How can a computational approach help us gain insights into the workings of the mind?
It is apparent that the human mind can act in a way a computer does, by following rules, such as manipulating symbols, to compute arithmetic expressions. Importantly the human executing the list of instructions does not need to comprehend what these symbols mean, he simply needs to obey the rules. The important analogy between human reasoning and execution of a computer program is that both need to continuously reduce a problem to more and more fundamental truths, which then can be understood in isolation. These then are iteratively combined until the initial statement is understood/computed.
These hints lead to the questions, if we could not simply assume that the nervous system is a computing system, consisting of individual computing units, the neurons. Even though neurons are physically analog, they follow a "all or nothing" rule.
Modeling these neurons as building blocks in logic networks, McCulloch, W. S. & Pitts, W. (1990) pioneered the idea of the brain as a logical inference engine. The usage of AND , OR or NOT in the interaction of neurons can model the response of any one neuron given its neighbors.
One now could assume that the mind is but a series of computed logical functions. Putnam, H. (1967) provides a different view. The mind and its mental states are functions of the computational process. Direct one-to-one mappings between physiological brain states and mental states would then not exist. This view is revised by Fodor, J. A. (1974). He argues that it is highly unlikely that we will find a decomposition of the brain that is a direct analog of the psychology of the brain. He makes the argument that even if that would be the case,
... then there are only epistemological reasons for studying the former instead of the latter.
In a extreme view, the functional state would be completely decoupled from the physical state of the underlying structure. There would be no hope to understand the mind by observing the structure it is implemented on. Chalmers, D. J. (1994) loosens this assumption by arguing the the causal structure of the physical system must mirror the formal structure of the computation. To whatever degree we assume the decouplement of function and structure, it opens the door to different realizations of the same mental state from different physical states. This in turn leads to the idea of machines possessing the same mental states as we humans do.
Following this functional paradigm we need to ask ourselves, what are these functions and what do they compute. We can view functions from a mathematical point of view. As mappings between in- and outputs. The inputs are perceptions of the physical world, proprioception and exteroception, and the outputs are meaning or models. This in essences means that perceptive functions apply meaning to what is being experienced and thus relate to it. From an evolutionary point of view this makes sense, as the better organisms can relate to or model what is being experienced the better they can act upon it. Dennett, D. C. (2017) put it the following way:
Brains are designed by natural selection to have, or reliably develop, equipment that can extract the semantic information needed for this control task.
Perception thus seems to be the first encounter that a mental state and its associated functions have. The act of perception is one of categorization. It a an impressive feat on its own, to decode raw sensory data and then infer on it. Models for this process of inferring meaning from data has their roots in Bayesian probability theory. Different hypothesis and their prio probability exist and by observing information/evidence the posterior distribution is inferred. The most likely explanation is then assigned as the meaning of the perception.
As an example we can take visual categorization. We start with a set of given categories, in a sense the prio distributions above, and a perception on our retina. The function the brain needs to implement maps this image into one of the given categories. This function needs to map a enormous amount of visual input to a small set of categories reliable and fast. We seem to do it effortless, but thinking about programming such a function in a imperative manner is almost incomprehensible. Nowadays this problem is solved using machine learning and exemplified data. A trained neural network can reach high amounts of fidelity in categorizing images. This process of training an algorithm seems familiar in the evolutionary context. The brain is a "living computational system" continuously learning from data and programming itself, on the level of individuals. In the machine learning space Deep Neural Networks are the frontier of computing such complex task, and they do with great precision. They are modeled after the neurons in the brain. In general the techniques use gradient descend methods to optimize a given loss function, e.g. categorizing cat pictures. The rise of machine learning in the last decades has given us the opportunity to create functions that compute a task the brain does and thus given us access to study those functions and systems they are implemented on.
There exist different opinions about neural networks as merely another specific implementation of a Turing machine, and as such not providing any more insight about mental representations, or a more fundamental process of extracting and reducing to relevant information, which is needed for mental representations. Staying at the example of categorizing images, we can also think of it as learning representations. Can deep neural networks also learn meaningful intermediate representations? In other words, the process of reducing the high dimensional data leads to the representation of features along the way to the actual task at hand. Fundamentally representations are created by reduction. The functions performing this information reduction have been acquired by organism for a purpose, usually to improve its chances of survival.
Another interesting area to investigate the creation and processing of representations is in the space of language. How can we acquire semantic representations? There are different opinions, from a "mental encyclopedia" in which the meaning of words is following the reference into the encyclopedia to find it, like a look-up in a table Pinker, S. (2011), to an innate existing of lexical concepts that are atomic and as such cannot be learned. Criticism for both exists, the former needs a preexisting table and the second one leads to absurd consequences of all conceivable meaning already innate in every human. Following a more deductive approach we can model the meaning of words as a point in a "vector space", where relating concept are "close" in a distant measure sense and together build a connected graph. These structures again can be learned, such that points correspond to probability distribution over relating concepts. New concepts can be acquired by locating it in the space and appropriately altering the connections and distributions. We can show that semantic and syntactic representations can be learned through these intermediate representations. This intermediate representation can again be used to translate between, e.g. visual and audio information, as shown by algorithms that can categorize an image and create language describing them. From language it is not far fetching to describe thought via an algorithm. We think in a mental language and thoughts are but a continuous stream of related mental representations.
Chalmers, D. J. (1994) argues that most mental properties and processes are organizational invariant, in that we might change and substitute the underlying structure but as long as we maintain its causal properties, we preserve its mental properties. The idea can be reformulated from a physics point of view. The first thing we can argue is that information is substrate independent. We may represent bits of information via transistors, neurons, magnetic states or light. The underlying, physical representation does not change the containing information. Otherwise we would need to physically move the matter to transmit information, a ghastly image. If information is substrate independent, so must be information processing. There exists an abstract notion of processing information, which does not rely on the physical implementation executing it. Furthermore we can argue that any computational process is merely one of information processing and thus we arrive at Chalmers statement. If we assume that there exist not such a thing as conscious or mind matter, a special sort of matter that, if information processing would be implemented on it, would expose of mental processes, we inevitably arrive at the notion of computational sufficiency, describe again in Chalmers, D. J. (1994). If a system implements the very same function as mental processes do, it possesses mental properties.
Chalmers proposes the next step in this reasoning, what he coins Computational Explanation, that the computational framework can be used to explain mental phenomena. In other words: If we understand the function that is being computed we understand the mental process and vice versa. It a mathematical description:
This does of course not answer the question which functions lead to mental states and which not, but it gives us a general framework in which we can investigate such properties.
Over the last years improvement in the artificial intelligence space shows that more and more, prior unthinkable, computational tasks have been solved. Learning is the prominent reason for that. Through this the evidence that mental state are describable via computation seems apparent. On the other hand neural networks are often black boxes and its not clear if any actual meaning is inferred. Adding to this are notorious robustness issues. Carlini, N. & Wagner, D. A. (2016) show that a small change in an input image can lead to completely different classifications, even though for a human observer nothing has changed. These and similar results, where neural networks are duped in such subtle ways, show that inside the neural network there exists no such thing like a mental representation of what has been learned. Or at least not yet.
To conclude, the basic premise that mental states are despicable in a functional and computational way is a very pervasive model and allows us to build and reason about what mental processes are, with a toolkit that has been developed over the last 50 years.