Editing Deductive reasoning (section)

== Difference from ampliative reasoning ==
Deductive reasoning is usually contrasted with non-deductive or [[ampliative]] reasoning.<ref name="Hintikka" /><ref name="Backmann">{{Cite journal |last=Backmann |first=Marius |date=1 June 2019 |title=Varieties of Justification—How (Not) to Solve the Problem of Induction |journal=Acta Analytica |volume=34 |issue=2 |pages=235–255 |doi=10.1007/s12136-018-0371-6 |issn=1874-6349 |s2cid=125767384 |doi-access=free}}</ref><ref name="IEPArguments">{{Cite encyclopedia |title=Deductive and Inductive Arguments |encyclopedia=Internet Encyclopedia of Philosophy |url=https://iep.utm.edu/ded-ind/ |access-date=4 December 2021 |archive-url=https://web.archive.org/web/20100528032124/https://iep.utm.edu/ded-ind/ |archive-date=28 May 2010 |url-status=dead}}</ref> The hallmark of valid deductive inferences is that it is impossible for their premises to be true and their conclusion to be false. In this way, the premises provide the strongest possible support to their conclusion.<ref name="Hintikka" /><ref name="Backmann" /><ref name="IEPArguments" /> The premises of ampliative inferences also support their conclusion. But this support is weaker: they are not necessarily truth-preserving. So even for correct ampliative arguments, it is possible that their premises are true and their conclusion is false.<ref name="IEPDeductiveInductive" /> Two important forms of ampliative reasoning are [[inductive reasoning|inductive]] and [[abductive reasoning]].<ref name="StanfordAbduction" /> Sometimes the term "inductive reasoning" is used in a very wide sense to cover all forms of ampliative reasoning.<ref name="IEPDeductiveInductive">{{Cite encyclopedia |title=Deductive and Inductive Arguments |encyclopedia=Internet Encyclopedia of Philosophy |url=https://iep.utm.edu/ded-ind/ |access-date=6 January 2022 |archive-url=https://web.archive.org/web/20100528032124/https://iep.utm.edu/ded-ind/ |archive-date=28 May 2010 |last1=IEP Staff |url-status=dead}}</ref> However, in a more strict usage, inductive reasoning is just one form of ampliative reasoning.<ref name="StanfordAbduction" /> In the narrow sense, inductive inferences are forms of statistical generalization. They are usually based on many individual [[observation]]s that all show a certain pattern. These observations are then used to form a conclusion either about a yet unobserved entity or about a general law.<ref name="MacmillanInduction">{{Cite encyclopedia |year=2006 |title=G. W. Liebnitz |encyclopedia=Macmillan Encyclopedia of Philosophy |publisher=Macmillan |url=https://philpapers.org/rec/BORMEO |edition=2nd |language=pt |last1=Borchert |first1=Donald}}</ref><ref>{{Cite encyclopedia |last1=Scott |first1=John |url=https://www.oxfordreference.com/view/10.1093/oi/authority.20110803095410661 |encyclopedia=A Dictionary of Sociology |last2=Marshall |first2=Gordon |publisher=Oxford University Press |year=2009 |isbn=978-0-199-53300-8 |title=Analytic induction}}</ref><ref>{{Cite encyclopedia |title=Induction |encyclopedia=New Catholic Encyclopedia |url=https://www.encyclopedia.com/science-and-technology/computers-and-electrical-engineering/electrical-engineering/induction |last2=Camacho |first2=L. |last1=Houde |first1=R.}}</ref> For abductive inferences, the premises support the conclusion because the conclusion is the best explanation of why the premises are true.<ref name="StanfordAbduction" /><ref name="Koslowski">{{Cite book |last=Koslowski |first=Barbara |title=International Handbook of Thinking and Reasoning |publisher=Routledge |year=2017 |isbn=978-1-315-72569-7 |chapter=Abductive reasoning and explanation |doi=10.4324/9781315725697-20 |doi-broken-date=27 December 2024 |chapter-url=https://www.taylorfrancis.com/chapters/edit/10.4324/9781315725697-20/abductive-reasoning-explanation-barbara-koslowski}}</ref>

