RationalWiki's 2020 Fundraiser

There is no RationalWiki without you. We are a small non-profit with no staff – we are hundreds of volunteers who document pseudoscience and crankery around the world every day. We will never allow ads because we must remain independent. We cannot rely on big donors with corresponding big agendas. We are not the largest website around, but we believe we play an important role in defending truth and objectivity.

If everyone who saw this today donated $5, we would meet our goal for 2021.

Fighting pseudoscience isn't free.
We are 100% user-supported! Help and donate $5, $20 or whatever you can today with PayPal Logo.png!

Donations so far: $720Goal: $3500

Modus ponens

From RationalWiki
Jump to: navigation, search
Cogito ergo sum
Logic and rhetoric
Icon logic.svg
Key articles
General logic
Bad logic

Modus ponens ("mode of affirming") is a logical rule of inference based on conditional propositions. Also called affirming the antecedent, modus ponens involves affirming the sufficient condition of the conditional proposition in order to prove the necessary condition. Modus ponens is closely related to modus tollens ("mode of taking").

A modus ponens argument has the following form:

P1: If X, then Y. (i. e. Either not X or Y)
P2: X.
C: Therefore, Y.

For example:

P1: If my friends are coming over tonight, I will bake a cake. (i. e. Either my friends are not coming over tonight, or I will bake a cake.)
P2: My friends are coming over tonight.
C: Therefore, I will bake a cake.

Confusing the directionality of the if-then statement in a modus ponens argument results in the fallacy of affirming the consequent, represented by the following invalid syllogism:

P1: If my friends are coming over tonight, I will bake a cake.
P2: I will bake a cake.
C1: Therefore, my friends are coming over tonight.

As a rule of inference, modus ponens is represented by the following in propositional logic:

\left\{X\rightarrow Y, X\right\} \models Y

See also[edit]