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observed only one, and having tasted one orange a notion is formed as to how oranges taste.
Thus induction ends with the general principles from which deduction begins. If induction has not established sound principles, deduction has no assurance of safe conclusions. A well-formed deductive syllogism admits of no doubt in its conclusion, provided the premises are well established. Because of the convincing force of the syllogism in itself, the mind is too often satisfied without raising a question as to its foundation in the premises. Deduction cannot increase the certainty of truth beyond the warrant of the induction on which it rests. At best, it can only be said that what it affirms is true provided something else is true. The ignoring of well-established premises and relying on the precision and strength of the deductive syllogism is a leading source of fallacy in argumentation. The two movements of induction and deduction are but the two arcs of a circle, which begin in the individual object and, moving out to the general, return to the individual.
Law of Inductive Inference. — Conviction through induction is based on the belief that what is essential to the part must be common to the whole. This is based on our faith that nature is an organic, systematic whole. If this faith were removed, all induction would be impossible. To carry on an argument by induction is to present such matter and in such a way as to make the strongest appeal to this faith.
A single act of deduction permits no further discussion, but a single act of induction may create only a
probability. What the single act lacks in convincing power must be made good by the repetition of inductive acts. At first thought this would seem a very unsatisfactory process of reasoning, but there comes a point in the accumulation of examples at which the feeling of probability becomés certainty. The number of examples given may range from one to complete enumeration. Other things equal, the certainty increases with the increase of the number to the point of complete enumeration, when absolute certainty is reached. If it be observed that each state has a public school system, then it is absolutely certain that all states have such a system. But this is generalization, and not induction proper; the unknown being reached by the logical judgment rather than by the faith of reason. Induction proper does not reach demonstration. If each state except one had been examined and found to have a school system, it is still possible to think that that one has no such system. But at this point induction ceases, for if the last one had been examined there could be no room for the exercise of inductive faith. Induction is to do service when an examination of all the individuals is impracticable or impossible.
1. Induction from one example is called analogy. An object or a class which resembles a known object in some respects will be expected to resemble it in others. The more complete the resemblance observed, the greater the assurance that they will resemble in the point under question. If it be known that a piece of chalk iş light, white, brittle, and can be used to make a mark, on seeing a second object having the first three marks, the presence of the fourth mark in the second object would be inferred. If, in this case, the second object resembled the first in only two respects, as lightness and brittleness, the tendency, if any, to make the inference would be much weaker. To argue by analogy is to present as many points of resemblance as possible between the known and the unknown terms of comparison.
The number of attributes, however, is not the safest basis of inference. Much more depends on the causal connection in the points of resemblance. If a strange animal were found to have a peculiar structure of the skeleton, it would be safer to infer that all of the class had the same structure than to infer that all of the class had the same color as the specimen examined, even if they resembled in many other superficial points. In arguing by analogy the points of comparison must be shown to be essential to the object. When this cannot be done, the mere accumulation of the number of points of resemblance must be resorted to. If it is to be proved, by its analogy to the earth, that Jupiter is inhabited, the accumulation of all the points of resemblance would have weight; but to show that Jupiter is like the earth in those points that condition human life, would be far more convincing.
2. The lowest phase of induction proper is based on the force of accumulated examples. The first orange observed being yellow does not justify the assertion that all oranges are yellow. But by repeated observations, the mind confidently extends this attribute to all oranges, and does so without perceiving any necessary connection between the color and the orange. We believe only on the ground that if there had been oranges of other colors we should have chanced upon them. As the number increases, probability grows into certainty. Not that this ever becomes the certainty of demonstration, for the opposite of what is affirmed may always be conceived; but the mind rests satisfied in its conclusion. As in the lowest phase of analogy the force of the argument is in the number of points of resemblance, so in the lowest phase of induction the convincing power is in the mere number of examples.
The highest phase of induction seeks a causal connection as the basis of inference. The more fundamental the attributes observed, the fewer the examples needed. It is sometimes impossible to discover an essential relation of the attribute under question to the object in which it is found; as, why an orange is yellow. In such cases there is no appeal from the mere force of accumulated examples. But in most cases arguing by induction consists in pointing out the essential relation of the property under discussion to the others in the examples produced. When the manner of the working of a cause is obvious, there is little difficulty in the process; as, in the rain wetting the ground. We see
have no hesitancy in saying that rain will always produce this effect. The relation the valves sustain to the function of the heart is easily determined, and that all hearts have such parts is confidently inferred. But the manner of the working of a cause cannot in all. cases be detected; as, the cause for a tree's growing more rapidly in one kind of soil than in another. We may not be able to see how two objects are connected, but to know that they are necessarily connected is safe ground for induction. The difficulty is in deciding that there is really a cause and effect relation. Especially is this true in complex phenomena, for in this case the essential is entangled with the accidental. For the methods of testing the presence of this relation, see Mill's “ Logic,” pages 278-291.
This introduces us to the real basis of all argumentation, namely, —
THE RELATION OF CAUSE AND EFFECT.
The primary reason for asserting a relation between two objects is not that of whole and part, but that of the causal connection in the objects themselves. We have seen that a general idea or force produces an individual, and that it is this connection which argumentation seeks to establish. All argumentation rests at bottom on the connection of a productive energy in the phenomena produced. To prove that a certain word is a noun is to prove that it arises under the same mental impulse which produces other words classed as nouns. To prove that the free coinage of silver would improve the condition of the country is to find in free coinage a causal energy which would produce the effect affirmed.
In establishing such causal connection all the thought relations previously discussed are involved;