Deductive reasoning Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.Anti-spam check. Do not fill this in! == Definition == Deductive reasoning is the psychological process of drawing deductive [[inference]]s. An inference is a set of [[premise]]s together with a conclusion. This psychological process starts from the premises and [[reason]]s to a conclusion based on and supported by these premises. If the reasoning was done correctly, it results in a [[Validity (logic)|valid]] deduction: the truth of the premises ensures the truth of the conclusion.<ref name="Johnson-Laird2009">{{cite journal |last1=Johnson-Laird |first1=Phil |title=Deductive reasoning |journal=WIREs Cognitive Science |date=30 December 2009 |volume=1 |issue=1 |pages=8β17 |doi=10.1002/wcs.20 |pmid=26272833 |url=https://wires.onlinelibrary.wiley.com/doi/abs/10.1002/wcs.20 |issn=1939-5078}}</ref><ref name="Houde">{{cite book |last1=Houde |first1=R. |title=New Catholic Encyclopedia |url=https://www.encyclopedia.com/philosophy-and-religion/philosophy/philosophy-terms-and-concepts/deduction |chapter=Deduction |quote=Modern logicians sometimes oppose deduction to induction on the basis that the first concludes from the general to the particular, whereas the second concludes from the particular to the general; this characterization is inaccurate, however, since deduction need not conclude to the particular and its process is far from being the logical inverse of the inductive procedure.}}</ref><ref name="Schechter"/><ref>{{cite journal |last1=Norris |first1=Stephen E. |title=The Intelligibility of Practical Reasoning |journal=American Philosophical Quarterly |date=1975 |volume=12 |issue=1 |pages=77β84 |jstor=20009561 |url=https://www.jstor.org/stable/20009561 |issn=0003-0481}}</ref> For example, in the [[Syllogism|syllogistic]] argument "all frogs are amphibians; no cats are amphibians; therefore, no cats are frogs" the conclusion is true because its two premises are true. But even arguments with wrong premises can be deductively valid if they obey this principle, as in "all frogs are mammals; no cats are mammals; therefore, no cats are frogs". If the premises of a valid [[argument]] are true, then it is called a [[Soundness|sound]] argument.<ref name="Evans"/> The relation between the premises and the conclusion of a deductive argument is usually referred to as "[[logical consequence]]". According to [[Alfred Tarski]], logical consequence has 3 essential features: it is necessary, formal, and knowable [[a priori]].<ref name="IEPLogical"/><ref name="Tarski">{{cite book |last1=Tarski |first1=Alfred |title=Logic, Semantics, Metamathematics: Papers from 1923 to 1938 |date=1983 |publisher=Hackett Publishing |isbn=978-0-915144-76-1 |url=https://books.google.com/books?id=2uhra9PEFZsC |language=en |chapter=16. On The Concept of Logical Consequence}}</ref> It is necessary in the sense that the premises of valid deductive arguments necessitate the conclusion: it is impossible for the premises to be true and the conclusion to be false, independent of any other circumstances.<ref name="IEPLogical"/><ref name="Tarski"/> Logical consequence is formal in the sense that it depends only on the form or the syntax of the premises and the conclusion. This means that the validity of a particular argument does not depend on the specific contents of this argument. If it is valid, then any argument with the same logical form is also valid, no matter how different it is on the level of its contents.<ref name="IEPLogical"/><ref name="Tarski"/> Logical consequence is knowable a priori in the sense that no [[empirical]] knowledge of the world is necessary to determine whether a deduction is valid. So it is not necessary to engage in any form of empirical investigation.<ref name="IEPLogical"/><ref name="Tarski"/> Some logicians define deduction in terms of [[possible world]]s: A deductive inference is valid if and only if, there is no possible world in which its conclusion is false while its premises are true. This means that there are no counterexamples: the conclusion is true in ''all'' such cases, not just in ''most'' cases.<ref name="Johnson-Laird2009"/> It has been argued against this and similar definitions that they fail to distinguish between valid and invalid deductive reasoning, i.e. they leave it open whether there are invalid deductive inferences and how to define them.