Comment by sfwc on Causal Diagrams and Causal Models · 2012-10-13T12:55:37.366Z · LW · GW

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:

[Description of a system with the following three theorems: ⊢ ALARM → BURGLAR, ⊢ EARTHQUAKE → ALARM, and ⊢ (EARTHQUAKE & ALARM) → NOT BURGLAR]

Which represents a logical contradiction.

This isn't a logical contradiction: perhaps what you mean is that we can deduce from this system that EARTHQUAKE is false. This would give us a contradiction in a modal system, if we also had the theorem ⊢ possibly(EARTHQUAKE), but as it stands it isn't yet contradictory.

Comment by sfwc on The Fabric of Real Things · 2012-10-13T12:32:21.137Z · LW · GW

On the other hand, while "post-utopian" is linked to "colonial alienation" and vice versa, these two elements don't connect to the rest of the causal fabric - so that must not be a universe.

If I really want to, there's an easy way for me to sidestep this. I just postulate something called "post-consciousness" which is caused both by colonial alienation and by particular arrangements of neurons in the brains of particular people (in a similar way to that in which epiphenomenalists would say consciousness is caused). Presto! A causal chain from my familiar causal fabric to colonial alienation.

In fact, we can add an extra node to any causal diagram without affecting the probabilities of observations only involving the other nodes, by making it an effect of all other nodes but not a cause of anything. By so doing we can connect the diagram up. Thus although we can't subvert the approach in Eliezer's post by postulating an ultimate cause (God), we can always subvert it by postulating an ultimate effect.

What I have said isn't normally a problem in real-life applications of the test `is it part of this connected causal fabric', since very often no such causal connection is postulated. My point is that this test can't in-principle rule out anything. It can only serve as an in-practice test by which we can temporarily rule out objects for which no such causal connection has been postulated.