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5.         Inductive Reasoning  --  Good and Bad

5.1       Introduction  --  Semmelweis’s Quandry: Deduction is Not Enough

            Try to imagine a time and place before we understood that “microscopic entities” (bacteria, viruses, etc.) could cause disease.  Vienna in 1847 was such a place.  Of course, even then medical doctors believed that various illnesses might have “natural causes.”  They understood that throughout history epidemics had been observed to spread from town to town as if the disease was somehow carried by earth, air or water.  That is, they spoke of “epidemic influences” as “atmospheric-cosmic-terrestrial changes, as yet not precisely defined, that often extend over whole countrysides.”  Consider the following precis of the autobiographical account of nineteenth century physician Dr. Ignaz Semmelweis in his The Etiology, Concept, and Prophylaxis of Childbed Fever.

Semmelweis was bewildered.  It had been seven years since the 1840 decree that separated male students studying to be obstetricians from female students studying to be midwives at his large Vienna maternity hospital.  During this time the male students took care of women about to give birth in the First Clinic while female students took care of women in the Second Clinic.  Unfortunately, many women (and newborns as well) died at both clinics from an illness called “childbed (puerperal) fever.”  But the per capita incidence of death from childbed fever in the First Clinic was more than three times as great as in the Second Clinic.  Why the difference?

Semmelweis tried to think of everything he could that might explain things.  First, however, he discounted “epidemic causes” since there was no reason to suppose that such “atmospheric-cosmic-terrestrial changes” would affect one clinic more than the other.  Indeed, there was a lower incidence of childbed fever among those women who delivered on the streets of Vienna than in either the First or Second Clinic.  Given this, how could the cause be “epidemic?”

No, Semmelweis decided, the cause could not be “epidemic,” rather it must be “endemic” to the hospital or its surroundings.  But what?  Could the cause be overcrowding?  No.  The Second Clinic was much more crowded than the First and, indeed, crowding had increased in the Second Clinic over the past seven years as word had spread concerning the many deaths that occurred in the First Clinic.  Poor ventilation?  No, it was the same in both clinics.  Could it be the “rough handling” of the women by the Male medical students, as one government appointed commission suggested?  This too seemed wrong.  Semmelweis could find little difference between the manners in which examinations were conducted in the two clinics.  Moreover, the “roughness of examinations” could not compare with the trauma of the birthing process itself.

There were some differences in technique between the clinics.  In the First, women gave birth lying on their backs.  In the Second on their sides.  Semmelweis changed the technique of birthing in the First Clinic to mirror that of the Second.  It had no effect.

Was the cause of the differences psychological?  The priest who administered to the dead had direct access to the Second Clinic  --  he could enter and leave with little disturbance.  To get to the First Clinic, however, the Priest had to walk through five rooms preceded by an attendant ringing a bell and this understandably caused great anxiety for First Clinic patients.  Semmelweis arranged with the Priest to come to the First Clinic by a stealthier route without the ringing of bells.  But again this had no effect.  [To be continued.]   

            As we saw in Chapter 4, the study of the structure and quality of deductive reasoning has had a long history and over the centuries many techniques have been developed for representing and testing the validity of deductive arguments.  It is unusual, however, when deductive reasoning by itself can solve any of our problems of living/action & reflection.  As suggested by the above, at the beginning of his inquiry Semmelweis has no idea about what might be the solution to the problem that he and his patients face.  Thus it is impossible that he give a deductive argument in support of a solution.  Instead, Semmelweis must engage in a process of inquiry to find both a solution as well as reasons for why his solution is a good one.  This requires a kind of reasoning that is quite different from the deductive reasoning thus far examined.  This non-deductive reasoning, or, as it has been traditionally called, inductive reasoning, is the subject of the present chapter.

5.2       Inductive Reasoning  --  Strength and Worthiness

What is inductive reasoning?  Here is a simple example:




(Just for the record, Angel Falls is located in southeastern Venezuela and is the highest waterfall in the World having an uninterrupted drop of over 800 meters.)

            Is this a good argument?  I think that most people would agree that it is.  But look at how we might symbolize this argument.

