An analogy may, at this point, be useful, even if the one that I propose — between satisfiable beliefs and colourable maps — can be grasped only by stretching.
If four different colours are available then any map can be coloured so that no territories sharing a border will have the same colour: Given a particular map, there is no need to check whether four colours will suffice to colour it. If only two colours are available then a colouring that avoids same-coloured borders may be impossible, but any given map would be easy to check, just by trying to colour it. If three colours are available then things are tricky. It can be hard to tell, on being given a map, whether three colours will be enough.
The task of working out whether some particular map is three-colourable is not merely tricky: it is one of the things that looks to be inexplicable in the sense that my previous posts indicated: If somebody is having success in identifying whether or not maps are three-colourable then they must be having some good luck—(we don’t really know how much)—in avoiding the hard-to-identify cases.
Checking for three colorability is therefore tricky, but producing it is quite straightforward. There would be nothing inexplicably lucky about someone who could be reliably depended upon to produce three-colourable maps. They could do it in the following way: Take three colours; apply blobs of these colours to a page until it is covered; stipulate that the borders on this map occur in all and only the places where two different colours meet.
Now for the analogy:
I have suggested that there would be something inexplicably lucky about the successful maintenance of satisfiable beliefs, if this were done by taking representations of our belief sets and checking to see whether they are satisfiable. This does not entail that there would be anything inexplicably lucky about creatures who can be reliably depended upon to have satisfiable beliefs. They could do it in the following way: Start out by encountering the world; derive beliefs from this encounter in such a way that those beliefs are guaranteed to be satisfiable because the world provides a model for them; add further beliefs to this set, ad lib, in accordance with some sound rules of logic.
The crucial point to notice is that the satisfiability of such a creature’s beliefs would be explained by the rapport between those beliefs and their model-providing world. It would not be explained by any process internal to the creature.
I suggest that something roughly similar is true of us. We are not guaranteed to have satisfiable beliefs, and sometimes we are rather bad at avoiding unsatisfiability, but such intelligence as we have is to be explained by reference to the rapport between our minds and the world.
Rather than starting from a set of belief states, and then supposing that there is some internal process operating on these states that enables us to update our beliefs rationally, we should start out by accounting for the dynamic processes through which the world is epistemically encountered. Much as the three-colourable map generator reliably produces three-colourable maps because it is essential to his map-making procedure that borders appear only where they will allow for three colorability, so it is essential to what it is for a state to be a belief that beliefs will appear only if there is some rapport between the believer and the world. And this rapport — rather than any internal processing considered in isolation from it — can explain the tendency for our beliefs to respect the demands of intelligence.
I’m aware that these remarks are no better than suggestive, but hope that The Unexplained Intellect goes some way towards making good on their suggestion. In my final post, tomorrow, I’ll try to say something about the fact that there is more to life than the maintenance of satisfiable beliefs, and something about the character of ’epistemic encountering’.