and more embroidered over time. Witnesses repeating a story can slowly change it, incorporating elements they only found out later, and which may not be correct. Because of this, it is important to get witness statements as soon as possible after an event, and to give more weight to the earliest statements. Subsequent re-tellings are intrinsically less credible, especially if months or years have gone by.

However, when we know about these effects, we can actually use them to our advantage when we interpret accounts from several witnesses. If the general outlines of a story are supported by many witnesses who disagree about details, we can still be confident that the general outline is correct. If a specific detail appears in many accounts which differ in other details, we can still be confident that the specific detail is correct. But if a group of witnesses tell practically the same story, with all details the same, then all we can really be sure of is that their story is to some extent a lie. The only way that many accounts could be identical is if they had been invented, if the witnesses had agreed beforehand on what to say, or been told.

Now that we have learned to be suspicious even of evidence we see with our own eyes, let’s move on from “facts,” the atoms of logical argument, to look at “reasons” and “conclusions,” out of which we can build complex molecules of rational thought. For literally thousands of years, children who had a classical education learned about logic in school. These children were always a small fraction of the population. (Holmes and Watson, being gentlemen, would of course have been amongst their number.) Even today, with mass education, only a small fraction of children are taught this material. Perhaps a mental tool that lets you think more clearly is too sharp to put in the hands of just anyone. Who knows what the consequences might be? But you need to know this, and since the odds are that you don’t already know it, I’ll attempt now to give you a crash course. If it seems a little dry, remember: it really is valuable, and we’ll get back to Holmes and Watson on Dartmoor quite soon.

Where to start? Well, I guarantee that all medieval school children learning about classical logic would be familiar with this illustrative example:

This example of logic from the ancient world seems both trite and obvious, but let’s use it the way a medieval schoolteacher would, to illustrate the parts of a logical argument:

Socrates is a man.	(fact)
All men are mortal.	(general rule)
Therefore, Socrates is mortal.	(conclusion)

The first line is a fact. You know all about them. They can be true or false, and you have to make your own mind up about each fact you meet. The second line is a general rule. Like a fact, it can also be true or false, and again you need to make your own mind up. Unlike a fact, which is about a particular thing, a general rule is about groups of things. It’s as though the general rule has a hole in it into which we can fit a particular fact, like slotting a shape into a child’s puzzle. The fact has to have the right shape. In this case the general rule is about all men. Since the previous fact tells us that Socrates is a man, the hole in the general rule is the right shape, and we can slot the fact in. The specific fact about Socrates and the general rule about all men can now be combined to to give a specific new fact about Socrates. This is the third line, the conclusion, which is a new fact derived solely from the first fact and the general rule, which we call the reasons for the conclusion.

Now, you might object that the conclusion is entirely obvious, that you already knew that. But notice that to reach the conclusion, we didn’t use any extra “common sense” knowledge. We only used what was explicitly stated in the reasons. This is the key to the method of logical argument: if we want to convince someone of the conclusion in a more complex argument, all we have to do is to convince them of each of the reasons in turn. When we have done that we can combine the facts and general rules in a purely mechanical way and the conclusion is inevitable. Or if we are uncertain about our own conclusion, we can go back and check our reasons one by one. Are all the facts and all the general rules really true? Do they fit together properly? If so, then despite our misgivings, the conclusion must be true too.

We can also work the method backwards: if we are certain that the conclusion is wrong, then it must be because one of the reasons is wrong, or because we have fitted them together wrongly. The conclusion doesn’t depend on anything else. If we go through the reasons carefully, we can find our mistake and correct our thinking. Or if someone else is trying to convince us of a conclusion and we don’t agree with it, perhaps we can go through their reasons one by one and show them their mistake. If we can’t find their mistake, then in fact they are correct, and we should believe their conclusion. Maybe we will find that we cannot agree on one particular reason: one of us thinks it’s true, the other thinks it’s false. However the conversation goes, logical argument helps us to understand each other better and to communicate what we understand.