                        EX. 5.2-b

The diagram indicates many individual instances of people jumping off Angel Falls and in each instance the person breaks his or her neck.  But unlike valid deductive arguments, the logical information contained in the premises of the above argument does not include the information contained in the conclusion.  Indeed, in this case the claim made by the conclusion contains those made by the premises and goes beyond them.  This is the hallmark of inductive reasoning.  The truth of the premises of a good inductive argument does not guarantee the truth of its conclusion but the truth of the premises does make the truth of that conclusion very likely.  Thus, inductive reasoning is by its nature inconclusive.  The premises of a good inductive argument give appropriately strong support to their conclusion yet it remains possible that if the premises are true, the conclusion may still be false.  If the premises are in fact true, however, we think that this provides strong support for the claim that the conclusion is also true.

            In a manner analogous to deductive arguments we may talk of both the hypothetical (if  --  then) structure of the argument and its factual or truth content.  As regards the “if  --  then” structure, inductive arguments can be evidentially adequate or evidentially inadequate.  If we consider a diminished version of EX. 5.2-a, in which we were told merely that “Joe jumped off Angel Falls and broke his neck” and we had no other information concerning Angel Falls and the results of people jumping off, the conclusion that “all persons who jump off Angel Falls will break their necks,” seems “inadequately based” since it is based on too little evidence.  We might say of such an argument that it is a generalization based on too few instances.  However, if we were to continue to add evidence, for example, that other jumpers have suffered similar fates or evidence concerning the nature of Angel Falls and the fragile nature of human beings, at some point our conclusion achieves “adequate support” and we say that our inductive argument is (evidentially) adequate.  On the other hand, analogous to deductive invalidity, in an inadequate inductive argument, if the premises are true, it does not render it likely that the conclusion is true.  Only an (evidentially) adequate inductive argument can do this.

            But we must be careful here.  Even if we formulated an argument with 1740 premises as in EX. 5.2-a, this would not allow us to say that if the premises are all true it renders likely a conclusion that “the moon is made of green cheese!”  Evidence for a conclusion must be not only quantitatively adequate but also qualitatively adequate.  That is, good inductive arguments must be both evidentially adequate and cogent.  If an inductive argument is either non-cogent or evidentially inadequate, it is not an argument such that if the premises are true, the conclusion is likely true.  To mark this, we say that such inductive arguments are weak.  On the other hand, if an inductive argument is both evidentially adequate and cogent, then we say it is strong.  Thus, analogous to the deductive notion of validity, a strong inductive argument is an argument such that if the premises are true, the conclusion is likely true.

            What should we say about strong inductive arguments where the premises are in fact true?  Analogous to the notion of a sound deductive argument, we will say that a strong inductive argument with all true premises is a worthy inductive argument.  Unlike deductive soundness, however, a worthy inductive argument does not guarantee the truth of its conclusion  --  it merely renders it likely.

            To summarize,

5.3       Varieties of Inductive Reasoning  --  Enumerative, Eliminative and Abductive

            Unsurprisingly, some inductive arguments are more complex than others.  Our “Angel Falls argument” (EX. 5.2-a) is an example of simple, enumerative induction.  Here we generalize over a number of individual instances that are similar in relevant respects and based on those relevant similarities, we draw a general conclusion regarding instances of just that kind.  Along with his discussion of deductive reasoning, in his Topics, Aristotle makes reference to such cases of enumerative induction.

[W]e must distinguish how many species there are of dialectical arguments.  There is on the one hand Induction [epagoge], on the other Reasoning [syllogismos].    Induction is a passage from individuals to universals, e. g. the argument that supposing the skilled pilot is the most effective, and likewise the skilled charioteer, then in general the skilled man is the best at his particular task.  (105 a. 10-16)

Aristotle goes on to draw some comparisons between inductive reasoning [epagoge] and deductive reasoning [syllogismos] that continue to be relevant.

Induction is the more convincing and clear: it is more readily learnt by the use of the senses, and is applicable generally to the mass of men, though [deductive] Reasoning is more forcible and effective against contradictious people.

As Aristotle suggests, those intellectual endeavors that rely most heavily on the five senses to obtain information are likewise most heavily invested in inductive reasoning.  Indeed, both the natural and social sciences seem particularly dependent on inductive accounts.  On the other hand, some intellectual pursuits that seem less bound by sensory stimuli  --  pure mathematics is the usual example  --  often depend primarily on deductive reasoning.

