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Abbreviate Method of Agreement to MoA, Method of Difference to MoD, Joint Method to JM, Necessary Conditions to NC, and Sufficient Conditions to SC.

Source: p 552, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley

[...] However, when any of these methods is used as a basis for a subsequent inductive generalization, the strength of the conclusion is proportional to the number of occurrences that are included. Thus, an application of the method of agreement that included, say, one hundred occurrences might offer stronger results than an application of the joint method that included, say, only six occurrences. By similar reasoning, multiple applications of the method of difference might offer stronger results than a single application of the joint method. [...]

To minimise post length, I have not quoted this textbook's (confusing) definitions of the Methods.

  1. Suppose that more occurrences exist for MoA and MoD than for JM. How do multiple applications of MoA and MoD overpower JM? JM reveals both the NCs and SCs.

  2. Same question as 1, but now suppose the same quantity of occurrences for all 3 Methods.

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I don't have Hurley's book, so I can only proceed from what you've quoted, but I take him to be saying that it is the quantity of the occurrences of the methods that is most significant, not the type. He is not saying that one type of method is intrinsically better than the others, only that the more occurrences you have of any the better. Roughly speaking, this is like saying the more data you have, the more confidence you can have in the inferences you draw from it.

Having said that, such a claim is fraught with difficulties. Merely having more occurrences, or data, is not in itself a guarantee of anything. To make plausible inferences from data one must attend to all kinds of considerations about how the data is gathered, the quality of the data, whether the data sources are independent, what possible biases might be present, what confounding variables might exist, etc.

In particular, the sentence

the strength of the conclusion is proportional to the number of occurrences that are included

is far too strong. No such proportionality can be justified. At most one might claim that an increase in the number of occurrences has a tendency to increase the strength of the conclusion.

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