Let’s go back to Socrates, and see how we might write the same argument in different ways. For example, the linking words might be different:

Socrates is a man and	(fact)
all men are mortal, so	(general rule)
Socrates is mortal.	(conclusion)

Or the conclusion might come first:

Socrates is mortal because	(conclusion)
all men are mortal and	(general rule)
Socrates is a man.	(fact)

Or the conclusion might be in the middle:

All men are mortal, so	(general rule)
Socrates is mortal because	(conclusion)
Socrates is a man.	(fact)

People usually signal that they are using a logical argument by using joining words like “so,” “because,” “therefore” and so on. When you read or hear a logical argument, your first task is therefore to work out exactly what the conclusion is, and then to work out what are the reasons supporting it. Are the reasons actually true? Do the facts really fit properly into the general rules, and if they do fit, do you actually get the stated conclusion?

It’s important to realise that the reasons people present for their conclusions can be wrong. Whether they are facts or general rules they can still be wrong. However, the word “because” has an almost magical effect on people. This is presumably due to the effect I mentioned earlier, where we initially believe what we are told and have to expend mental effort to disbelieve it. When you use the word “because,” people tend to believe that the following reason really is a valid reason, particularly when they are short of time or there isn’t much at stake.

For example, say that two cabs are coming down Baker Street, and Holmes hails the first one at the same time as another gentleman. Who gets that first cab?, If Holmes says to the other gentleman “Do you mind? I need this cab,” the other gentleman is unlikely to be impressed. We would expect some further discussion. However, if Holmes says “Do you mind? I need this cab because I have to get to Paddington Station,” the other gentleman is likely to give way quite meekly and take the second cab. Holmes hasn’t really given a convincing reason: obviously he had to get to somewhere, otherwise he wouldn’t have hailed a cab. But such is the power of “because,” that even when the reason offered is completely bogus, it’s quite convincing. Be careful if someone hands you a cheeky “because” like this. Take another look. note 36

When we take a closer look at more proper arguments, they can also be wrong, but for more complex reasons. Let’s have a look at some simple examples of logical argument—can you label the parts? And when you check the argument, does it work?

The phrase “detectives catch criminals” is short for “all detectives catch criminals.” In this case the reasons are true, and they lead to the conclusion.

The phrase “London is in England” is short for “all things that are in London are also in England.” Again, the reasons are true, and they lead to the conclusion.

The conclusion “Holmes is going to Dartmoor,” though true, is not supported by the reasons: we have two facts, not a fact and a general rule. They are the wrong reasons for this conclusion, even though they are both true. They don’t combine to produce the conclusion, so the argument is false, even though the conclusion happens to be true.

The phrase “authors like cheese” is short for “all authors like cheese.” This is a general rule which is false. Not all authors like cheese. Some do, perhaps most, but not all. The conclusion might be true or false: Watson may or may not like cheese. I’m not sure. Either way, the argument is wrong because the reasons don’t support the conclusion. (Even if we had said “some authors like cheese,” which would be true, the conclusion would still be false: we could only conclude that Watson might like cheese.)

The conclusion is true, but it is not supported by the reasons. We have a fact and a general rule, but the fact doesn’t fit into the “hole” in the general rule. The general rule concerns authors, but the fact is not about authors. Again, we have the wrong reasons for the conclusion, so the argument is false even though the conclusion happens to be true.

Of course, these are very simple arguments. Real arguments have more facts and more general rules, but they slot together in just the same sort of way. For example we could have the following argument regarding when Holmes and Watson’s train can leave Paddington Station:

The train can leave only if the engine is ready
and the driver is allowed to start.	(general rule)
The engine is ready when it has enough coal
and water for the journey and steam is up.	(general rule)
The engine has enough coal for the journey.	(fact)
The engine has enough water for the journey.	(fact)
The engine has steam up.	(fact)
The driver is allowed to start when the signal is set to “proceed”
and the guard blows his whistle.	(general rule)
The signal is set to “proceed”.	(fact)
The guard has blown his whistle.	(fact)
Therefore, the train can leave.	(conclusion)

We can slot each fact into a hole in a general rule, but this time each general rule has several holes to fill before it disgorges its conclusion. We need the fact “the engine is ready” to slot into the first general rule, but we can only get that by making it as a conclusion using the second general rule and some more facts. It is in the nature of more complex arguments that some intermediate facts, like “the engine is ready,” are derived as conclusions from other general rules.

