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Vladimir_Nesov comments on Consequentialist Formal Systems - Less Wrong

12 08 May 2012 08:38PM

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Comment author: 09 May 2012 02:55:54PM *  2 points [-]

You're right, this shows that the moral axioms as stated don't work. Essentially [(Prf(C) -> U=v) and U<=v] -> C simplifies to (Prf(C) -> U=v) -> C, and if C is absurdity, then ~(Prf(C) -> U=v), that is (~U=v and Prf(C)). Both Prf(C) and ~U=v shouldn't hold. Thus, moral axioms in the present form shouldn't be added for any easily-provably-false statements. Will try to figure out if the damage can be contained.

(Updated the post and its summary to mention the problem.)

Comment author: 09 May 2012 04:21:54PM 1 point [-]

One immediate idea is to replace the conditional [(Prf(S) -> U=u) and U<=u] -> S with the rule of inference "from [(Prf(S) -> U=u) and U<=u], deduce S". That way you can't get a contrapositive, and you probably need to get Loebian to hope to find a contradiction.

Not confident at all that would work, though.

Comment author: 09 May 2012 04:40:17PM 0 points [-]

Yes, that was the intention, and the problem is that the implication can be tugged from the wrong side, but implication can't be one-sided. I'd prefer to stay with standard inference rules though, if at all possible.

Comment author: 11 May 2012 08:05:32AM 0 points [-]

Pulling on one side but not the other seems textbook of what relevance logics were designed for.