“To review, the reductionist thesis is that we use multi-level models for computational reasons, but physical reality has only a single level.”
But wouldn’t an ultimate/complete physical model of reality have to explain why our brains, when hit with certain stimuli, produce a world of solid coloured objects? (To disagree would be to admit the content of our minds is mystical and other worldly.) And if the model does explain it, then aren’t our maps part of reality too (i.e. real)? So therefore isn’t reality multi-level?
I don’t see how you get to multi-level reality by this thinking. But part of the problem of speculating about the philosophical consequences of reducing mind to brain is that we don’t have a complete actual reduction to point to.
There is only one example I know of where a map of the territory has been perfectly embedded within the territory; where the map elements really correspond to territory elements; where every territory element is represented by a map element; and where some particular territory elements correspond to (are the physical substrate for) map elements. That example is the proof of Godel’s incompleteness theorem for arithmetic.
The details of the mappings in each direction between map and territory are complicated, but mundane. However, the consequences of this embedding are
at least a little bit interesting in this context. Godel finds that the embedding must be disappointing to an Eliezer-like reductionist. I don’t think that you can twist his result into support for a multi-level reality (or multi-level territory). But he does show that the territory is rich enough so that no single map can completely cover it; that you may need infinitely many levels of map to completely cover everything that is out there in the territory.
Now Godel’s theorem is just an analogy here. There is no particular reason why difficulties in finding a compact and satisfactory first-order logical foundation for mathematics necessarily tell us anything useful about difficulties in finding a foundation for physical reality. But still, since we all admit that we don’t really know how deep the true territory lies below our best modern maps, and since the history of physics is that the maps keep getting improved with no end in sight, shouldn’t we at least remain open to the possibility that the territory is non-existent (or at least inaccessible) and that all of science is just a series of better and better maps? If it is “maps all the way down” and if our current best map is not the territory, doesn’t that kind of turn around our intuitions as to who is committing the Mind Projection Fallacy here? Is it Mind Projection to imagine that the territory actually exists simply because you have a map of the places you are interested in? Or is it Mind Projection to deny that a map exists simply because you don’t have a map for your area of interest?
I’m no mathematician, but Godel’s theorems seem to have some heavy constraints placed on them. I also don’t see how this maps territory to the map, it still seems like a map of the territory. More like saying “under certain conditions, it’s impossible to draw a better map.”
I think an important thing to realize is that the map is never the territory. It is merely a description of the territory. Some maps more accurately portray the territory than others, but it doesn’t make them any closer to actually being the territory. Even a map that perfectly describes the territory in every possible detail is still just a map, it is not the territory itself. The map is the map, the territory is the territory, the map describes the territory. There can be as many maps as you need, covering as much detail as you need for your given application, but there is still only ever one territory.
The same way, there is a concrete reason that mathematics works the way it does, else it wouldn’t work the way it does, and since there is such a reason we should be able to find it. Godel’s theorems are no reason to stop looking, though they may be a reason to look somewhere else.
“To review, the reductionist thesis is that we use multi-level models for computational reasons, but physical reality has only a single level.”
But wouldn’t an ultimate/complete physical model of reality have to explain why our brains, when hit with certain stimuli, produce a world of solid coloured objects? (To disagree would be to admit the content of our minds is mystical and other worldly.) And if the model does explain it, then aren’t our maps part of reality too (i.e. real)? So therefore isn’t reality multi-level?
I don’t see how you get to multi-level reality by this thinking. But part of the problem of speculating about the philosophical consequences of reducing mind to brain is that we don’t have a complete actual reduction to point to.
There is only one example I know of where a map of the territory has been perfectly embedded within the territory; where the map elements really correspond to territory elements; where every territory element is represented by a map element; and where some particular territory elements correspond to (are the physical substrate for) map elements. That example is the proof of Godel’s incompleteness theorem for arithmetic.
The details of the mappings in each direction between map and territory are complicated, but mundane. However, the consequences of this embedding are at least a little bit interesting in this context. Godel finds that the embedding must be disappointing to an Eliezer-like reductionist. I don’t think that you can twist his result into support for a multi-level reality (or multi-level territory). But he does show that the territory is rich enough so that no single map can completely cover it; that you may need infinitely many levels of map to completely cover everything that is out there in the territory.
Now Godel’s theorem is just an analogy here. There is no particular reason why difficulties in finding a compact and satisfactory first-order logical foundation for mathematics necessarily tell us anything useful about difficulties in finding a foundation for physical reality. But still, since we all admit that we don’t really know how deep the true territory lies below our best modern maps, and since the history of physics is that the maps keep getting improved with no end in sight, shouldn’t we at least remain open to the possibility that the territory is non-existent (or at least inaccessible) and that all of science is just a series of better and better maps? If it is “maps all the way down” and if our current best map is not the territory, doesn’t that kind of turn around our intuitions as to who is committing the Mind Projection Fallacy here? Is it Mind Projection to imagine that the territory actually exists simply because you have a map of the places you are interested in? Or is it Mind Projection to deny that a map exists simply because you don’t have a map for your area of interest?
I’m no mathematician, but Godel’s theorems seem to have some heavy constraints placed on them. I also don’t see how this maps territory to the map, it still seems like a map of the territory. More like saying “under certain conditions, it’s impossible to draw a better map.”
I think an important thing to realize is that the map is never the territory. It is merely a description of the territory. Some maps more accurately portray the territory than others, but it doesn’t make them any closer to actually being the territory. Even a map that perfectly describes the territory in every possible detail is still just a map, it is not the territory itself. The map is the map, the territory is the territory, the map describes the territory. There can be as many maps as you need, covering as much detail as you need for your given application, but there is still only ever one territory.
The same way, there is a concrete reason that mathematics works the way it does, else it wouldn’t work the way it does, and since there is such a reason we should be able to find it. Godel’s theorems are no reason to stop looking, though they may be a reason to look somewhere else.