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provisional opinion. He is the inductive reasoner. He recognizes that one instance is not sufficient to prove the existence of a law; that laws are arrived at only by long observation and careful comparison.
Perhaps on no subject are men so prone to generalize on the strength of a few instances as on the subject of weather, and so we have numberless “ weather signs.” If the sun shines on a certain day known as “ground-hog day,” spring will not open for six weeks. If it rains on Easter Sunday it will rain every Sunday thereafter for seven weeks.
green Christmas, a white Easter," etc., etc. But the majority of such statements express probabilities only, not laws. Many of them are even counter to probability. Some one has observed them to be true once or twice and taken the rest for demonstrated. To prove their unreliability as general statements we have only to extend the series of observations. A dozen concordant observations do not definitively prove; one discordant one disproves.
Bearing in mind this last truth, it is usually not very difficult to expose an error which has grown out of imperfect induction. It requires only the same appeal to facts upon which we relied in the last exercise but one. With this difference, however: the kind of error alluded to in that exercise was due to a thoughtless or willful disregard of facts; the kind of error alluded to here has a certain show of truth because it seems to be supported by facts, the only difficulty being that it is supported by too few of them. The refutation of this last may require an acuteness of perception or a patience in investigation not possessed by many, or it may depend on some fortunate discovery
of one invalidating instance among a host of corroborative ones.
Expose if you can any fallacy expressed or implied in the subjects for discussion offered at the head of this exercise.
INDUCTIVE REASONING (CONTINUED).
Subjects: All Dream Images Derived Solely from Waking Sensations. Some Relations between Animals and Plants in the Struggle for
The kind of argument contemplated in the last exercise was destructive, not constructive. That is, it was devoted to the overthrow of errors that may
have arisen from imperfect induction — a matter, we found, often not difficult. The opposite process, like most constructive processes, is not so simple. But let us, if possible, get a clear idea of what induction is, before we attempt to establish any truth by it.
We expose a piece of oak wood to a flame ; it catches fire. We try a piece of hickory, with a similar result. We try ash, maple, pine, mahogany ; in every case the same phenomenon results — ignition. We conclude that wood is ignitible. We subject gold, silver, iron, lead, bismuth, platinum, to heat; all melt at some temperature or other. We say, metals are fusible. This is inductive reasoning. Logical induction then is the process of discovering general laws - laws which will be found
true throughout entire classes of particulars. These laws are reached only by carefully examining and comparing large numbers of particular instances.
How can we be sure that because twenty metals are fusible, a twenty-first will be ? How can we be sure that the laws arrived at by this inductive process will hold true in cases not yet examined ? We can not be sure. And herein lies the difference between perfect and imperfect induction. Where all the similar cases that can possibly exist have been examined, then only is the induction perfect and the truth arrived at eternally
It may be unassailably true that every state in the United States has a divorce law; it is by no means so certain that every citizen of the United States advocates a divorce law of some kind. So soon as we resort to imperfect induction we render ourselves liable to
Not only ignorant weather prophets but great scientists and philosophers often go astray here. For a long time astronomers felt practically certain that all the satellites in our system revolved about their planets in the same direction. But satellites of Uranus and Neptune were discovered which revolved in the opposite direction.
And yet we make use of imperfect induction. The great majority of our so-called general truths are founded upon it. Rarely are all the particular instances within our reach. They lie beyond us, in the future, out in the universe, we know not where. Nevertheless, we venture to make general assertions in regard to them on the strength of the instances within our reach. We do so because we know we may be right, and because we want some anchorage, even though a temporary one, among the shifting sands of doubt. Scientific induction,
including imperfect induction, is both a legitimate and a valuable means for the extension of knowledge. It is more than that. According to some philosophers it is the only process of reasoning that furnishes us with knowledge at all, and all our knowledge is ultimately due to it.
When the investigation that precedes inductive inference, whether in the world of matter or in the world of thought, is given in detail together with the results and the inferred generalizations, we have one kind of argumentation. Such is our object here: to draw from an array of particular facts a general law or truth, and to present the whole in as convincing a form as may be.
The greatest work that has yet been done in the field of modern science owes its value to the long and patient investigation of facts which preceded every theory the investigator ventured to propound. Note what Darwin says in the introduction to his Origin of Species :
When on board H. M. S. “ Beagle,” as naturalist, I was much struck with certain facts in the distribution of the organic beings inhabiting South America, and in the geological relations of the present to the past inhabitants of that continent. These facts, as will be seen in the latter chapters of this volume, seemed to throw some light on the origin of species —— that mystery of mysteries, as it has been called by one of our greatest philosophers. On my return home, it occurred to me, in 1837, that something might perhaps be made out on this question by patiently accumulating and reflecting on all sorts of facts which could possibly have any bearing on it. After five years' work I allowed myself to speculate on the subject, and drew up some short notes ; these I enlarged in 1844 into a sketch of the conclusions, which then seemed to me probable : from that period to the present day I have steadily pursued the same object. I hope that I may be excused for entering on these personal details, as I have given them to show that I have not been hasty in coming to a decision.
As an example of the investigator's methods, bearing on one of the subjects given above, read the following from the same book :
I am tempted to give one more instance showing how plants and animals, remote in the scale of nature, are bound together by a web of complex relations. I shall hereafter have occasion to show that the exotic Lobelia fulgens is never visited in my garden by insects, and consequently, from its peculiar structure, never sets a seed. Nearly all our orchidaceous plants absolutely require the visits of insects to remove their pollen-masses and thus to fertilize them. I find from experiment that humble-bees are almost indispensable to the fertilization of the heartsease (Viola tricolor), for other bees do not visit this flower. I have also found that the visits of bees are necessary for the fertilization of some kinds of clover : for instance, 20 heads of Dutch clover (Trifolium repens) yielded 2290 seeds, but 20 other heads protected from bees produced not one. Again, 100 heads of red clover (T. pratense) produced 2700 seeds, but the same number of protected heads produced not a single seed. Humble-bees alone visit red clover, as other bees cannot reach the nectar. It has been suggested that moths
fertilize the clovers ; but I doubt whether they could do so in the case of the red clover, from their weight not being sufficient to depress the wing-petals. Hence we may infer as highly probable that, if the whole genus of humble-bees became extinct or very rare in England, the heartsease and red clover would become very rare, or wholly disappear. The number of humble-bees in
any district depends in a great measure on the number of fieldmice, which destroy their combs and nests ; and Col. Newman, who has long attended to the habits of humble-bees, believes that “ more than two-thirds of them are thus destroyed all over England.” Now the number of mice is largely dependent, as every one knows, on the number of cats ; and Col. Newman says, “ Near villages and small towns I have found the nests of humble-bees more numerous than elsewhere, which I attribute to the number of cats that destroy the mice.” Hence it is quite credible that the presence of a feline animal in large numbers in a district might