A falsifiable hypothesis is not a fraudulent or inappropriate hypothesis but rather one that is susceptible to being disproved (see Chapter 1). An example of a falsifiable hypothesis is: “The patient has consolidation in the left lower lobe.” This is falsifiable because it is possible to demonstrate that there is no consolidation in the left lower lobe.

In contrast, Galen’s hypothesis about his cure for the plague was not falsifiable: “This cure is efficacious in all cases in which it has been tried; except in those that were so sick that they were going to die anyway.” One cannot prove that the survivors would have died if they had not received his cure (or that those who did die would not have lived without it).

A differential diagnosis (vide infra), as discussed in Chapter 3, should be a list of falsifiable hypotheses.

Negative propositions are frequent in medicine. Here are some clinical examples:

Although negative propositions such as these are difficult to prove, they can be easily disproved (as by counterexample). In other words, they are falsifiable.

As a general rule, negative propositions, if universal, cannot be proved. For instance, if I say, “There are no unicorns,” this implies that neither you nor I have yet seen a unicorn; furthermore, neither of us will find a unicorn in the future; and finally, there are no unicorns hiding in the basement (or perhaps on Mars) that we have overlooked. Such a universal proposition cannot be proved. However, a sufficiently restricted negative proposition can be proved, for example, “There are no visible unicorns in this room right now.” Furthermore, the latter can be disproved (if you open your eyes and see one), so it is falsifiable.

Every positive proposition in a differential diagnosis list implies negative propositions regarding the other entries on the list, assuming that Occam’s razor (see Chapter 26) holds. That fact, plus the general difficulty of proving negative propositions, may be the ultimate basis for the rule that “one should never say never in medicine.”

A restricted kind of negative proposition that is commonly used in science is called the null hypothesis. This is the hypothesis that states there are no differences between two groups.

Let us say that we have randomly allocated some patients suffering from a given disease into two groups. One group (the experimental group) is given a new medicine and the other (the control group) is treated identically except that it does not receive the new medicine. Differences in outcome between the two groups can legitimately be attributed to the new medicine; we avoid the post hoc ergo propter hoc fallacy (vide infra) by including a prospective control group.

Although we are seeking positive information by doing the experiment—about whether the new medicine does (or does not) work—we proceed by attempting to disprove the null hypothesis (i.e., by trying to refute the proposition that the two groups are as alike as two random samples drawn from the same population or universe). Customarily, we usually consider the null hypothesis to be disproved if the probability of the differences arising randomly is shown to be less than 5% (p < 0.05). Remember, however, that only a fraction of studies are published. The published one may have been the only one of 20 to show a “statistically significant” result.

In clinical medicine, we examine one patient at a time. In this setting, the null hypothesis is that he falls within the normal distribution of the rest of the population of healthy people (or of people who do not have the disease that is under consideration).

The student who is philosophically inclined will ask: Does this mean that medical research, and worse, clinical medicine, is basically probabilistic? The answer is yes. The conclusions are arrived
at in medical research by probabilistically refuting the restricted negative proposition known as the null hypothesis. (The restrictions are generally hidden in the case record or in the “Materials and Methods” section of a journal article.)

Indeed, all “proofs” related to real phenomena (that is, phenomena outside the abstract worlds of mathematics and symbolic logic) involve just this type of probabilistic thinking. This tends to be frustrating to the medical student, who is not trying to do something negative but rather to arrive at a positive diagnosis. In a fundamental sense, all positive diagnostic statements are umbilically related to the act of rejecting other possibilities (such as “normality”). In conditions like “essential hypertension,” which are generally recognized to be “diagnoses of exclusion,” the process is simply more obvious.

In summary, science cannot prove anything. The scientist is engaged in the activity of trying to disprove things.

To illustrate this point, there is an apocryphal story about Galileo. While he and a friend watched ice float down the river one winter, they fell into a dispute as to whether the ice floated because of surface tension and the flat shape of the ice floe or because the specific gravity of the ice was less than that of the water. The sun was shining, and they reasoned that if the sun melted the ice floe from the sides and changed its shape and if it then sank while they were watching it, those events would support the surface tension theory—but the ice floated around a bend in the river and disappeared.

They then proposed to go to the laboratory and carve a small piece of ice in the shape of the ice floe they were observing. This model could be placed in a vessel containing hot water. Again, if it melted from the side and if it then sank, those events in tandem would support the surface tension theory.

As they were proceeding to place the ice model into the water, Galileo suddenly had an idea and changed the experiment. “Instead,” he exclaimed, “let’s place the ice at the bottom of the water and see what happens.”

Some historians of science consider this a pivotal point in the history of ideas. The advantage of Galileo’s modification of the experiment was that whether the ice floated to the top or stayed on the bottom, the result would admit of one and only one of the two available hypotheses, having effectively refuted the other. This is the same type of reasoning that an effective clinician employs in his handling of signs, symptoms, and laboratory tests. He seeks tests whose results exclude one of the possibilities.

