Modus Tollendo Tollens
Jump to navigation Jump to search
- If we can conclude $\phi \implies \psi$, and we can also conclude $\neg \psi$, then we may infer $\neg \phi$.
|\(\ds p\)||\(\implies\)||\(\ds q\)|
|\(\ds \neg q\)||\(\)||\(\ds \)|
|\(\ds \vdash \ \ \)||\(\ds \neg p\)||\(\)||\(\ds \)|
- 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, abbreviated M.T.
- 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): $2$ Arguments Containing Compound Statements: $2.3$: 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