Provided that the structure of the argument is correct, provided all the facts and general rules slot together correctly, then we can also use an argument like this as a plan to make the train leave. What do we have to do? Does the engine have enough coal? Check. Does it have enough water? Check. Does it have steam up? Check. And so on: if we can make all the facts come true, then we can make the conclusion come true.

On the other hand, if we observe that the train has not left and want to know why, we can play detective, and work backwards. Is the signal set to “proceed”? Yes. Has the guard blown his whistle? Yes. Then the driver is allowed to start, so the problem must be that the engine is not ready. Why is that? We can work our way further backwards, eliminating reasons and eventually we will find the false “fact” which is the reason for our delayed departure. (This process is called “debugging” by computer hackers and “detection” by Holmes.)

Another way we can use an argument like this is as an explanation. With an explanation, we accept that the conclusion is obviously true. For example, when the train has actually left the station, and the platform is empty, the conclusion is certainly true. With an explanation we are looking for causes; we want to know why it happened.

However, when we try to use a complex argument in any of these ways, as a plan to make something happen, for debugging what went wrong or as an explanation why something happened, we find that we have an unpleasant problem: hidden assumptions. What if we had a failure of imagination, and we left out some vital condition from one of the general rules? For example, what if the driver is in the canteen, still drinking his cup of tea? The train couldn’t leave yet, could it? We should really have had an extra condition before we said that the engine was ready, something like “the driver is in the engine.” Then we could check that was true too. But in practice, however complete we try to be, there will always be something else that could go wrong. What if the driver was in the engine, but he was hit by a meteor? Should we put that in as a extra condition? No! We have to draw the line somewhere, and only choose general rules which are practically relevant. But clearly, this is a matter of judgement, and we might disagree about particular choices.

All of the examples we have seen so far are what the medieval school teacher would have called “syllogisms” — we are presented with all the general rules and all the facts needed to form the conclusion. We don’t need to bring any commonsense knowledge, everything we need is there already. But in practice when we use logical arguments, we tend to be not quite so thorough. We tend to leave unsaid some things that we rely on. For example:

Socrates is a man so	(fact)
Socrates is mortal.	(conclusion)

The medieval school teacher would call this an “enthymeme” (pronounced “enth-i-mee-m”). It’s a syllogism with some of the reasons missing. In this case the general rule is left out, and the reader has to use their stock of commonsense knowledge — they have to supply a general rule which bridges the gap. In practice most real logical arguments are like this. We usually don’t supply all the necessary reasons. Our listeners would be dreadfully bored and cut us off, saying “Yes, I see what you mean.” So we leave out lots of facts and general rules that we take for granted as commonsense knowledge. We call these missing reasons assumptions. Notice that they are not quite as invisible as the previously mentioned hidden assumptions, because as we try to follow the reasons in an enthymeme and form the conclusion for ourselves, we will find that one of the reasons we need is missing. You don’t need imagination to notice the missing reason, just diligence. Still, some people use arguments with such a host of missing reasons that some of their assumptions are actually quite well disguised: it’s a lot of effort to work them all out explicitly. (But this is exactly the kind of argument where it really is worth the effort, since the weak point in their argument is most likely in some assumption that they have swept under the carpet.)

We are now nearly finished with the lightning course on logical argument, but before we can rejoin Holmes and Watson (currently travelling on another train from Exeter to Tavistock) we need to look a bit more closely at general rules and introduce hypothetical facts.

We have seen general rules like “all men are mortal” and like “if the engine is ready then the train can leave.” At first sight these seem quite different in nature. But behind the scenes they are really very similar when we re-phrase them in terms of hypothetical facts, things that we explicitly suppose to be true, without concerning ourselves yet whether they really are. For example, all these general rules really say the same thing:

All general rules implicitly have this kind of “suppose” inside them, which is why only some facts will slot into the “hole” in the general rule. The hypothetical fact and the actual fact need to match up in their properties or we can’t replace one with the other.

We can also invent our own hypothetical facts and put them into an argument. Sometimes we do this because we don’t think it matters whether a particular fact is true or not, and we think we can prove our conclusion either way. In that case, to avoid getting bogged down in a futile quarrel about whether or not that fact is true, we can let our opponent have it their way “for the sake of argument” and show them that we can prove our conclusion regardless. When we suppose a fact to be true for the sake of argument we are not admitting that it is true, we are saying “look, even if you were right about that, it doesn’t make any difference to the conclusion.”

