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Page 157
Induction, and Abduction. Let's try to understand these three modes by turning to one of Peirce's examples. I will summarize it without boring the reader with logical and semiotic technical jargon.
Let's suppose that on this table I have a sack full of white beans. I know that it is full of white beans (let's say I bought the sack in a store in which the merchant, whom I trust, sells sacks of white beans); consequently, I can assume the Rule "All the beans in this sack are white." Once I know the Rule, I produce a Case; I blindly take a fistful of beans from the sack (blindly: it's not necessary to look at them), and I can predict the Result: "The beans in my hand are white." Deduction from a (true) Rule, by means of a Case, predicts a Result with absolute certainty.
Alas, except for a few axiomatic systems, we can make very few safe deductions. Let's move now to Induction. I have a sack, and I don't know what's in it. I stick in my hand, pull out a handful of beans, and observe that they are all white. I put my hand in again, and still come up with white beans. I repeat this procedure x number of times (the number of trials depends on how much time I have, or on how much money I've received from the Ford Foundation to establish a scientific law about the beans in the sack). After a sufficient number of trials, I make the following assessment: all the Results of my trials produce a fistful of white beans; I can reasonably infer that all these outcomes are Cases of the same Rulethat is, all the beans in the sack are white. From a series of Results, inferring that they are Cases of the same Rule, I arrive at the inductive formulation of this (probable) Rule. As we know, all it takes is one trial in which one of the beans drawn from the sack is black, and my entire inductive effort vanishes into thin air. This is why epistemologists are so suspicious with regard to Induction.
Actually, since we don't know how many trials are necessary, before an Induction can be considered a good one, we really don't know what a valid Induction is. Are ten trials enough? And why not nine? Or eight? And why not even one?
At this point, Induction moves over and makes room for Abduction. With Abduction, I find myself confronted by a strange and unexplainable Result. To keep to our example, I have a sack of beans on the table, and nearby, also on the table, is a bunch of white beans. I don't know how they've gotten there or who has placed them there, or even where they come from. Let's consider this Result a strange Case. Now I need to find a Rule such that, if it were true, and if the Result were considered a Case of that Rule, the Result would no longer be strange, but rather extremely reasonable.

 
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