Modus Tollendo Tollens
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- If we can conclude $\phi \implies \psi$, and we can also conclude $\neg \psi$, then we may infer $\neg \phi$.
- $p \implies q, \neg q \vdash \neg p$
- If the truth of one statement implies the truth of a second, and the second is shown not to be true, then neither can the first be true.
Modus Tollendo Tollens is also known as:
- Modus tollens
- Denying the consequent.
The following are related argument forms:
These are classic fallacies:
Modus Tollendo Tollens is Latin for mode that by denying, denies.
The shorter form Modus Tollens means mode that denies.
- 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $2.3$: Argument Forms and Truth Tables
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Entry: modus tollens
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: modus tollens