Editing Modus ponens (section)

== Status ==

While ''modus ponens'' is one of the most commonly used [[argument form]]s in logic, it must not be mistaken for a logical law; rather, it is one of the accepted mechanisms for the construction of deductive proofs that includes the "rule of definition" and the "rule of substitution".<ref>Alfred Tarski 1946:47. Also Enderton 2001:110ff.</ref> ''Modus ponens'' allows one to eliminate a [[material conditional|conditional statement]] from a [[formal proof|logical proof or argument]] (the antecedents) and thereby not carry these antecedents forward in an ever-lengthening string of symbols; for this reason modus ponens is sometimes called the '''rule of detachment'''<ref>Tarski 1946:47</ref> or the '''law of detachment'''.<ref>{{cite web|url=https://www.encyclopediaofmath.org/index.php/Modus_ponens|title=Modus ponens - Encyclopedia of Mathematics|website=encyclopediaofmath.org|access-date=5 April 2018}}</ref> Enderton, for example, observes that "modus ponens can produce shorter formulas from longer ones",<ref>Enderton 2001:111</ref> and Russell observes that "the process of the inference cannot be reduced to symbols. Its sole record is the occurrence of ⊦q [the consequent] ... an inference is the dropping of a true premise; it is the dissolution of an implication".<ref name="auto">Whitehead and Russell 1927:9</ref>

A justification for the "trust in inference is the belief that if the two former assertions [the antecedents] are not in error, the final assertion [the consequent] is not in error".<ref name="auto"/> In other words: if one [[statement (logic)|statement]] or [[proposition]] [[material conditional|implies]] a second one, and the first statement or proposition is true, then the second one is also true. If ''P'' implies ''Q'' and  ''P'' is true, then ''Q'' is true.<ref>{{cite book | last=Jago | first=Mark | title=Formal Logic | publisher= Humanities-Ebooks LLP |year= 2007 |isbn=978-1-84760-041-7 }}</ref>