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====''Deduction, Induction, and Hypothesis'' (1878)==== In 1878, in "Deduction, Induction, and Hypothesis",<ref name="DIH" /> there is no longer a need for multiple characters or predicates in order for an inference to be hypothetical, although it is still helpful. Moreover, Peirce no longer poses hypothetical inference as concluding in a ''probable'' hypothesis. In the forms themselves, it is understood but not explicit that induction involves random selection and that hypothetical inference involves response to a "very curious circumstance". The forms instead emphasize the modes of inference as rearrangements of one another's propositions (without the bracketed hints shown below). {| cellspacing=1 cellpadding=3 style="background-color:#999" |- vAlign=top style="background-color:#fff" |Deduction. ''Rule:'' All the beans from this bag are white. <br />''Case:'' These beans are from this bag. <br /><math>\therefore</math> ''Result:'' These beans are white. | Induction. ''Case:'' These beans are [randomly selected] from this bag. <br />''Result:'' These beans are white. <br /><math>\therefore</math> ''Rule:'' All the beans from this bag are white. |Hypothesis. ''Rule:'' All the beans from this bag are white. <br />''Result:'' These beans [oddly] are white. <br /><math>\therefore</math> ''Case:'' These beans are from this bag. |}
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