Cognitive closure
“Cognitive closure” means, in short, that there are things our brains are not able to think, not because they are inherently unthinkable but because our brains are the way they happen to be. The cognitive closure thesis is a thesis about the limitations of human cognition, which suggests that there may be some mental constructs that are to us as calculus is to tortoises: mentally unconstructible.
What the cognitive closure thesis asks us to suppose is that there is some cognitive ability X which we lack, and some mental representation Y, as nameless and mysterious to us as calculus is to tortoises, such that if we were capable of X, we would then be able to construct Y; but as we lack the ability to do X, Y is inaccessible to us. In other words, “cognitive closure” is not concerned with representations that are unconstructible by any cognitive apparatus whatsoever, but with representations which the particular limitations of our own cognitive apparatus place out of reach. The science fiction scenario in which cosmonauts discover an alien artifact the design and purpose of which completely eludes them dramatizes this particular sense of cognitive limitation. The primary evidence for our limitations in such a scenario is technological: not only are there certain alien mental constructs we can’t construct, there are also in consequence certain alien technologies we can’t operate, mimic or understand.
It’s fairly easy to come up with a capability X that would enable a creature to have all kinds of mental constructs that we know are inaccessible to us as we are. One such capability is what we might call computational clairvoyance: the ability to see into the future of computations. Given an initial mental representation of an algorithm, a creature blessed with computational clairvoyance would instantly be able to tell you what the state of the algorithm would be after any finite number of steps had been completed (that is, at any point in the “future” of the computation of that algorithm).
One consequence of this would be that all forms of encryption known to human beings would be useless against an alien attacker with this capability, since all algorithmic forms of encryption are breakable in finite time (they are only useful to us because the finite time required to crack some of them is impractically huge). Another would be that the solutions to problems solvable in non-polynomial time would be available to the aliens just as instantaneously as the solutions to problems solvable in polynomial time. The aliens’ travelling sales-entities would be able to plan their routes with optimal efficiency all the time; in fact all kinds of “hard” optimizations would be easy for them. They would have no need for any concept of heuristics, being able to effortlessly “brute force” any problem solvable in finite time. As a result, they would have the satisfaction of being right a great deal of the time, and of being able to be right about things that are necessarily a matter of conjecture for human minds.. Sudoku would hold no interest for them.
If it were physically possible for a biological entity to have computational clairvoyance, it might also be possible for such alien creatures to produce technological devices which replicated their own abilities. Such hypercomputers would never do any actual computing (as we understand it), but might be useful for delivering instantly – via hypercomputational operations inconceivable to us – the results of algorithms too large and complex for the biological aliens to hold in their heads. Hypercomputers would extend the reach of the aliens’ cognitive abilities rather as computers extend the reach of our own.
However, even these aliens with their hypercomputers would not be able to divine the results of uncomputable functions. In particular, they would be struck with awe, and filled with an appropriately humbling sense of their own cognitive limitations, if they were ever to encounter a species that possessed the oracular ability to know instantly whether a given algorithm would ever finish computing its result. Such a species would be able to circumvent the so-called “halting problem”, and would be able to compute all kinds of uncomputable things.
Spooky abilities such as computational clairvoyance and halting divination are not however what most proponents of the “cognitive closure” thesis have in mind when they argue that human cognitive abilities are limited by human neurobiology. This is because it’s difficult to imagine a neurobiology that could actually support these abilities. It might even be physically impossible in a strong sense: not only unachievable by evolutionary means, but physically ruled out by, say, the second law of thermodynamics. It might be impossible not only for us to construct the mental representations supported by such alien brains, but also for us to comprehend the physics of their biological operation. Such beings would have seemingly god-like cognitive abilities on account of their seemingly god-like biology.
The cognitive closure thesis would not be especially interesting if all of our examples involved god-like beings, because all it would really then be saying is that human beings are not god-like: our biological bodies are the products of evolution, and are bound by the same physical constraints as matter in general. It’s not especially interesting that we can’t compute uncomputable functions, for much the same reason that it’s not especially interesting that we can’t build perpetual motion machines. Our “cognitive” closure in that case would turn out to be a broadly physical or logico-mathematical rather than specifically neurobiological limitation.
The cognitive closure thesis becomes more meaningful when we narrow the scope of the example, so that the question becomes whether there is any ability X that an animal brain might have – without going beyond our present understanding of physics and evolutionary biology – that would enable that brain to support a mental representation Y that was unconstructable by us.
If the answer to this question was no, then there would be nothing thinkable by any conceivable biological thinker that we could not think. It would not then be meaningful to speak of our cognitive range as “closed” by the particular limitations of our human biology: we could not say that there was any biologically possible competence necessary for arriving at any biologically possible mental representation that we lacked. To put it another way, nothing that we could not think could properly be classed as a mental construct. The fact of its unthinkability would be a fact about what mental constructs are (qua possible states of possible biological brains, as opposed to ethereal vibrations of alien hypercomputers), not a fact about the cognitive apparatus of human beings specifically.
If the answer to the above question was yes, then there would indeed be non-impossible mental acts of which we were incapable, mental representations that we were unable to access on account of a specific cognitive incompetence. We know that other animals’ brains can do things that our brains cannot. A cat’s brain, for example, acts in concert with the cat’s nervous system to co-ordinate the movements of the cat so that it can fall from a considerable height and land safely on its four feet. Human bodies are unlike cat bodies, and human brains cannot co-ordinate human bodies (and in all likelihood could not co-ordinate cat bodies) to accomplish the same feat. However, it is not clear that any of the cat’s cognitive activity in this case is involved on the construction of a representation, such that we would say that the cat can think something we cannot.
It may be that once you have the cognitive keys to the kingdom of representations, the whole of that kingdom is in principle available for exploration. The constraints on what can be thought by human beings would then be down to the time available (life’s too short to really consider all of the ramifications of some conjectures) and the allocation of mental resources. We are easily distracted, and have to work very hard at not fooling ourselves about things. But these limitations can be overcome to some degree by patterns of co-operation with other thinkers (peer-reviewed science, for example) and the use of tools such as computers that are much better than we are at crunching through algorithmic steps without getting bored and making silly mistakes. Our cognitive limitations are plastic not only because our brains are capable of learning new tricks, but also because the limitations of the technology we use to augment their capabilities are also plastic.