srn347 comments on Second-Order Logic: The Controversy - LessWrong

24 Post author: Eliezer_Yudkowsky 04 January 2013 07:51PM

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Comment author: abramdemski 08 January 2013 04:38:58AM *  1 point [-]

What I'm saying is it doesn't matter, and therefore doesn't obviously make sense to ask, what language the world is written in. Even if the world actually runs on paraconsistent logic, we can still do fine with classical logic. It will alter our prior somewhat, but not a while lot, because the encoding of one into the other isn't so hard.

Eliezer is attempting to make some comparison between the structure of the actual world and the structure of the logic, to determine which logic most seems to be what the world is written in. But the existence of encodings of one logic in another makes this exercise somewhat unnecessary (and also means that the structure of the world is only weak evidence for "what logic it was written in").

To answer your question: in addition, because having strong negation in addition to weak negation only increases the expressive power of the system. It does not increase the risk you mention, because the system is still choosing what to believe according to its learning algorithm, and so will not choose to believe strong negatives that cause problems.

EDIT:

In response to srn347, I would like to clarify that I do not intend to belittle the importance of comparing the effectiveness of different logics. The existence of an encoding will only get you specific things (depending on the nature of the encoding), and furthermore, encodings to not always exist. So, specifically, I'm only saying that I don't see a need for paraconsistent logic. Other possibilities need to be judged on their merits. However, looking for encodings is an important tool in that judgement.

Comment author: [deleted] 08 January 2013 04:58:34AM 1 point [-]

If I may interject (assuming it isn't too early to start proposing solutions), it does turn out to be the case that computability logic is a superset of linear logic, which encodes resource-boundedness and avoids material entailment paradoxes, intuitionistic logic, which encodes proof/justification, and classical logic, which encodes truth. To accept less is to sacrifice one or more of the above attributes in terms of expressiveness.

Comment author: abramdemski 08 January 2013 05:54:07AM 0 points [-]

Thanks; I certainly didn't intend to say that all logics are equivalent so it doesn't matter... edited to clarify...