It depends on how you phrase the question, but there is a possibility that the human mind really is a particular type of computer. The reverse would not hold: few people would claim that a wristwatch with basic circuitry is a human mind. But to make the claim that the human mind computes using its organic hardware is not so unreasonable.
As one of my instructors explained it: anything knowable (computable) can be done on a computer; if it can't be known then we (as humans) can't know it either, we just make good guesses, and those guesses are themselves representations of knowable processes given the right heuristics and data.

What is missing from a computer is essentially embodiment and motivation, or what some might call "consciousness" or even a "soul"-- a machine is not human because it doesn't act like we do. But that says nothing about the computational processes in our minds.

I'm not entirely convinced by that position, but I can't find any conclusive way to deny it either.

The only tangible difference (aside from organization and motivation), which might be a crucial one, might be that the brain could be gradient rather than binary, with some neurons activated more than other neurons, rather than just a bunch of 1s and 0s floating around. But even that relies on certain physical/chemical processes that might be effectively reduced to 1s and 0s. I'm not sure...

I think the reason "Philosophers have long since given up on the notion that the mind could be understood as a computer" may be because we don't understand it well enough as a whole for any particular analysis to be effective. That doesn't mean that, in theory, the mind isn't a computer. It means that we don't yet understand it.

I don't have 30 minutes at the moment to watch all of that-- any parts in particular I should check out?

I think that on this issue, at least, we are all agreed.

This is a good way to start 2015 peacefully...

“Is," "is," "is"—the idiocy of the word haunts me. If it were abolished, human thought might begin to make sense. I don't know what anything "is"; I only know how it seems to me at this moment.”

-Robert Anton Wilson

Edited disclaimer: I haven't watched the original video.

It's totally pointless to have this discussion while such vastly different interpretations of the word computer can be assumed and be used to argue both sides of the point. Many people have a modern understanding of what a computer is and do apply that meaning to the analogy of a brain being a computer. Other people, however, can take a more etymological perspective and treat the word as signifying any entity that performs computation. People need to stick to one definition before embarking on an explanation of their argument.

Who can deny that the brain at some metaphysical level implements procedures that can be described as a sort of computation? Not very many, my instincts would lead me to believe. Therefore, a reductionist position would be that we've equated computation to the processes in the brain, therefore it must be some sort of computer (I see jkpate took this line of reasoning in an earlier post).

But once you factor in more encompassing and less abstract details of what makes a computer a computer in the modern day, it becomes easier and easier to argue the opposite point. Computers contain discrete subsystems while the brain has a lot more contemporary inter-dependency and no serious (modern) neuroscientist would opt for the modular approach (well, they're out there - but in the vast minority in my experience and usually are proponents based in a non-neuroscientific field where this modular approach helps them in their, let's say, psychological, philosophical or even linguistic frameworks). The brain has been equated to the modern technology of the day for as long as serious study of the brain/mind has had a potential candidate in the realm of technology. For example, Freud equated the brain with a steam-engine, telephone systems were equated with the brain before widespread adoption of computers and now the modern computer is the analogy of choice. I'd bet that in 50 years with whatever new quantum device we're all familiar with that this, instead, will be the technological counterpart to the human brain. If anything, I think the notion of the brain being like the internet is a better analogy to make, at least that way we can factor in disruptions and show how information can, in many cases, still find alternate paths to keep the information flowing. That is, unless the damage is that severe that it does actually block out whole ISP services and not just individual nodes.

If you apply the definition of computer the same way I do, to this argument, then hopefully I can convince you that at least the answer should be more of a maybe if not a full no.

Computers implement serial-processing and are restricted at the most fundamental level by the fact, while brains are fundamentally parallel-processors of information. Though speed might give the impression that computers can enact processing of information in a parallel way, that is just an extremely advanced implementation of shared streams of serial processing. In computers, information is fed upwards and processed by a higher-order device. Processor is king. In brains, neuron is king in the sense that the pattern of firing enacts the representation of information. Computers are fundamentally digital, while brains cross the analog/digital boundary via the electro-chemical ways that information is sent through the system (while computers are wholly electrical). There is an all-or-nothing representation in the binary system that underlies computers while the way the brain works is fundamentally probabilistic in how neurons fire and current affects the thresholds that determines if an action potential will fire.

