Bibliography

Deduction, Induction, and Hypothesis

We may say, therefore, that hypothesis produces the sensuous element of thought, and induction the habitual element. As for deduction, which adds nothing to the premisses, but only out of the various facts represented in the premisses selects one and brings the attention down to it, this may be considered as the logical formula for paying attention, which is the volitional element of thought, and corresponds to nervous discharge in the sphere of physiology.

But, because all inference may be reduced in some way to Barbara, it does not follow that this is the most appropriate form in which to represent every kind of inference. On the contrary, to show the distinctive characters of different sorts of inference, they must clearly be exhibited in different forms peculiar to each. Barbara particularly typifies deductive reasoning; and so long as the is is taken literally, no inductive reasoning can be put into this form. Barbara, is, in fact, nothing but the application of a rule. The so-called major premiss lays down this rule; as, for example, All men are mortal. The other or minor premiss states a case under the rule; as, Enoch was a man. The conclusion applies the rule to the case and states the result: Enoch is mortal. All deduction is of this character; it is merely the application of general rules to particular cases.

Induction infers a rule. Now, the belief of a rule is a habit. That a habit is a rule active in us, is evident. That every belief is of the nature of a habit, in so far as it is of a general character, has been shown in the earlier papers of this series. Induction, therefore, is the logical formula which expresses the physiological process of formation of a habit.

We may say, therefore, that hypothesis produces the sensuous element of thought, and induction the habitual element.

Hypothesis is where we find some very curious circumstance, which would be explained by the supposition that it was a case of a certain general rule, and thereupon adopt that supposition. Or, where we find that in certain respects two objects have a strong resemblance, and infer that they resemble one another strongly in other respects. [—]

As a general rule, hypothesis is a weak kind of argument. It often inclines our judgment so slightly toward its conclusion that we cannot say that we believe the latter to be true; we only surmise that it may be so. But there is no difference except one of degree between such an inference and that by which we are led to believe that we remember the occurrences of yesterday from our feeling as if we did so.

Suppose I enter a room and there find a number of bags, containing different kinds of beans. On the table there is a handful of white beans; and, after some searching, I find one of the bags contains white beans only. I at once infer as a probability, or as a fair guess, that this handful was taken out of that bag. This sort of inference is called making an hypothesis. It is the inference of a case from a rule and a result. We have, then–

      DEDUCTION.

Rule.–All the beans from this bag are white.
Case.–These beans are from this bag.
.·.Result.–These beans are white.

      INDUCTION.

Case.–These beans are from this bag.
Result.–These beans are white.
.·.Rule.–All the beans from this bag are white

      HYPOTHESIS.

Rule.–All the beans from this bag are white.
Result.–These beans are white.
.·.Case.–These beans are from this bag.

Induction infers a rule. Now, the belief of a rule is a habit. That a habit is a rule active in us, is evident. That every belief is of the nature of a habit, in so far as it is of a general character, has been shown in the earlier papers of this series. Induction, therefore, is the logical formula which expresses the physiological process of formation of a habit. [—] We may say, therefore, that hypothesis produces the sensuous element of thought, and induction the habitual element.

… the distinction between induction and hypothesis. In the main, it is broad and decided. By induction, we conclude that facts, similar to observed facts, are true in cases not examined. By hypothesis, we conclude the existence of a fact quite different from anything observed, from which, according to known laws, something observed would necessarily result. The former, is reasoning from particulars to the general law; the latter, from effect to cause. The former classifies, the latter explains. It is only in some special cases that there can be more than a momentary doubt to which category a given inference belongs. One exception is where we observe, not facts similar under similar circumstances, but facts different under different circumstances–the difference of the former having, however, a definite relation to the difference of the latter. Such inferences, which are really inductions, sometimes present, nevertheless, some indubitable resemblances to hypotheses.

… So that induction is the inference of the rule from the case and result.
But this is not the only way of inverting a deductive syllogism so as to produce a synthetic inference. [—] We have, then–

      DEDUCTION.

Rule.–All the beans from this bag are white.
Case.–These beans are from this bag.
.·.Result.–These beans are white.

      INDUCTION.

Case.–These beans are from this bag.
Result.–These beans are white.
.·.Rule.–All the beans from this bag are white

      HYPOTHESIS.

Rule.–All the beans from this bag are white.
Result.–These beans are white.
.·.Case.–These beans are from this bag.

We, accordingly, classify all inference as follows:

      Inference.

      |——————————|
Deductive or Analytic.   Synthetic.
                                 |—————–|
                            Induction.   Hypothesis.

Induction is where we generalize from a number of cases of which something is true, and infer that the same thing is true of a whole class. Or, where we find a certain thing to be true of a certain proportion of cases and infer that it is true of the same proportion of the whole class.