<ref name="Vorobej"/><ref name="Wilbanks"/> Some authors define deductive reasoning in psychological terms in order to avoid this problem. According to Mark Vorobey, whether an argument is deductive depends on the psychological state of the person making the argument: "An argument is deductive if, and only if, the author of the argument believes that the truth of the premises necessitates (guarantees) the truth of the conclusion".<ref name="Vorobej"/> A similar formulation holds that the speaker ''claims'' or ''intends'' that the premises offer deductive support for their conclusion.<ref name="Copi1">{{cite book |last1=Copi |first1=Irving M. |last2=Cohen |first2=Carl |last3=Rodych |first3=Victor |title=Introduction to Logic |date=3 September 2018 |publisher=Routledge |isbn=978-1-351-38696-8 |url=https://books.google.com/books?id=jDOoDwAAQBAJ |language=en |chapter=1. Basic Logical Concepts}}</ref><ref name="IEPDeductiveInductive"/> This is sometimes categorized as a ''speaker-determined'' definition of deduction since it depends also on the speaker whether the argument in question is deductive or not. For ''speakerless'' definitions, on the other hand, only the argument itself matters independent of the speaker.<ref name="Wilbanks"/> One advantage of this type of formulation is that it makes it possible to distinguish between good or valid and bad or invalid deductive arguments: the argument is good if the author's [[belief]] concerning the relation between the premises and the conclusion is true, otherwise it is bad.<ref name="Vorobej"/> One consequence of this approach is that deductive arguments cannot be identified by the law of inference they use. For example, an argument of the form [[modus ponens]] may be non-deductive if the author's beliefs are sufficiently confused. That brings with it an important drawback of this definition: it is difficult to apply to concrete cases since the intentions of the author are usually not explicitly stated.<ref name="Vorobej">{{cite journal |last1=Vorobej |first1=Mark |title=Defining Deduction |journal=Informal Logic |date=1992 |volume=14 |issue=2 |doi=10.22329/il.v14i2.2533 |url=https://philpapers.org/rec/VORDD|doi-access=free }}</ref> Deductive reasoning is studied in [[logic]], [[psychology]], and the [[cognitive sciences]].<ref name="Schechter"/><ref name="Johnson-Laird2009"/> Some theorists emphasize in their definition the difference between these fields. On this view, psychology studies deductive reasoning as an empirical mental process, i.e. what happens when humans engage in reasoning.<ref name="Schechter"/><ref name="Johnson-Laird2009"/> But the descriptive question of how actual reasoning happens is different from the [[Normativity|normative]] question of how it ''should'' happen or what constitutes ''correct'' deductive reasoning, which is studied by logic.<ref name="Schechter"/><ref name="BritannicaPhilosophy"/><ref name="IEPLogical"/> This is sometimes expressed by stating that, strictly speaking, logic does not study deductive reasoning but the deductive relation between premises and a conclusion known as [[logical consequence]]. But this distinction is not always precisely observed in the academic literature.<ref name="Schechter"/> One important aspect of this difference is that logic is not interested in whether the conclusion of an argument is sensible.<ref name="Johnson-Laird2009"/> So from the premise "the printer has ink" one may draw the unhelpful conclusion "the printer has ink and the printer has ink and the printer has ink", which has little relevance from a psychological point of view. Instead, actual reasoners usually try to remove redundant or irrelevant information and make the relevant information more explicit.<ref name="Johnson-Laird2009"/> The psychological study of deductive reasoning is also concerned with how good people are at drawing deductive inferences and with the factors determining their performance.<ref name="Schechter"/><ref name="Evans"/> Deductive inferences are found both in [[natural language]] and in [[formal logical systems]], such as [[propositional logic]].<ref name="Johnson-Laird2009"/><ref name="Hintikka"/> Summary: Please note that all contributions to Christianpedia may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here. You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see Christianpedia:Copyrights for details). Do not submit copyrighted work without permission! 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