Definition
Modus ponens (Latin for "mode that affirms") is the inference rule: from premises A and A ⊃ B, conclude B. It is the central rule of propositional and predicate logic — most other derivable inferences ultimately use modus ponens. It is also the rule the Tortoise paradoxically refuses to accept in Carroll's 1895 regress.
Why it matters
How it works
To apply modus ponens: have a derivation containing both A and A ⊃ B as established lines. Add B as the next line, citing modus ponens. The rule is a pattern-match: any specific propositions in place of A and B work. Most formal proofs are largely sequences of modus ponens applications interleaved with axiom or hypothesis introductions.