The whole underlying structure of computers is incredible uniform in how information is sent through at the basic level, while the chemical structures and individual basic elements of the brain show much more complexity. There are hundreds of types of neurons and the giant concoction of neurotransmitters that send the information around the brain is just fundamentally more complicated than the basic elements of a computer (the so-called Von Neumann Architecture). Yes, this might be a physical difference I'm pointing out which many people would see as obvious, but that also highlights the fact that they would rely on a functional definition and what we know about equating functionality is that it can be done without any regard for inferring that X is the same as Y, though they both perform some functions at the same level. All computers are at the fundamental level is a way to implement fetching of information, apply predefined operations to said data and then store the result somewhere else.

We all know computers can perform calculations at speeds and levels of complexity that are beyond, in all senses of the term, anything that a human brain can perform. We know and accept this, yet this doesn't seem to strike a lot of people as an argument against the fundamentally different processes that both 'entities' exhibit. Brains are susceptible to all sorts of fallacies and tricks that we know computers are not susceptible to, that's actually a huge argument for using computers in many aspects of our society - precisely because they behave qualitatively different to human thought processes. Computers are designed to be so effective, ingenious inventions in modern engineering and brains carry our evolutionary heritage in multiple layers and highly-specialised functional areas that are massively parallel bottom-up processing units.

It's no secret that the processing of the brain influenced many disciplines such as AI or Machine Learning, but even with recurrent neural nets, the fundamentals are still wholly different and unworthy of any 'serious' analogy. The concepts are the same, naturally, because one was based on the other but you'd struggle to find anyone who was even slightly convinced that even the most pioneering deep-learning neural nets can in any massively convincing way be considered to be accurate representations of human learning. That being said, such learning mechanisms are promising and it's mainly due to the lack of understanding from the field of neuroscience that efforts in computing couldn't approximate neuronal behaviour even more closely, but here we're delving out of the the main topic and talking about replication of learning, while the initial question was set more in terms of an equivocation between the two concepts on a much deeper level. Even though such learning is promising, it's well known that computers are just awful when it comes to pattern recognition, as was discovered back in the 60's and yes a lot of progress has been made, but the design of computers hasn't changed since then, we've just changed how we apply higher-level processing which in theory shouldn't change what it fundamentally means to be a computer and to be a brain. There is no evidence whatsoever that the brain implements backprop the way neural nets do, and why should there be? It just further highlights that having a similarly-inspired architecture doesn't really bridge any fundamental gaps in the comparison of brains as computers.

We can do the exact same calculations that computers can do, but being able to approximate the same results says absolutely nothing about the similarity of the processes we used to arrive at that conclusion, something which I hinted at earlier in regard to equating functionality in two different systems. It just says nothing about the similarity and the calculation ability goes way beyond the limits of our brain, just as our brains go way beyond pattern recognition in anything that even the most state of the art computer can do now. 

As you can tell, I am very much in the "No" camp when it comes to the "Are brains like computers?" question. Then again, that's because my interpretation of the word computer is a lot more specific when applied to this question. If that definition was taken away and all I had was the line "Anything that can be thought of as exhibiting a computation (in any sense)" then I would have no choice but to be in the "Yes" camp.

Why do we seem destined in academia to constantly have debates that roar on where people don't see how two radically different definitions can completely change the fundamentals of a specific argument?  I think we'd save so much time if before detailing an argument we were forced to write out the definitions of the words we were using. Then, someone wouldn't need to read a whole paper in order to figure out that the author was using a considerably different definition of the specific concept under consideration.

The Dartmouth Conferences were a huge turning-point in the field of AI and it's there that a division arose in the way people made their fundamental interpretations of intelligent machines. The two divisions were GOFAI (Good old-fashioned Artificial Intelligence) and Connectionism. The first group of people split off and dealt with issues to do with symbol manipulation and computation proving of theorems, geometric proofs and propositional logic / reasoning and so on and so on. They didn't have much regard for trying to mirror the processes of the brain as they took a more goal-orientated approach. The Connectionists, on the other hand, believe that the only intelligent machine is the brain and therefore the studies into computational intelligence and implementations of machines should be guided by and help inform the study of the brain. In contrast to the goal-orientated approach, you can think of these guys as more journey-orientated (though of course the goal still matters)).