To return to the ice floe experiment, if the piece of ice failed to float to the top, then it could not be of less specific gravity than the water, and the surface tension theory must be correct. If it did float, it refuted the idea of surface tension as the explanation because surface tension did not operate at the bottom of the container, and so the specific gravity theory would stand. Of course, if there were a third explanation that neither Galileo nor his friend had considered, they could well draw an incorrect inference from the result of the experiment. Similarly, diagnosis by exclusion is treacherous if the differential diagnosis is incomplete.

To avoid error, it is important to keep the probabilistic nature of medicine constantly in mind whenever you listen to case presentations and read about clinical medicine. The probabilistic nature of your conclusions should be made as explicit as possible.

When negative propositions are presented, there are several possible levels of certainty. If someone makes a statement such as example 1 or 2 under the “Negative Propositions” section above, it might mean a number of different things.

First, the speaker may simply be stating a belief. Second, he may be recounting a remembered experience. Without documentation, this level is approximately as reliable as a statement of belief. (I have done a number of clinical projects in which I collected data prospectively by writing the clinical experience on a card and filing it out of sight. On a regular basis, I have found, on reviewing the written records, one or more situations I would otherwise have sworn I had never seen. Most clinical scientists have had similar experiences.) Third, the speaker or author may have documented personal experience. In this case, the proposition might be proved, if sufficiently restricted. (Proposition 1 is a good example. If the speaker cannot determine the heart borders by percussion, then the limited negative proposition might be true … for him. A problem is born, however, when he assumes that all others are equally lacking in this skill, that is, when he extrapolates from a limited negative proposition to a universal one.) Fourth, the speaker may intend to make a much stronger, more general statement: “It never was and we don’t expect it to.” The expectation may be based on a scientific body of work that predicts (but does not prove) that something will not happen in the future. Expectation, however reasonable, is still not a proof.

The scientific physician will strive to achieve the highest level of certainty that is possible and not to overstate the level of certainty that exists.

You will recognize inferential reasoning as illustrated in this anecdote:

Medical Student: “I saw Smith get on the bus this morning. He had been drinking and gambling.”

Scientist: “Did you see him drinking?”

Medical Student: “No.”

Scientist: “Did you see him gambling?”

Medical Student: “No.”

Scientist: “Then how can you scientifically make the statement that he had been drinking and gambling?”

Medical Student: “When he got on the bus, he gave the driver a blue chip and told him to keep the change.”

Still, inferential reasoning is full of potential for error (vide infra).

The logical handling of clinical data has been discussed in extended form (Bernard, 1957; Feinstein, 1967), but a few principles are listed here, in addition to those discussed above. I take them to be self-evident, and they were generally accepted by house staff, faculty, and students when presented in the form of an opinion questionnaire (Sapira, 1980). Nevertheless, they are frequently violated in practice.

Rule 1. If some of the findings supporting a new diagnosis can be reasonably rejected as either artifactual or related to a preexistent or coexistent diagnosis, such rejection of these findings does not, per se, refute either the new diagnosis or the verity of the other findings.

Rule 2. The fact that a finding is elicited by only a minority of observers does not mean that the finding can reasonably be rejected as artifactual.

Comment. If a finding is elicited, it is a finding, assuming that clinicians are not hallucinatory or tending toward intentional obfuscation. The finding could have been transient, or perhaps only a minority of the observers might have the skills to elicit it, or perhaps it was misinterpreted or overinterpreted by an unskilled examiner.

Dr Claude Bernard was frequently asked how one could determine which of two identical experiments yielding contrary results should be considered the correct one. Dr Bernard answered that both should be considered correct because two identical experiments could not yield different results. He then pointed out that to yield opposite results, there must have been unrecognized and differing conditions between the two experiments and these would ultimately be shown to be the cause of the differing results. I believe Bernard’s rule is the antecedent of this second principle.

Rule 3. If there are findings whose validity is not contested, supporting a diagnosis with which a consultant does not agree, the consultant is obligated to offer an alternative diagnosis that will also explain the findings.

Rule 4. Positive findings are more important than negative findings, except for those negative findings that are known as “excluders.” (For example, the absence of an increase in the serum bromide concentration would be an “excluder” for the diagnosis of bromism.)

Comment. The antecedent of this principle was apparently formulated by Dr Jack Myers and popularized by Dr Eugene Stead:

Rule 5. If a patient has n findings, the patient’s diagnosis (or diagnoses) should explain all n findings.

Comment. This principle is most frequently violated by sophomore medical students. Because of their praiseworthy intent to “get the diagnosis” (which they correctly assume to be a precondition for the patient’s selection for examination by medical students), students emphasize those positive findings that support their first diagnosis but fail to consider other findings that would suggest an alternative diagnosis.