Carroll Paradox
Contents |
Paradox
Modus Ponens leads to infinite regress.
Proof
To be proven: $q$.
1. Assume $p \implies q$.
2. Assume $p$.
3. $p \land (p \implies q) \vdash q$.
4. From 2 and 1, $p \land (p \implies q)$.
5. $(p \land (p \implies q) \land (p \land (p \implies q) \vdash q)) \vdash q$.
6. From 4 and 3, $(p \land (p \implies q))\land ((p \land (p \implies q)) \vdash q)$.
$\ldots$
Source of Name
This entry was named for Lewis Carroll.
Sources
- Douglas R. Hofstadter: Gödel, Escher, Bach: an Eternal Golden Braid (1979): Two-Part Invention, quoting What the Tortoise Said to Achilles by Lewis Carroll
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