Carroll Paradox

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Paradox

Modus Ponendo Ponens leads to infinite regress.


Proof

To be proven: $q$.

$(1).\quad$ Assume $p \implies q$.
$(2).\quad$ Assume $p$.
$(3).\quad$ $p \land \left({p \implies q}\right) \vdash q$.
$(4).\quad$ From $(2)$ and $(1)$, $p \land \left({p \implies q}\right)$.
$(5).\quad \left({p \land \left({p \implies q}\right) \land \left({p \land \left({p \implies q}\right)}\right) \vdash q}\right) \vdash q$.
$(6).\quad$ 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

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