Editing Deductive reasoning (section)

==== Modus ponens ====
{{Main|Modus ponens|selfref = None}}

Modus ponens (also known as "affirming the antecedent" or "the law of detachment") is the primary deductive [[rule of inference]]. It applies to arguments that have as first premise a [[Material conditional|conditional statement]] (<math>P \rightarrow Q</math>) and as second premise the antecedent (<math>P</math>) of the conditional statement. It obtains the consequent (<math>Q</math>) of the conditional statement as its conclusion. The argument form is listed below:
# <math>P \rightarrow Q</math>&nbsp; (First premise is a conditional statement)
# <math>P</math>&nbsp; (Second premise is the antecedent)
# <math>Q</math>&nbsp; (Conclusion deduced is the consequent)

In this form of deductive reasoning, the consequent (<math>Q</math>) obtains as the conclusion from the premises of a conditional statement (<math>P \rightarrow Q</math>) and its antecedent (<math>P</math>). However, the antecedent (<math>P</math>) cannot be similarly obtained as the conclusion from the premises of the conditional statement (<math>P \rightarrow Q</math>) and the consequent (<math>Q</math>). Such an argument commits the [[logical fallacy]] of [[affirming the consequent]].

The following is an example of an argument using modus ponens:
# If it is raining, then there are clouds in the sky.
# It is raining.
# Thus, there are clouds in the sky.