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Confutus wrote:
> In Lukasiewicz three valued logic, interestingly, Modus Ponens does not
> hold.
>
> (A & (A > B)) > B is not a tautology. it fails in one case.
>
> This must be one of the reasons Lukasiewicz logic has been regarded as
> more of a curiosity than a successful attempt to extend classical
> logic. If Modus Ponens isn't valid, then how is one supposed to do any
> kind of deductive reasoning with it?
You really shouldn't confuse rules with formulas. The invalidity of [A
& (A -> B)] -> B does not show that modus ponens fails in Lukasiewicz's
system. Would you care to show that
A, A -> B |= B
fails, where the only designated value is truth?
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