blue and black, and others saw it as white and gold, is that their visual systems are computing colours from different estimates of what the illumination is like.
Progress in cognitive science regularly consists in saying with mathematical precision exactly what is being computed – what direction should be estimated from some interaural time difference? – and exactly how the computation is performed. Hypotheses concerning these details can be and are tested against experimental observations, both of how people perform on tests (point to the loud noise, please) and of how populations of neurons respond to stimuli. There’s pretty stable agreement about what would count as evidence for or against hypotheses of this sort. Nobody has any real idea of how else to understand our abilities to, for example, perceive the locations of sounds or the depths, outlines and colours of objects.
Cognitive scientists seem to speak literally when they say that the brain computes
That’s a level of clarity and commitment to a premise that is uncharacteristic of metaphorical claims. Typically, if you press someone to explain just what type of oyster the world is, and where on Earth its gills are, everybody will agree that you’ve missed the point. But in cognitive science, hypothesising what specific kinds of computations the brain carries out and devising experiments to test these hypotheses is, far from missing the point, very often the job description.
Cognitive scientists seem to speak literally when they propose that the brain computes a certain function in a certain way. And the claim that the brain literally computes something implies that the brain is literally a computer (at least in part).
If it were just a metaphor to say that the brain is a computer, then we would expect it to be forever unclear what literal truths we are trying to convey with the use of this (presumably literally false) metaphor. But if the claim is meant literally, then we should hope for some precise account of what one is saying when one says that the brain computes. Some have dug in their heels, confident that cognitive scientists do know just what they are saying when they say that brains are computers: the claim is in fact a concrete, well-understood scientific hypothesis.
Unlike metaphors, whose value is independent of their literal falsity, scientific hypotheses are valuable insofar as they are (likely close to being) true and offer concrete, insightful explanations of phenomena. And, unlike metaphors, ideally one should be able to state precisely and with some completeness what a scientific hypothesis says about the world, and what experimental observations it predicts (give or take some background assumptions).
But the suggestion that we have on hand a precise and well-understood claim when we say that the brain is a computer feels forced. There really isn’t much clarity or agreement at all on what it means to say that the brain is a computer, even among those who agree that the claim is meant literally.
There is a whole mathematical field dedicated to understanding computation. Yet you might be surprised about how little clarity there is about what computation is. Foundational to the field is the Church-Turing thesis, named after the American philosopher-logician Alonzo Church (1903-95) and the English logician-mathematician Alan Turing (1912-54). Both Church and Turing were working to figure out what sorts of mathematical problems can and cannot be solved by blindly following rules of the sort you learn in order to do long division, long multiplication, or to solve quadratic formulas. In other words: what mathematical problems can be solved by rule-based calculation or, as it was called back then, computation? To answer this question, both Church and Turing developed, around the same time in the 1930s, mathematical models to capture what happens when one calculates the solution to a problem.
Church’s model of computation, the ‘lambda calculus’, emphasises giving explicit definitions of functions in terms of a small stock of very basic functions. To give