Sometimes we might invent a hypothetical fact and put it into an argument so that we can make a new general rule as a conclusion. For example, suppose Watson wanted to buy a pork-pie while they changed trains on Exeter station. Could he do it?

Watson can buy an pork-pie at Exeter if the shop sells pork-pies
and he has time between connections.	(general rule)
The shop sells pork-pies.	(fact)

We don’t have enough facts to fill in the two slots in the general rule. We only have one fact, so we can’t make any progress. Let’s invent a hypothetical fact, which can fill that other slot:

Suppose Watson has time between connections.	(hypothetical fact)
Therefore: Supposing Watson has time between connections,
he can buy a pork-pie at Exeter.	(general rule)

In this case we don’t say that Watson definitely has time between connections, we just suppose it is true. Fitting the reasons together as before we end up with a new general rule, which includes our hypothetical fact as a condition. The fact which we knew to be true — that the shop does sell pork-pies — has disappeared from sight. The final conclusion could be rephrased as:

Lastly, we might invent a hypothetical fact because we want to disprove it. This is known as “proof by contradiction,” but our medieval school teacher would probably call it “reductio ad absurdum.” If we suppose something to be true, and with other reasons we can reach a conclusion which we know to be false, then something about our argument must be wrong. If the other reasons are true and the argument is constructed properly, then the only possibility is that our hypothetical fact is false. By assuming that something is true, we prove that it’s false. This is a strange, but perfectly respectable technique. We’ll see a great example of this shortly, when Holmes and Watson inspect the scene of the crime on Dartmoor. Let’s return to them now.

Holmes and Watson arrive at King’s Pyland in the early evening sunlight. Inspector Gregory and Colonel Ross, the owner of Silver Blaze, greeted them a few minutes ago at the railway station in Tavistock. The steeples of Tavistock are now just visible over the faded brown curves of the landscape. The moor stretches out in all directions from the isolated house and stables. Colonel Ross’s landau (a kind of open-top horse-drawn carriage) stops and they all get out. Except for Holmes, who is lost in thought, mulling over what they discussed on the way from the station. Watson has to prod him. Colonel Ross is already leaning towards the conclusion that Holmes is a bit of a nutter.

The only suspect for the murder is Fitzroy Simpson, a somewhat disreputable thirty-something gentleman who makes a living as a bookmaker, taking bets at London clubs on the results of horse races. Two days ago, on the night of the crime, he appeared out of the rain and darkness about 9 p.m., just as the maid from the house was taking a mutton curry supper to Ned Hunter, the stable-boy keeping watch over Silver Blaze. At first Simpson claimed to be lost, then he tried to offer money for racing tips. The maid ran back to the house, but the stable-boy came out with the dog to chase him off. By the time he had unlocked the door and locked it again behind him, Simpson had gone.

After this disturbance, the stables were locked up again for the night. Ned Hunter was on watch downstairs with the horses. The two other stable-boys, who were eating their supper at the trainer’s house when Simpson appeared, went to sleep upstairs in the loft over the harness-room. Later that night, the trainer John Straker and his wife woke, rain still pattering on the windows. Straker had a bad feeling and told his wife he was going out to check on the horses.

In the morning, the rain had gone and so had Silver Blaze. The stable door was wide open and Ned Hunter, who should have been on watch, was sound asleep in a chair. So deeply asleep that no-one could wake him. Drugged. Straker was found clubbed to death in a hollow on the moor about a quarter of a mile away. Simpson’s cravat was on the ground nearby.

That was yesterday. The police quickly tracked down Simpson and arrested him. When they tested the remains of the mutton curry they found traces of opium. Hunter the stable-boy swore that Simpson had slipped it into his food when the maid was passing it in through the stable window. But considering the story again this evening, Holmes is not convinced.

Inspector Gregory thinks they can make a case against Simpson, but he isn’t entirely convinced either. Gregory takes Holmes from the house to the stable and then to the hollow where the body was found. Holmes can’t find anything to fault in Gregory’s investigation. Whatever he asks, Gregory is there already. Until Holmes picks a spent match off the ground near where Straker was found dead.

