False Cause, Misdiagnosis, and the Fallacy of Affirming the Consequent
Rick Garlikov

I recently overheard two physicians discussing the following medical mistake.  A teenage girl had come down with mono that even after the fever and other signs went away, left her with a lump in her neck area.  At least one, if not both parents were physicians and they told her it was just from the mono.  Her pediatrician also had said that was what it was.  The girl complained about it repeatedly but every physician said the same thing until years later one did a biopsy and found out it was a malignancy that had been growing from the beginning and then spreading.

The physicians discussing the story lamented about the case and felt bad for the parents (and the girl) but seemed to think it was just a dumb, uncharacteristic, accidental mistake on the part of the physicians involved.

I want to argue here there is strong logical and psychological reason for the error and that it is indicative of many kinds of mistakes, not only in medicine but in all areas of life.  The reasons the misdiagnosis seems dumb in hindsight are that in hindsight mistakes are always more clear than at the time, but in this particular case we also, by just knowing the story is being told and likely has a point, know to look for the less than obvious and normal diagnosis.  The same people who hear the story and say “they should have checked for that” would have made the same mistake, most likely, if faced with the same combination of circumstances with a patient.  Physicians, like everyone else, rarely look for a different explanation once they have thought up one that fits the facts, unless new facts present themselves that confound or deny that explanation.  This is particularly true if the second explanation is so much less likely to occur than the first.

There are a number of common reasons for why this error was made however.   What happened in the above case was that because the parents and the physicians knew she had mono and knew that mono easily caused swollen nodes, some of which stayed swollen or hard, they had a satisfactory explanation for the lump and didn’t seek a different one because they thought there was  no need. 

The first reason they thought there was no need was that it would be rare for this lump to have formed independently of the mono but at the same time as the mono.  Thus, by Occam’s Razor, you don’t seek two causes for phenomena when one will serve (in this case mono and the lump), particularly if the one cause is highly likely (occurs with the phenomena frequently) and the two causes occurring simultaneously are highly unlikely since the second cause – in this case the malignancy – is very unlikely on its own.  The problem with using Occam’s Razor is that it will be wrong sometimes, and the simpler explanation will not be the correct one.  That only shows up though if you discover differentiating circumstances.  In science that occurs when someone notices that some (usually newly discovered), phenomena cannot be explained by the hypothesis that accounted for other  previously known phenomena thought to be relevant.  Then a different explanation has to be sought.  But not until then. However, that shows that in any situation, it is at least logically possible that the initial explanation may not be sufficient. 

When it is known there are likely multiple possible causes for a sign or symptom, physicians know to do differential diagnoses.  The above kind of misdiagnosis tends to occur when multiple causes are thought to be too improbable to have to rule out.  Unfortunately, in a case where one of the possible causes, though rare, can be deadly, it does need to be ruled out because one should not only taken into account probabilities of a diagnosis being wrong but also the value and significance of the possible alternative causes/explanations for the sign or symptom.  Even if a potentially fatal cause has only a 1 in 10,000 chance of occurring, you need to rule it out in every case because you don’t know which case is the 1.  If there are 100,000 cases of the symptom’s appearing every year, and none of them are investigated because each is considered to be highly unlikely, ten people will die unnecessarily.

The second logical and psychological cause of this mistake is the error of “false cause” or often a corollary error known by its latin designation: post hoc ergo propter hoc, which means that if something occurs after an event it was caused by the event.  In most logic books, the examples are clearly not causally related and are examples of either stupidly jumping to a conclusion or examples of how a silly superstition can begin – such as an athlete’s winning or playing well after having had an unusual food the night before, and so he wants that same food before every event; and when he plays well, he attributes it to the food.  The problem is that the fallacy occurs even in cases that seem to be causally related because of frequency of combined occurrence, as in the mono and swollen nodes case, or because there seems to be a reasonable causal connection; that is, the connection seems to make sense even if it is not correct, e.g., attributing a misdeed to greed on the agent’s part because he had a vested interest in the result that occurred, whereas it might simply have been a mistake on his part (and he may not even have known the result would be in his favor).  The equivalent mistake of this sort in a medical diagnosis would be to know that a result could occur from some biochemical pathway that exists, and so it “makes sense” that the first condition caused the second, even though another (unconsidered) pathway would also give the result.

