Relation to Induction
Induction commences with an entity that is labelled X. Whenever it is
observed, X has property A. Therefore, in all instances X has property A. By
this reasoning process induction has established that all instances of X have a
common property A. This is set out in a table in the following way:
Premise
In all observed instances X has property A.
Conclusion
In all instances X has property A.
Figure 8.2 Illustration of Induction
Induction observes the similarity between X and Y. X has property A. Since X
and Y are similar, Y has property A. This means that both X and Y have
property A. This is set out in the following diagran;
Premise 1
X has property A
Premise 2
X is similar to Y
Conclusion 1
Y has property A
Conclusion 2
X and Y both have property A
Figure 8.3 Analogy and Induction
This analysis reveals how induction and analogy are linked. Induction is able to
establish that all instances of X have a common property. Analogy is able to
argue from this that when Y is similar to X, all instances of Y have this
common property as well.
Illustration
Analogy or some similar type of reasoning is commonly used in ordinary
communication. Some examples consist of comparisons such as metaphors
and
and common place phrases such as
“so on
and so
forth”, “and the like” and “as if”. These incorporate analogical reasoning.
A poignant historical illustration comes from the song the Battle Hymn of the
Republic. The lines “As he died to make men holy, Let us die to make men
free” are pure analogy.
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Another example is the saying of Confucius: “I was
angry because I had no shoes then I met a man who had no feet”.
Some proverbs involve analogy in one way or another. (i) There is a hint of
analogy in the proverb: “The first time it is a favour, the second time it is a
right” because repetition echoes the notion of law as a general rule. (ii) The
proverb “if you are in for a penny, you should be in for a pound” is explicitly
analogical. (iii) Two proverbs are based on eschewing analogical reasoning.
___________________
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Julia W Howe Battle Hymn of the Republic 1861. This is the original version of
this line. Later it was altered to read: “As he died to make men holy, Let us live
[not die] to make men free”.
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