            Some commentators on Aristotle have argued that Aristotle’s account of induction as merely “enumerative” does not go far enough.  Early in the 17th century, Francis Bacon argued that good inductive arguments must include not only cases that directly support the general conclusion but also cases that rule out some other conclusion.  This seems particularly relevant for cases of inductive reasoning that purport to draw conclusions about the “cause of something.”  So, for example, if we take EX. 5.2-a to establish the claim that jumping off Angel Falls causes one to break his or her neck, then Bacon would claim that we should also list instances where people do not jump off and do not break their necks.  This may seem silly in this case but Bacon’s variety of eliminative induction does seem relevant in other kinds of cases.  If I claim on the basis of many positive instances that “smoking causes cancer” it seems that I must also be able to show that “cancer is not likely to occur if I don’t smoke.”  Thus “positive instances” by themselves may not prove evidentially adequate to establish causal connection.  (We will return to this point in section 5.4 in our discussion of Mill’s Methods.)

Indeed, some inductive arguments seem far removed from our “Angel Falls” example of simple enumerative induction.  In illustration of this, let’s continue with our story of “Dr. Semmelweis’s bewilderment.”

What was behind these different rates of childbed fever in the First and Second clinics?  Semmelweis was at a loss.  After returning from a much needed rest in Venice he was saddened to learn that his colleague Professor Kolletschka had died while he was away.  Remarkably, it would be the manner of Kolletschka’s death that would provide an important clue in Semmelweis’s ongoing attempts to explain the etiology of childbed fever.

            Kolletschka’s case history was as follows: Kolletschka often conducted autopsies for legal purposes and often he would be accompanied by the medical students from the First clinic.  A few days before he died, he was conducting such an autopsy when a student accidentally pricked Kolletschka’s finger with a scalpel that had been used in the autopsy.  Within 36 hours Kolletschka became very ill and, to the amazement of Semmelweis, the reports of the progression of his symptoms/phases of his disease mirrored perfectly the symptoms of childbed fever.

            Semmelweis had the clue that he needed.  Kolletschka’s “childbed fever” was caused by some kind of “cadaverous particles” that were introduced into his bloodstream by the scalpel used in the autopsy.  Might there be a similar explanation for the greater rate of childbed fever in the First clinic?  Yes.  Semmelweis was well aware that, as part of their training, the medical students would often participate in an autopsy and then proceed to the First clinic where they would conduct examinations of the women about to give birth.  Semmelweis concluded that this often lead to the transfer of cadaverous particles on the hands of the medical students to the patients of the First clinic often resulting in childbed fever.

            To stop this from occurring (and to test his hypothesis), Semmelweis ordered that all medical examinations were to be preceded by handwashing with chlorina liquida (and later chlorinated lime.)  Very quickly, the rate of childbed fever in the First clinic dropped to a level similar to that in the Second.

            In this sophisticated example of largely inductive reasoning we see Dr. Semmelweis going beyond either enumerative or eliminative induction and practicing what the American philosopher C. S, Peirce called abduction.  Sometimes referred to as inference to the best explanation, abductive reasoning is probably the most commonly employed variety of inductive reasoning but it is also the least understood.  In examining the passage above we are likely to agree that Semmelweis’s reasoning was “on the right track,” but why?  What is an “inference to the best explanation” and how do we know when we have achieved a “best explanation?”

            In attempting to answer these questions it is important to remember that abduction is a kind of inductive reasoning.  As such, a good abductive argument must be strong, that is, evidentially adequate and cogent.  This suggests that if we are to understand what counts as an inference to the best explanation we must come to understand what counts as “good evidence” and what doesn’t.  This is difficult.  We do know, however, that when it comes to “evidence” it is not the case that “anything goes.”  Peirce understood this as we can see from the following (slightly modified) passage:

[I]f there be nothing to guide us to the discovery; if we have to hunt among all the events in the world without any scent; if, for instance, [Kolletschka’s contraction of childbed fever] might equally be supposed to depend upon the configuration of the planets, on what was going on at the antipodes, or on anything else  --  then the discovery would have no chance of ever being made. (W3:317)

            What Peirce implies in this passage is that our understanding of what counts as evidence is bound up with our ordinary, commonsense understanding of how our world works.  That is, we do not think that what went on at the South Pole this morning could count as evidence for why I decided to walk to work.  On the other hand, the fact that it was a beautiful Spring Day might well enter into the best explanation of my perambulations.  

            But even if we accept that as regards “good evidence” it is not the case that “anything goes,” we are still left with the difficult question of what makes some “good evidence” better than other “good evidence.”  It is at this point that we must retreat to heuristics  --  “rules of thumb.”  What follows then is a very general statement of the close relationship that exists between “better evidence” and “good abductive reasoning.”

Clearly, much more work needs to be done here if we are to capture this elusive notion of “inference to the best explanation.”  At present, it remains something that, at best, “we recognize when we see it” but about which we can give no definitive analysis.