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CronoDAS comments on Compartmentalization as a passive phenomenon - Less Wrong
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Comments (71)
GEB has a section on this.
In order to not compartmentalize, you need to test if your beliefs are all consistent with each other. If your beliefs are all statements in propositional logic, consistency checking becomes the Boolean Satisfiability Problem, which is NP-complete. If your beliefs are statements in predicate logic, then consistency checking becomes PSPACE-complete, which is even worse than NP-complete.
Not compartmentalizing isn't just difficult, it's basically impossible.
Reminds me of the opening paragraph of The Call of Cthulhu.
Glenn Beck:
P.S. The trick is to use bubble sort.
It took me several seconds to guess that GEB refers to Godel, Escher, Bach.
Sorry about that!
I agree, save that I think Academian's proposal should be applied and "compartmentalizing" replaced with "clustering". "Compartmentalization" is a more useful term when restricted to describing the failure mode.
Could I express what you said as:
A person is in the predicament of:
1) having a large number of beliefs
2) the mathematically impossible challenge of validating those beliefs for consistency
Therefore:
3) It is impossible to not compartmentalize
This leads to a few questions:
Edwin Jaynes discusses "lattice" theories of probability where propositions are not universally comparable in appendix A of Probability Theory: The Logic of Science. Following Jaynes's account, probability theory would correspond to a uniformly dense lattice, whereas a lattice with very sparse structure and a few dense regions would correspond to compartmentalized beliefs.
Yes, that's basically right.
As for those questions, I don't know the answers either.
Rationalism is faith to you then?
[EDIT: An explanation is below that I should have provided in this comment; obviously when I made the comment I assumed people could read my mind; I apologize for my transparency bias]
I'm not sure what you mean...
Compartmentalization is an enemy of rationalism. If we are going to say that rationalism is worthwhile, we must also say that reducing compartmentalization is worthwhile. But that argument only scratches the surface of the problem you eloquently pointed out.
Mathematically, we have a mountain of beliefs that need processing with something better than brute force. We have to be able to quickly identify how impactful beliefs are to our belief system, and focus our rational efforts on those beliefs. (Otherwise we're wasting our time processing only a tiny randomly chosen part of the mountain.)
Rationality, if it's actually useful, should provide us with at least a small set of consistent and maximally impactful beliefs. We have not escaped compartmentalization of all our beliefs, but at least we have chosen the most impactful compartment within which we have consistency.
Finally, if we can't perfectly process our mountain of beliefs, then at least we can imperfectly process that mountain. Hence the need for probabilistic reasoning.
To summarize, I want to be able to answer "yes" to all of these questions, to justify the endeavor of rationalism. The problem is like you, my answer for each is "I don't know". For this reason, I accept my rationalism is just faith, or perhaps less pejoratively, intuition (though we're talking rationality here, right?).