The support ampliative arguments provide for their conclusion comes in degrees: some ampliative arguments are stronger than others.<ref name="IEPDeductiveInductive" /><ref name="StanfordInductive">{{Cite encyclopedia |year=2021 |title=Inductive Logic |encyclopedia=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/entries/logic-inductive/ |access-date=6 January 2022 |last1=Hawthorne |first1=James}}</ref><ref name="StanfordAbduction" /> This is often explained in terms of [[probability]]: the premises make it more likely that the conclusion is true.<ref name="Hintikka" /><ref name="Backmann" /><ref name="IEPArguments" /> Strong ampliative arguments make their conclusion very likely, but not absolutely certain. An example of ampliative reasoning is the inference from the premise "every raven in a random sample of 3200 ravens is black" to the conclusion "all ravens are black": the extensive random sample makes the conclusion very likely, but it does not exclude that there are rare exceptions.<ref name="StanfordInductive"/> In this sense, ampliative reasoning is defeasible: it may become necessary to retract an earlier conclusion upon receiving new related information.<ref name="BritannicaPhilosophy" /><ref name="StanfordAbduction">{{Cite encyclopedia |year=2021 |title=Abduction |encyclopedia=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/entries/abduction/ |last1=Douven |first1=Igor}}</ref> Ampliative reasoning is very common in everyday discourse and the [[science]]s.<ref name="Hintikka" /><ref name="Bunge">{{Cite journal |last=Bunge |first=Mario |year=1960 |title=The Place of Induction in Science |journal=Philosophy of Science |volume=27 |issue=3 |pages=262–270 |doi=10.1086/287745 |issn=0031-8248 |jstor=185969 |s2cid=120566417}}</ref>

An important drawback of deductive reasoning is that it does not lead to genuinely new information.<ref name="Evans" /> This means that the conclusion only repeats information already found in the premises. Ampliative reasoning, on the other hand, goes beyond the premises by arriving at genuinely new information.<ref name="Hintikka" /><ref name="Backmann" /><ref name="IEPArguments" /> One difficulty for this characterization is that it makes deductive reasoning appear useless: if deduction is uninformative, it is not clear why people would engage in it and study it.<ref name="Hintikka" /><ref name="D'Agostino">{{Cite journal |last1=D'Agostino |first1=Marcello |last2=Floridi |first2=Luciano |year=2009 |title=The Enduring Scandal of Deduction: Is Propositional Logic Really Uninformative? |journal=Synthese |volume=167 |issue=2 |pages=271–315 |doi=10.1007/s11229-008-9409-4 |issn=0039-7857 |jstor=40271192 |s2cid=9602882 |hdl-access=free |hdl=2299/2995}}</ref> It has been suggested that this problem can be solved by distinguishing between surface and depth information. On this view, deductive reasoning is uninformative on the depth level, in contrast to ampliative reasoning. But it may still be valuable on the surface level by presenting the information in the premises in a new and sometimes surprising way.<ref name="Hintikka" /><ref name="Evans" />

A popular misconception of the relation between deduction and induction identifies their difference on the level of particular and general claims.<ref name="Houde" /><ref name="Wilbanks">{{Cite journal |last=Wilbanks |first=Jan J. |date=2010 |title=Defining Deduction, Induction, and Validity |url=https://philpapers.org/rec/WILDDI |journal=Argumentation |volume=24 |issue=1 |pages=107–124 |doi=10.1007/s10503-009-9131-5 |s2cid=144481717|url-access=subscription }}</ref><ref>{{Cite encyclopedia |title=Deductive and Inductive Arguments |encyclopedia=Internet Encyclopedia of Philosophy |url=https://iep.utm.edu/deductive-inductive-arguments/ |access-date=17 March 2022}}</ref> On this view, deductive inferences start from general premises and draw particular conclusions, while inductive inferences start from particular premises and draw general conclusions. This idea is often motivated by seeing deduction and induction as two inverse processes that complement each other: deduction is ''top-down'' while induction is ''bottom-up''. But this is a misconception that does not reflect how valid deduction is defined in the field of [[logic]]: a deduction is valid if it is impossible for its premises to be true while its conclusion is false, independent of whether the premises or the conclusion are particular or general.<ref name="Houde" /><ref name="Wilbanks" /><ref name="Johnson-Laird2009" /><ref name="Evans" /><ref name="Schechter">{{Cite web |last=Schechter |first=Joshua |year=2013 |title=Deductive Reasoning |url=https://philpapers.org/rec/SCHDR |access-date=16 March 2022 |website=The Encyclopedia of the Mind |publisher=SAGE Reference}}</ref> Because of this, some deductive inferences have a general conclusion and some also have particular premises.<ref name="Houde" />