I hope this makes sense... I've always been curious about attempts to understand the way our minds work. To me, it seems paradoxical and in some ways even hopeless. I suspect that in order for the mind to understand or learn something new, the mind itself (or at least the way it works) needs to be more complex than what it it processing. In other words, the "size" of the new information cannot exceed the "capacity" of the mind itself in order to store it. An example of this would be the way computers work: Let's say I have a PC with an old operating system (Windows 2000) and I wish to run a software CD designed for a more advanced operating system (Windows 8). My old computer will most likely not recognize any of the information on that new CD, either because my old computer requires more free space (capacity of mind) or because the information stored on that CD requires a different kind of technology to decrypt (complexity of idea). Thus, you can use a computer to fully process programs (according to its own capacity), but can you use it to fully process itself? Similarly, if one accepts the idea that the mind, like a computer, is built to understand and make sense of the world outside itself, is there really any hope of ever fully understanding the mind itself?

I don't work in this sort of area myself, but this kind of view has been held. The position is known as mysterianism, and its main proponent is Colin McGinn. Considerations in the same ballpark also fuel the (in)famous arguments against mechanism due to John Lucas.

What certainly does seem clear is that this kind of possibility can't be ruled out a priori. Surely there are some things human minds simply could not ever understand. That's true of all other creatures. Cats, for example, clearly do not have minds complex enough to understand calculus, let alone the nature of their own minds. We all have cognitive limitations. Perhaps we are in a similar position with respect to our minds.

But it is not obvious either that our minds are limited in this particular way. The "self-reflective" aspect of understanding our own minds does not, by itself, show that we couldn't possibly do it. Your references to complexity and the like are suggestive, but there are many ways to measure of complexity.

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