“I cannot think how I came to overlook it,” says Gregory, crestfallen.

Holmes is on a roll now, and tells Gregory that he and Watson need a little more time to look around the moor. Gregory leaves them to it. With the sun on the horizon and the ferns and brambles golden red, they set off to find Silver Blaze. They apply the scientific method to their problem, and an hour later, with the twilight turning the landscape grey they succeed where Gregory failed.

“See the value of imagination,” says Holmes to Watson. “It is the one quality which Gregory lacks. We imagined what might have happened, acted upon the supposition, and find ourselves justified.”

Now they have found the missing horse, Holmes decides to play a little game with Colonel Ross, to pay him back for his failure so far to be impressed. He insists to Watson that they keep their discovery a secret.

But what about the murder? It’s dark by the time they get back to King’s Pyland. Holmes announces that they have done all they can and are going to catch the night train back to London. He’s quietly pleased with himself. Colonel Ross is disappointed and entirely unimpressed with Holmes. Holmes and Watson get into the carriage to ride back to the railway station. As they are about to leave, Holmes asks one of the stable-boys an apparently unconnected question about the medical problems of local sheep, and is very pleased with the answer. Inspector Gregory is intrigued.

“Is there any other point to which you would wish to draw my attention?” he asks.

“To the curious incident of the dog in the night-time,” says Holmes.

“But the dog did nothing in the night-time.”

“That was the curious incident.”

And with that the carriage sets off. What is Holmes getting at? He is inviting Gregory to invent a proof by contradiction, along the following lines:

Suppose that Simpson came to the stable that night.	(hypothetical fact)
There was a dog in the stable.	(fact)
Simpson is a stranger.	(fact)
Dogs bark at strangers in the night.	(general rule)
Therefore, supposing that Simpson came to the stable that night,
the dog would have barked.	(conclusion)
But we know the dog didn't bark that night.	(fact & contradiction)
So Simpson can't have come to the stable that night.	(conclusion)

We know the dog didn’t bark because the other stable-boys, asleep in the loft, would have woken up. They were not drugged. We can go further and say that whoever came to the stable was not a stranger to the dog. Whoever came presumably also arranged for Ned Hunter’s curry to be drugged. This narrows down the number of suspects rather sharply. If you haven’t read the story already I won’t completely spoil the ending for you. Needless to say, eventually the horse is recovered and the murderer unmasked. Reading between the lines we notice that Holmes probably makes a considerable amount of money out of the case by betting on Silver Blaze at 15-to-1 in the Wessex Cup while the rest of the world believes that the horse is lost for good. Colonel Ross is finally impressed with Holmes. Holmes offers him a cigar.

 

While Conan Doyle’s Sherlock Holmes stories are entertaining, to be honest they are mostly not very good examples of logical argument. A lot of the stories rely on Holmes’ remarkable powers of observation. Sometimes there is a lesson for us — for example in The Norwood Builder the police at first miss a key piece of evidence. They miss it because at first it wasn’t there. It was planted later. But generally, we need to look elsewhere to practice our skills of logical argument.

Newspaper articles are good places to look. When you do this you will find that many down-market newspapers don’t present conclusions justified by reasons, but merely string together a sequence of opinion and speculation: unsupported “facts” that the reader is asked to accept on trust. (Most readers are happy to do this because they already believe these “facts.” Remember confirmation bias? People tend to seek out and accept new information which confirms their existing beliefs.) note 37

Better newspapers and news magazines attempt to give reasons for their conclusions, but of course they don’t hand you syllogisms. That would be far too boring. Instead they are written as enthymemes, with many assumptions that you, the reader, have to fill in for yourself. Rather than just reading these articles and believing their conclusions, you should always think “Exactly what is being assumed here? Is that really true?” Practice talking back to the article. After each paragraph, say “So what?” A well written article, for example from the Economist or the New Yorker, is like one half of a conversation. The next paragraph will actually pick up on the other side of the discussion and answer your “So what?”

