Editing Material conditional (section)

== Discrepancies with natural language ==

Material implication does not closely match the usage of [[conditional sentence]]s in [[natural language]]. For example, even though material conditionals with false antecedents are [[vacuous truth|vacuously true]], the natural language statement "If 8 is odd, then 3 is prime" is typically judged false. Similarly, any material conditional with a true consequent is itself true, but speakers typically reject sentences such as "If I have a penny in my pocket, then Paris is in France". These classic problems have been called the [[paradoxes of material implication]].{{sfn|Edgington|2008}} In addition to the paradoxes, a variety of other arguments have been given against a material implication analysis. For instance, [[counterfactual conditional]]s would all be vacuously true on such an account, when in fact some are false.{{refn|For example, "If [[Janis Joplin]] were alive today, she would drive a [[Mercedes-Benz]]", see {{harvtxt|Starr|2019}}}}

In the mid-20th century, a number of researchers including [[Paul Grice|H. P. Grice]] and [[Frank Cameron Jackson|Frank Jackson]] proposed that [[pragmatics|pragmatic]] principles could explain the discrepancies between natural language conditionals and the material conditional. On their accounts, conditionals [[denotation|denote]] material implication but end up conveying additional information when they interact with conversational norms such as [[Cooperative principle#Grice's maxims|Grice's maxims]].{{sfn|Edgington|2008}}{{sfn|Gillies|2017}} Recent work in [[formal semantics (natural language)|formal semantics]] and [[philosophy of language]] has generally eschewed material implication as an analysis for natural-language conditionals.{{sfn|Gillies|2017}} In particular, such work has often rejected the assumption that natural-language conditionals are [[truth function]]al in the sense that the truth value of "If ''P'', then ''Q''" is determined solely by the truth values of ''P'' and ''Q''.{{sfn|Edgington|2008}} Thus semantic analyses of conditionals typically propose alternative interpretations built on foundations such as [[modal logic]], [[relevance logic]], [[probability theory]], and [[causal graph|causal models]].{{sfn|Gillies|2017}}{{sfn|Edgington|2008}}{{sfn|Von Fintel|2011}}

Similar discrepancies have been observed by psychologists studying conditional reasoning, for instance, by the notorious [[Wason selection task]] study, where less than 10% of participants reasoned according to the material conditional. Some researchers have interpreted this result as a failure of the participants to conform to normative laws of reasoning, while others interpret the participants as reasoning normatively according to nonclassical laws.{{sfn|Oaksford |Chater|1994}}{{sfn|Stenning|van Lambalgen|2004}}{{sfn|Von Sydow|2006}}