Editing Modus ponens (section)

==Alleged cases of failure==

Philosophers and linguists have identified a variety of cases where ''modus ponens'' appears to fail. [[Vann McGee]], for instance, argued that ''modus ponens'' can fail for conditionals whose consequents are themselves conditionals.<ref>Vann McGee (1985). "A Counterexample to Modus Ponens", ''The Journal of Philosophy'' 82, 462–471.</ref> The following is an example:

# Either [[Shakespeare]] or [[Thomas Hobbes|Hobbes]] wrote ''[[Hamlet]]''.
# If either Shakespeare or Hobbes wrote ''Hamlet'', then if Shakespeare did not do it, Hobbes did.
# Therefore, if Shakespeare did not write ''Hamlet'', Hobbes did it.

Since Shakespeare did write ''Hamlet'', the first premise is true. The second premise is also true, since starting with a set of possible authors limited to just Shakespeare and Hobbes and eliminating one of them leaves only the other. However, the conclusion is doubtful, since ruling out Shakespeare as the author of ''Hamlet'' would leave numerous possible candidates, many of them more plausible alternatives than Hobbes (if the if-thens in the inference are read as material conditionals, the conclusion comes out true simply by virtue of the false antecedent. This is one of the [[paradoxes of material implication]]).

The general form of McGee-type counterexamples to ''modus ponens'' is simply <math>P, P \rightarrow (Q \rightarrow R)</math>, therefore, <math>Q \rightarrow R</math>; it is not essential that <math>P</math> be a disjunction, as in the example given. That these kinds of cases constitute failures of ''modus ponens'' remains a controversial view among logicians, but opinions vary on how the cases should be disposed of.<ref>Sinnott-Armstrong, Moor, and Fogelin (1986). "A Defense of Modus Ponens", ''The Journal of Philosophy'' 83, 296–300.</ref><ref>D. E. Over (1987). "Assumption and the Supposed Counterexamples to Modus Ponens", ''Analysis'' 47, 142–146.</ref><ref>Bledin (2015). "Modus Ponens Defended", ''The Journal of Philosophy'' 112, 462–471.</ref>

In [[deontic logic]], some examples of conditional obligation also raise the possibility of ''modus ponens'' failure. These are cases where the conditional premise describes an obligation predicated on an immoral or imprudent action, e.g., "If Doe murders his mother, he ought to do so gently," for which the dubious unconditional conclusion would be "Doe ought to gently murder his mother."<ref name="SEP_Deontic_Logic">{{cite web |url=https://plato.stanford.edu/entries/logic-deontic/#4.5 |title=Deontic Logic |access-date=January 30, 2020 |date=April 21, 2010}} ''[[Stanford Encyclopedia of Philosophy]]''.</ref> It would appear to follow that if Doe is in fact gently murdering his mother, then by ''modus ponens'' he is doing exactly what he should, unconditionally, be doing. Here again, ''modus ponens''' failure is not a popular diagnosis but is sometimes argued for.<ref>E.g., by Kolodny and MacFarlane (2010). "Ifs and Oughts", ''The Journal of Philosophy'' 107, 115–143.</ref>