Before these two groups split off, there wasn't much of an appreciation of the fundamental difference between both approaches and some saw the fact that machines could do things that humans could also do as an indication of being a good model of the human mind. Russell & Norvig's book on Artificial Intelligence mentions this in the opening pages:

In the early days of AI there was often confusion between the approaches: an author would argue that an algorithm performs well on a task and that it is therefore a good model of human performance, or vice-versa. Modern authors separate the two kinds of claims: this distinction has allowed both AI and cognitive science to develop more rapidly.

This is how they describe the fallacy. If system X and system Y are given the same input, and return the same output, and we don't know how both systems processed the information, then we know absolutely nothing about the internal workings or whether both system X and Y are identical or if they are built on fundamentally different workings. Just like the field of AI in its early days, people used to equate the fact that a system had good results with the fact that it therefore must be a good model of human performance. The trouble is, without looking at the steps in between, such a system tells us absolutely nothing about human performance, only that the output is the same.

I can perform basic calculations in my head to basic multiplication problems, but calculators would do the process in a different way, yet we get the same results. A calculator is not a good model of human performance. We do, however, get the same results. Having made that point, I wanted to reference some of the things you said in your response, Daniel:

ask whether that machine could parallel the human brain in some relevant way.

If they are, then it is not clear why, in theory, some computer (roughly like my laptop, but with some major differences, or potentially any implementation of a Turing machine) could not also do it.

Therefore, we could use a different algorithm in a different implementation and approximate the brain in function.

An interesting question here is whether or not the brain uses an algorithm and one that could be copied on a computer.

If so, then the algorithm and computation could be equivalent while using a different implementation

I choose to interpret this in the only interesting way, which is to ask whether the in-out processing of the brain words in a way that is equivalent to types of logic used in computing. Could all of the behavior of the mind be isomorphically captured in 1s and 0s (or scalar values of the same sort)? If so, it is a computer, and that is interesting.

This is where I think we get to the heart of the disagreement (and it's nice when it comes to an interpretational difference rather than one based on something much deeper) as I can totally understand and appreciate everything you said, it's just that what you're pointing to links strongly to artificially recreating brain processes and my belief is that artificial recreation is itself an argument against the premise of the brain being a computer. Replication, capture, parallel, copy and approximate as much as possible, but the fact that such things can be done provides no sort of evidence for the opinion that the brain is a computer in my opinion.

Those are answers to the questions:

Can we model the brain using computers?
Can aspects of human cognition be informed by computational procedures?
Can neuroscience and computer science inform each other to teach us more about the brain and methods of artificially recreating human cognition?

If those were the questions being asked, I would have a 60ft sign with "YES" in huge, red capital letters. I just don't get the sense that when this question is asked, this is what people mean. I get the impression people mean on a much more fundamental level are these two systems the same. For me it's a categorical no, based on how I apply my definition to the problem, i.e. I define a system by how it goes about getting an answer, it's fundamental physical parts AND the result it returns for a given input. If X and Y giving the same output on the same input regardless of how the answer was worked out is someone's definition of "X is Y" then I can't argue with that. All I can say is that for me, "X is Y" requires a lot more fundamental similarities.

I think we're just taking our own interpretations of what it means to equate two concepts and we have slightly different strictness levels on how we apply it, but I don't really see that we would fundamentally disagree, but I might be wrong.

The whole underlying structure of computers is incredible uniform in how information is sent through at the basic level, while the chemical structures and individual basic elements of the brain show much more complexity. There are hundreds of types of neurons and the giant concoction of neurotransmitters that send the information around the brain is just fundamentally more complicated than the basic elements of a computer (the so-called Von Neumann Architecture). Yes, this might be a physical difference I'm pointing out which many people would see as obvious, but that also highlights the fact that they would rely on a functional definition and what we know about equating functionality is that it can be done without any regard for inferring that X is the same as Y, though they both perform some functions at the same level. All computers are at the fundamental level is a way to implement fetching of information, apply predefined operations to said data and then store the result somewhere else.

While you are quite right that it is obvious that the brain is not a von Neumann machine, it seems strange to me to limit our definition of "computer" to those machines that happen to be cheap and easy to manufacture with 20th-century material science. What is the motivation for choosing a definition that is on its face so arbitrary?

