Editing Inductive reasoning (section)

=== Eliminative induction ===
[[Eliminative induction]], also called variative induction, is an inductive method first put forth by [[Francis Bacon]];<ref name=":2">{{Cite book |last1=Goodenough |first1=John B. |last2=Weinstock |first2=Charles B. |last3=Klein |first3=Ari Z. |chapter=Eliminative induction: A basis for arguing system confidence |date=2013 |title=2013 35th International Conference on Software Engineering (ICSE) |chapter-url=https://ieeexplore.ieee.org/document/6606668 |pages=1161–1164 |doi=10.1109/ICSE.2013.6606668 |isbn=978-1-4673-3076-3 |via=IEEE}}</ref> in it a generalization is constructed based on the ''variety'' of instances that support it. Unlike enumerative induction, eliminative induction reasons based on the various kinds of instances that support a conclusion, rather than the number of instances that support it. As the variety of instances increases, the more possible conclusions based on those instances can be identified as incompatible and eliminated. This, in turn, increases the strength of any conclusion that remains consistent with the various instances. In this context, confidence is the function of how many instances have been identified as incompatible and eliminated. This confidence is expressed as the Baconian probability i|n (read as "i out of n") where n reasons for finding a claim incompatible has been identified and i of these have been eliminated by evidence or argument.<ref name=":2" />

There are three ways of attacking an argument; these ways - known as defeaters in [[defeasible reasoning]] literature - are : rebutting, undermining, and undercutting. Rebutting defeats by offering a counter-example, undermining defeats by questioning the validity of the evidence, and undercutting defeats by pointing out conditions where a conclusion is not true when the inference is. By identifying defeaters and proving them wrong is how this approach builds confidence. <ref name=":2" />

This type of induction may use different methodologies such as quasi-experimentation, which tests and, where possible, eliminates rival hypotheses.<ref>{{Cite book|last1=Hoppe|first1=Rob|title=Knowledge, Power, and Participation in Environmental Policy Analysis|last2=Dunn|first2=William N.|year=2001|publisher=Transaction Publishers|isbn=978-1-4128-2721-8|pages=419}}</ref> Different evidential tests may also be employed to eliminate possibilities that are entertained.<ref>{{Cite book|last=Schum|first=David A.|title=The Evidential Foundations of Probabilistic Reasoning|publisher=Northwestern University Press|year=2001|isbn=0-8101-1821-1|location=Evanston, Illinois|pages=32}}</ref>

Eliminative induction is crucial to the scientific method and is used to eliminate hypotheses that are inconsistent with observations and experiments.<ref name="dan" /><ref name="jm" /> It focuses on possible causes instead of observed actual instances of causal connections.<ref>{{Cite book|last1=Hodge|first1=Jonathan|title=The Cambridge Companion to Darwin|url=https://archive.org/details/cambridgecompani00hodg_248|url-access=limited|last2=Hodge|first2=Michael Jonathan Sessions|last3=Radick|first3=Gregory|publisher=Cambridge University Press|year=2003|isbn=0-521-77197-8|location=Cambridge|page=[https://archive.org/details/cambridgecompani00hodg_248/page/n189 174]}}</ref>
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