[kylebrown]

The other day, I ran across this in a Yudkowsky article[1]:

> Suppose that earthquakes and burglars can both set off burglar alarms. If the burglar alarm in your house goes off, it might be because of an actual burglar, but it might also be because a minor earthquake rocked your house and triggered a few sensors. Early investigators in Artificial Intelligence, who were trying to represent all high-level events using primitive tokens in a first-order logic (for reasons of historical stupidity we won't go into) were stymied by the following apparent paradox: [.. snip ..] Which represents a logical contradiction, and for a while there were attempts to develop "non-monotonic logics" so that you could retract conclusions given additional data.

1. http://lesswrong.com/lw/ev3/causal_diagrams_and_causal_model...

[dpflan]

Thanks for this, though I may not be fully comprehending. If earthquakes can set off burglar alarms, and if burglars can set off burglar alarms , why would there be no -|ALARM->EARTHQUAKE theorem? Understandably the ALARM is for detecting burglars not earthquakes, but it does function as a detector for both.

[orodley]

It doesn't function as a detector for both, it functions as a detector for either. I'm not being pedantic, there is a subtle difference. ALARM -> EARTHQUAKE is false: the correct theorem is ALARM -> (EARTHQUAKE | BURGLAR). If the alarm goes off then you have no certain knowledge about which one caused it, only probabilities.

[scrupulusalbion]

It would seem that an additional source of information (e.g. a nearby seismograph bolted to bedrock) would be the solution to this problem. This is analogous to a blind person trying to identify whether a sound is a recording or the Real McCoy. The solution is to either somehow make him able to see or to allow him to use some other sense (e.g. touch) by which to measure the origin of the sound. If he hears a dog barking, then if he sees/feels a dog, he is almost completely assured [0] that it is a real dog that was barking and not a recording playing from a machine.

Thus, adding another sense (a seismograph and sightedness/touch, respectively) would seem to eliminate the problem. If this is correct, then such problems are more ones of a lack of relevant, heterogeneous information and less of a lack of logical expressiveness of probabilities.

[0] = I say "almost", because knowledge is a fundamental philosophical problem. The usual means to "almost" assurance is, as I am arguing, to employ more heterogeneous sources of information until the only logical alternatives to what you believe are absurdities (e.g. impossible).

[dpflan]

Ah, I wasn't picking up on the subtlety; thanks for adding clarity.