Other than this kind of practice, is there anything else that you can do to improve your powers of logical analysis? Some kind of “performance enhancing drug” for the mind, perhaps? We like to think that modern science can produce frightening and magical chemicals to turbo-charge our brains, but the evidence is equivocal. Some of the “smart drugs” appear to merely give their user the impression that their performance is being enhanced, without actually improving it. Others seem to increase short-term concentration at the price of long-term amnesia about whatever you were concentrating on. And we know almost nothing about the long-term health impact of routinely taking these new drugs.

However, there are two drugs that we know do improve your performance at logical analysis. They have been around a long time, and their side effects and long-term health impact are well understood. They have been used in Europe since the seventeenth century and they were commonplace in Victorian England. Holmes uses them routinely — in The Hound of the Baskervilles we find Holmes sitting in his Baker Street rooms, thinking hard about the case in Devon. He tells Watson that his body has “consumed in my absence two large pots of coffee and an incredible amount of tobacco.” The drugs are caffeine and nicotine.

Scientists and engineers, social and political revolutionaries, all of them were absolutely wired on caffeine and nicotine for the 300 years from about 1650 to 1950. After that, the rate of smoking tobacco dropped off due to its bad long-term effects on the health of its users. The rate of coffee consumption is of course still pretty high. Personally, I’m quite happy drinking two or three cups of coffee a day. I’m absolutely not suggesting to you that it is a good idea to smoke tobacco. But in a spirit of historical enquiry, I think we should have a good idea what help our predecessors had in their analytical thinking.

A cup of coffee contains about 100mg of caffeine. It takes between 30 minutes and an hour to take its full effect after you drink it. After that it slowly decays, with a “half-life” which varies widely between people, but is generally around 5 hours. (So 5 hours later it will have half as strong an effect, then 5 hours after that half as much again, and so on.) In pregnant women, or women on the pill, the half life is about twice as long.

Caffeine is a stimulant, boosting attention and memory. Users of caffeine suffer withdrawal symptoms such as feelings of fatigue and inability to concentrate for a few days when they stop taking it. This has led some researchers to conclude that the supposed benefits come solely from alleviating these withdrawal symptoms. However, there’s evidence that this withdrawal effect is weak and is only significant in people consuming 5 to 10 cups a day. For lower levels of consumption, caffeine really does boost mental performance. note 38

The optimum level appears to be about 200mg, which you could achieve by having two cups of coffee. Pearl Martin and her colleagues at the University of Queensland in Australia performed an intriguing experiment that demonstrated that at these levels their subjects became more easily convinced of the truth of a strong logical argument, but caffeine made no difference with a weak argument. It appears that caffeine really is the drug of reason.

The problem with caffeine is of course that it keeps you awake, so having it late in the day is a bad idea. As we have seen, if you sleep badly you will be impaired in lots of ways. In previous centuries when smoking was widespread, people could offset the effects of caffeine with nicotine because the two drugs interact in an interesting way.

Nicotine has its effect within a few seconds of inhaling tobacco smoke and has a half-life in the body of about two hours. At low doses it is a stimulant, increasing concentration and alertness. (It appears to improve the symptoms of ADHD, and perhaps in the past people with ADHD self-medicated by smoking.) However, it also reduces the half-life of caffeine to around two hours, so it is possible to drink more coffee or to get to sleep sooner after drinking coffee. In addition, at high doses, nicotine becomes a sedative. So the eighteenth-century gentleman could smoke and consume coffee all day in a coffee-house then smoke himself to sleep in the evening.

Of course the problem with nicotine is that it is highly addictive — no less addictive than cocaine or heroin. And smoking kills you in various ways, principally by lung cancer or heart disease. There are suggestions that the lung cancer might be a recent development, caused by the use of mildly radioactive apatite fertiliser since the early twentieth century. But even if that is true and you can find organic tobacco, the other health risks would still be severe. I really wouldn’t recommend it. note 39

 

Before we leave the topic of logical arguments, I need to mention another health risk. This is a matter of recent research, and still highly contentious, but I think I owe it to you to warn you about it.

