The analogy usually offered is the carburettor, or the clock. What makes something a clock is not what it is made of — brass, quartz, water — but what it does: tracking and displaying the passage of time. Ask what a clock is made of and you have misunderstood the kind of thing it is. Functionalists say mental states are like this.
The theory arrived as a solution to a specific problem. Behaviourism had tried to define mental states purely as dispositions to behave, and failed because behaviour depends on other mental states: whether you wince depends not only on pain but on whether you want to conceal it. Identity theory then proposed that mental states simply are brain states — pain is a particular neural firing pattern. That is more plausible, but it implies that a creature without our neurology cannot be in pain, which seems wrong about octopuses and clearly wrong about any conceivable alien or machine.
Multiple realisability is the argument that follows. If a mental state can be realised in many different physical substrates, it cannot be identical to any one of them — just as being a clock is not identical to any particular mechanism. Functionalism accommodates this by moving up a level of abstraction: what matters is the pattern of causal relations, and that pattern can be instantiated in many materials. This is also why functionalism sits naturally with computational theories of mind and with the possibility of machine mentality.
ObjectionsWhere it strains.
Absent qualia. The most persistent problem. It seems conceivable that a system could occupy every functional role — take in information, process it, produce appropriate behaviour — while there is nothing it is like to be that system. Philosophical zombies press exactly this. If the functional description can be complete while experience is absent, then function does not exhaust the mental.
Inverted qualia. Two people might be functionally identical while your experience of red is what mine is of green. Since both of us learned the same words for the same objects and behave identically, no functional difference exists — yet something differs. If so, functional role cannot fully determine experience.
The Chinese Room. Searle's argument targets the computational version directly. A person following symbol-manipulation rules could produce fluent Chinese output while understanding nothing, so the right functional organisation appears insufficient for genuine understanding.
The China brain. If mental states are just functional organisation, then the population of a large country, each person passing signals according to the rules describing your neurons, would collectively be in pain. Many find this absurd. Functionalists tend to reply that the intuition is untrustworthy, since we have no experience of minds at that scale — a reply critics regard as more of a shrug than an answer.
Functionalism nonetheless remains the default framework in philosophy of mind and cognitive science, largely because the alternatives fare worse. What it has not done, and what its critics insist it cannot do, is explain why any functional organisation is accompanied by experience at all.