It's no secret that the processing of the brain influenced many disciplines such as AI or Machine Learning, but even with recurrent neural nets, the fundamentals are still wholly different and unworthy of any 'serious' analogy. The concepts are the same, naturally, because one was based on the other but you'd struggle to find anyone who was even slightly convinced that even the most pioneering deep-learning neural nets can in any massively convincing way be considered to be accurate representations of human learning. That being said, such learning mechanisms are promising and it's mainly due to the lack of understanding from the field of neuroscience that efforts in computing couldn't approximate neuronal behaviour even more closely, but here we're delving out of the the main topic and talking about replication of learning, while the initial question was set more in terms of an equivocation between the two concepts on a much deeper level. Even though such learning is promising, it's well known that computers are just awful when it comes to pattern recognition, as was discovered back in the 60's and yes a lot of progress has been made, but the design of computers hasn't changed since then, we've just changed how we apply higher-level processing which in theory shouldn't change what it fundamentally means to be a computer and to be a brain. There is no evidence whatsoever that the brain implements backprop the way neural nets do, and why should there be? It just further highlights that having a similarly-inspired architecture doesn't really bridge any fundamental gaps in the comparison of brains as computers.

Ok, first, we need to observe that "neural nets" and "connectionist models" are really sociological categories rather than natural computational classes. Kohonen self-organizing maps, multilayer perceptrons, and recurrent nets are all introduced under the "connectionist" or "neural network" umbrella, but are algorithmically and computationally quite different -- I can't see a mathematical class that includes these three classes of models but does not include markov random fields, for example, even though MRFs are not generally considered connectionist.

Having made this observation, we need to take care to distinguish the two issues you bring up in your paragraph. First, we should consider the representational capacity of Turing machines and neural nets: the set of functions they can compute, for some rule table, or for some set of connection weights, respectively. As the papers I've provided show, recurrent nets and Turing machines can compute the same set of functions: for some rule table, there will be a set of connection weights that produce the same output set, and vice versa. Some of the comments so far have worried over the difference between continuous and discrete weights. However, the Siegelmann and Sontag (1991) paper only assumes rational weights, and a Turing machine could easily work with rational weights by representing the integer numerators and denominators exactly.

The second issue that you bring up is one of learning: how do we obtain the set of connection weights or the rule table in the first place?  I agree that this is a much harder and more interesting problem. However, backpropagation is not the only story for training neural net-like models. Broadly, the strategy in machine learning has been to recast learning problems as optimization problems, where the objective function is some trade-off between an error-like measure of predicting the observed data and a prior. Learning takes place by minimizing this error-like measure (which may be the difference between the predicted value and the observed value, or the negative log probability of the observed data) and the distance from the prior. To do this, in turn, we need to take the gradient (a multidimensional derivative) of the objective function (the error and the prior) with respect to the parameters, which in this case are connection weights, and then adjust the parameters in the direction opposite the gradient (i.e. "down hill"). The gradient pretty much always involves a difference between the predicted value and the observed value.

Backpropagation tries to squeeze as much as possible out of every data point by updating all the weights in the network with each comparison, but it's not the only approach to training neural nets. Modern neural nets are largely the same as the nets from the 1980's, except they are bigger, and most or all of the training happens in a phase called "pre-training." In pre-training, each layer is trained in isolation to reproduce the patterns of outputs of the previous layer (Hinton and Salakhutdinov 2006). This training scheme relies on a cheap, local approximation to the true gradient, and nowadays backpropagation is considered to be a "fine-tuning" of this learning. There are a variety of other cheap and local approximations to the true gradient as well. While backpropagation is biologically implausible, approximations to its object of computation (objective function gradients with respect to connection weights) may not be.

I think an interesting point to be made is that the parallels between computer science and Psychology may be more convincing than those between Computer Science and Linguistics. The reason is that it is much easier to assert an overly abstract and simplistic model for language processing because we see the data as some sort of code. If we turn to a topic like emotions, though, finding parallels in computation is much more difficult, and the rest is probably a better thought out and more accurate version of how "emotions" are "computed". All of the problems with the comparisons are due to, as I've said above, attempting to overly simplify the problem and solve it with a simple program. But if we take the opposite extreme-- the human mind is a very very complex program, it's much harder to argue against that.

You said it well, Guijarro, here:

It is nonsensical to compare human minds with present-day computers...

...or to think that we might be able to "solve" this at the moment.