In 2009, psychiatrist J. Anderson Thompson and psychologist Paul Andrews published a survey paper The Bright Side of Being Blue: Depression as an Adaptation for Analyzing Complex Problems in Psychological Review, a journal of the American Psychological Association. Analysing the findings of 352 other papers and books, Thompson and Andrews put forward the radical theory that depression might have a purpose, that rather than merely being “malignant sadness,” it might actually be good for something. note 40

This is a dangerous theory, because it directly contradicts the conventional wisdom that depression is essentially a chemical disorder of the brain, best cured by drugs. It’s only to be expected that people who sell drugs or prescribe drugs are going to be hostile to an alternative theory. People don’t like having their beliefs challenged, particularly when there is money at stake. However, as Thompson and Andrews point out, in clinical trials antidepressants often have no significant effect compared with placebos. When they do have an effect, it seems to be only in cases of severe depression. Relapse occurs promptly when the drugs are discontinued. This looks like evidence that the drugs are treating a symptom rather than the cause of depression.

Thompson and Andrews suggest that depression may be like a fever. A fever hurts us and disrupts our life, but it has a purpose in fighting infection. Of course, in some cases the fever can run out of control and kill us, but that’s rare. Perhaps it is the same with depression. Although there are a few cases where the depression is so severe it can cause death by suicide, that’s rare too. Although like a fever it causes suffering, perhaps mostly depression could be helpful, and merely treating the symptoms might only prolong the suffering. But how could depression be helpful?

Thompson and Andrews think that a depressed mood is actually triggered in response to an important complex problem. Just as our adaptive unconscious triggers different emotions in response to the world around us, and those emotions steer our thinking, in their analytical rumination hypothesis the adaptive unconscious triggers a depressed mood in response to an important complex problem that we are unable to solve. This depressed mood then steers us into slow, sustained analytical thinking in several ways: we find that we can’t stop thinking about the problem; it’s difficult to concentrate on other things. We don’t feel like doing other distracting things; we are not interested in enjoying ourselves, even in having sex. We are not interested in engaging with other people, and we lose our appetite, further reducing distractions. And of course, we feel pain and suffering. But the purpose is achieved: in their paper, Thompson and Andrews survey a large number of apparently contradictory experiments and demonstrate that people in a depressed mood really are better at analytical thinking.

If their idea is correct, then something rather clever is going on here: the adaptive unconscious registers that there is a serious problem that it can’t resolve, that can only be resolved by conscious analytical reasoning. Its as though there’s a box labelled “in case of emergency break glass.” The adaptive unconscious registers that there is an emergency and smashes the glass. And so our mood darkens and our analytical powers are focused on to a task not consciously chosen. There’s no reason why we would consciously know what was happening, just as the house-buyers in the previous chapter did not consciously know what kind of house they really wanted to buy. We don’t have privileged access to our own unconscious minds. Often other people can see us better than we can ourselves.

So why did I feel the need to warn you about this? Am I suggesting that you should play sad music and think bleak thoughts to improve your analytical reasoning? No, I’m not. That would probably work, but it would be quite dangerous. No, I’m actually concerned about another effect. Unfortunately, Paul Andrews has shown that the the link between depression and analysis runs both ways: when you are thoroughly focused on an analytical task, that makes you feel more depressed. Which of course, makes you better at the task. Presumably the adaptive unconscious, observing you devoting so much attention to a particular task, comes to the conclusion that this is an Important Complex Problem. So if you focus for a long time on any analytical task that you treat as very important, you risk becoming depressed.

This is the danger. You might feel that you are walking through life wearing lead boots. Whatever you achieve won’t seem good enough. You’ll doubt yourself, whether you can ever do what you set out to, whether you are any good at all. It will be an effort to go on. You’ll ask yourself, “What’s the point?” This pattern of thought has happened countless times to analytical thinkers, from artists to engineers, throughout recorded history.

If you solve the problem, or decide that it isn’t important, then the depression will ebb away. The colour will start to seep back into your life. But if you don’t realise what is happening to you, then you might notice that you are depressed, and be frightened about that. You might fall into the kind of pointless recursive rumination about being depressed that seems to be a key feature of long-term depression. (If your Important Complex Problem is being depressed, rumination will certainly not solve that.) You might decide to dull the pain by taking drugs, either legal anti-depressants, alcohol or illegal drugs. It really is best if you can avoid that. So, notice what is happening to you. You can keep going and use the depression to help solve your problem. You can reconsider whether the problem actually is important. Maybe it isn’t. Either way, realise what is happening and don’t get stuck.

 

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