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! ==== Modus tollens ==== {{Main|Modus tollens}} Modus tollens (also known as "the law of contrapositive") is a deductive rule of inference. It validates an argument that has as premises a conditional statement (formula) and the negation of the consequent (<math>\lnot Q</math>) and as conclusion the negation of the antecedent (<math>\lnot P</math>). In contrast to [[modus ponens]], reasoning with modus tollens goes in the opposite direction to that of the conditional. The general expression for modus tollens is the following: # <math>P \rightarrow Q</math>. (First premise is a conditional statement) # <math>\lnot Q</math>. (Second premise is the negation of the consequent) # <math>\lnot P</math>. (Conclusion deduced is the negation of the antecedent) The following is an example of an argument using modus tollens: # If it is raining, then there are clouds in the sky. # There are no clouds in the sky. # Thus, it is not raining. 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! Cancel Editing help (opens in new window) Discuss this page