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Kinds of induction, Mill's five experimental methods, and how to judge the strength of an argument from analogy.
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In brief
Induction extends from observed to unobserved cases.
Induction extends from observed to unobserved cases. The conclusion is only probable, and the argument is judged strong or weak. Perfect induction (complete enumeration) is deductive in force; imperfect induction rests on a sample. The inductive leap is justified by the uniformity of nature and the law of causation.
In brief
Method Principle Key idea Agreement If instances of a phenomenon have only one circumstance in common, that circumstance is the cause (or effect) Look for what is common…
| Method | Principle | Key idea |
|---|---|---|
| Agreement | If instances of a phenomenon have only one circumstance in common, that circumstance is the cause (or effect) | Look for what is common |
| Difference | If an instance where the phenomenon occurs and one where it does not differ in only one circumstance, that circumstance is the cause | Look for the single difference |
| Joint Method of Agreement and Difference | Combines the two to reduce error | Double check |
| Residues | Subtract the part known to be caused by earlier antecedents; the remainder is caused by the remaining antecedent | Look at the remainder |
| Concomitant Variation | Two phenomena that vary together in degree are causally connected | Look at variation in degree |
The method of difference is the most reliable (it is the basis of the controlled experiment); agreement is the weakest because common factors may be coincidental. Concomitant variation is used when the cause cannot be removed (the tides and the moon).
In brief
An analogy argues that because two or more things are alike in some known respects, they are likely alike in a further respect.
An analogy argues that because two or more things are alike in some known respects, they are likely alike in a further respect. It is an inductive argument; the conclusion is probable; it is judged strong or weak.
Form: A has properties a, b, c and d; B has properties a, b and c; therefore B probably has d.
What strengthens an analogy:
A larger number of relevant similarities.
A larger number and variety of cases compared.
Greater relevance of the shared properties to the conclusion property.
A more modest (less ambitious) conclusion relative to the premises.
What weakens it: relevant dissimilarities, irrelevant or superficial similarities (false analogy), and an over-ambitious conclusion.
Related points: Paley's watchmaker argument (design implies a designer) is a classic analogy. Refutation by logical analogy shows an argument is invalid by producing a parallel argument of identical form with obviously true premises and a false conclusion. In Indian logic the corresponding pramana is upamana.
Verbal and number analogy items ("Pen : Write :: Knife : Cut") test the relationship: part–whole, cause–effect, tool–function, genus–species, synonym, antonym, producer–product, degree, sequence. First find the relation between the first pair, then apply it to the second pair.
Practise with free MCQs and answer keys, then return here to fix what you got wrong.
↑ Module 3: Western Logic: Induction, Analogy and Venn Diagrams · All 19 topics in Logical Reasoning · Unit overview and sample MCQs
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