It feels like this article sets up something of a straw man. The analogy that a mind is like a computer is just that, an analogy. It's used to present the high-level structure of the brain in a accessible, understandable way, not as a logical argument.

This analogy is not the justification for why people believe that "the mind can be replicated on a computer". And yet the article tries to disprove the latter, deep and meaningful point by attacking the relatively superficial analogy between [current] computers and minds.

To me, the reasoning behind why I think a computer can theoretically do anything a brain can is much simpler. Programs are ultimately nothing more and nothing less than mathematics. Their capabilities are a finite (but theoretically arbitrary) subset of what mathematics models. And so far, mathematics has been able to model everything. Purely inductively, it seems mathematics should be able to model the mind just like everything else. After all, there is nothing magical about the brain!

At the limit of plausibility, we could just reproduce a mind by modelling a brain using the laws of physics. Sure, this is wildly impractical with current hardware. Perhaps we will never have the hardware to make it practical. But it also demonstrates how it should be possible theoretically: and if something is possible, no matter how impractically, there's a reasonable chance that it's possible in some significantly easier ways.

Saying that a computer can never fundamentally replicate a human mind is the same as saying the mind is beyond mathematical description. To me, this idea does not make sense. I'm not even sure it's well-formed! Mathematics is not a finite set of ideas or a bounded language: it is more like a standard of formality which we can extend in an incredible amount of different ways.

Sure, math has some internal limitations like incompleteness. But these are not really absolute bounds, at least not in the most obvious way. One thing to keep in mind is that mathematics is purely self-contained: all that matters is internal consistency, not a parallel to anything in our actual universe. This means the fundamental limitations are inevitably meta-limitations: they come up when we turn math on itself. Moreover, they only come up when we start encountering the infinite. The human mind may present some meta facets, but it is not infinite, so incompleteness cannot prevent us from modelling it.

It's interesting to note that all the actual arguments for why a computer cannot represent the mind are not actually logical themselves. They rely on vague analogies and emotions, quoting Ionesco but not providing actual reasoning.

Ultimately, it feels like this article is trying to establish a false balance between the two sides of the argument. But they are not anywhere near equal: the people that don't think a computer can model the mind need to present an actual case for why it's beyond the capabilities of mathematics, the system which has fared so well in describing everything else. Where does the line between physics and cognition (which exists on a purely physical plane) come from? Why are they divided? To me, that line simply seems to arbitrary to accept without more cause.

I can see why this line of thought is appealing: consciousness certainly feels magical, so you want to find some real magic there. But I am not convinced real magic exists. Or even makes sense. It would require the human mind to somehow be special in a way that would, at best, be a really suspicious coincidence. I'm not buying it.