Unfortunately, third, there is a different, even more prevalent and psychologically compelling fallacy that also applies, which is the fallacy of affirming the consequent, which means that one presumes that one can tell a cause from a result, forgetting that since other causes can have the same result, you therefore cannot tell the cause from the result.  Specifically in logic the fallacy is stated in the following form:
1) If A is true, then B will be true.  (E.g., if someone was murdered, they are dead.)
2) B is true. (Abraham Lincoln is dead.)
Therefore 3) A must be true.  (Abraham Lincoln was murdered.)

Now clearly in this case, Lincoln was murdered, but we don’t know it from the information in 1 and 2.  We know it from historical accounts of the story of his assassination by John Wilkes Booth.  If you were to substitute the name “Jones” for Abraham Lincoln, you would not know whether the conclusion was true or not in the above argument.  That shows that argument form is never reliable, even when the conclusion happens to be correct:
1¹) If A is true, then B will be true.  (E.g., if someone was murdered, they are dead.)
2¹) B is true. (Jones is dead.)
Therefore 3¹) A must be true.  (Jones was murdered.)

In science, in medicine, in everyday life, we often commit this fallacy, and often are right purely by coincidence or because we know something else that is not stated in our reasoning.  Most of the time, for example, the conclusion of the following argument would be true:
1²) If the girl in the case above had mono, that would cause the lump and it is just a swollen node.
2²) The girl did have mono.
Therefore 3²) mono caused the lump and it is just a swollen node.

This argument never works; it is always invalid, and what it serves to substitute for is either of the following two arguments, which, if stated would more likely have led to the correct diagnosis:
Argument A:
1³) Only if the girl had mono, would she have such a lump, and it would be benign.
2³) She had mono.
Therefore 3³) the lump is benign.
Since 1³ is clearly not true, and the lump could have a different cause and then be malignant, a differential would likely have been made, particularly a biopsy – just as it would have been made almost automatically if there had not been the mono in the first place which through everyone off track through faulty logic.  Without the mono, the faulty deduction and thus the misdiagnosis would not likely have been made.

Argument B:
1⁴) If the lump is malignant, it is highly improbable she would have mono at the same time the lump appears.
2⁴) She has mono at the same time.
 Therefore 3⁴) It is highly improbable the lump is malignant.

As explained in my essay “The Nature of the Logic of Confirmation in Science”, that is the form I believe accurately describes and validly justifies the scientific method.  The invalid justification of the scientific method is the one most often given, which is the fallacy of affirming the consequent:
1⁵) if a hypothesis is true, its consequences will be observed under certain conditions.
2⁵) the consequences are observed under those conditions.
Therefore 3⁵) the hypothesis is true.
That is the same form of the fallacy of affirming the consequent above and is the same form as the “Jones is dead” argument above.  And, unfortunately this is the form most often used in normal reasoning, though it is never right.

But if argument B had been explicit in the minds of the parents or the pediatrician, there is a chance they would have realized the conclusion -- that the lump’s being malignant is highly improbable – meant it still needed to be checked because they would possibly have realized that even if improbable, it needed to be definitely ruled out because it was so potentially dangerous.  E.g., the reason you don’t play Russian roulette – even with only 1 bullet among 1000 guns is that the improbability of shooting yourself with the bullet is more than compensated for in a bad way by the harm caused if it did occur, and since there is no real “up side” of pulling the trigger if the bullet is not in that chamber, the low probability of the risk does not make it worth taking.  Similarly in the neck lump case, the low probability of the risk the lump is malignant does not justify taking that risk by not checking to rule it out as a possibility.  And that might have been realized by the physicians involved if they had just thought about the logic of the diagnosis correctly.  But that is difficult to do, particularly if one is unaware of the problem, as most people, even intelligent and educated people, are not.  And it is difficult to do in the rush of everyday circumstances, even when one is intellectually aware of the problem.