I don't think you even really need a materialist rebuttal for most of arguments. Is this article a joke? I'll go point by point. I won't be able to contradict all of them or at least most likely I won't but still.
- The unreasonable effectiveness of mathematics. [...] This ability could not have arisen through natural selection because it would have had no selective advantage until very recent times.
Sure. A monkey doesn't have any use for understanding algebra. Neither would a human ancestors. But you know what is very useful to an early human? Throwing rocks. You don't have claw, your teeth aren't all that sharp, you're not that strong, but you can throw a rock like nobody's business. So you kill a tiger with it, you kill a leopard or an eagle, and you have babies.
When you're throwing a rock today, what you're doing is calculating, without thinking, distance to the target, force behind the throw, release point of the rock, angle of the release based on shape, motion of target, and so on and so forth until you know exactly when and where and how to throw that rock. So actually there's a lot of advantages to having an innate understanding mathematics.
More importantly, "math" as we know it isn't an evolved process, it's the result of the development of abstraction. Abstraction is incredibly advantageous for survival because it allows you to communicate complex ideas to other members of your group which in turn allows for planning and not just survival but incredible growth. So sure, math is not a direct benefit to survival, but every other part of it is.
Numbers arise from the mind contemplating the empty set in the total absence of any 'things' to to be counted.
Now this is just straight up ignorant of history. Set theory is fairly recent, numbers are not. Numbers most likely started just to show in writing the number of animals/beads/ugly wives you had. This is also why the concept of a zero was so revolutionary when it was introduced to Western Europe. The idea that there was such a thing as a nothing, an empty space? That was crazy.
Math did not start as pondering empty sets, it started as counting apples. From there you move in to geometry because it helps you build temples and pyramids and the like, and you can kind of work from there to the rest of mathematics. Geometry is far more fundamental to the development of math than set theory is, which you can see simply by taking any calculus course at a college. Integrals and derivatives are extensions of geometry.
I won't pretend to know anything about quantum physics since I dislike the taste of foot. Skipping to #4.
All physical systems, including machines, can be simulated by computer hardware and software in terms of algorithms and datastructures.
Yes.
Some attributes of the mind appear to be non-algorithmic, and consequently non-physical and non-mechanistic. This explains why after decades of hype, artificial intelligence is still no nearer to reality.
Artificial intelligence is actually fairly close to reality for one. It governs how a lot of Amazon warehouses are organized, it runs our stock markets. It's not generalized but still, that's a matter of power or design not some mystical impossible barrier. At the end of the day with enough power you could just simulate the behavior of a human brain. That's not efficient but there's no reason we can't do that if we can fold proteins.
In all likelihood the brain behaves in a more probabilistic manner than algorithmic. The glands in your brain that release hormones don't do so at a set rate, all cells just kind of produce chemicals all willy-nilly and that ends up as a general rate of chemical creation. This element of slight randomness also probably gives us a good deal of our creativity since it allows for "mistakes" i.e. deviations from the norm.
I'm not sure how #5 is an argument against the mind being a machine? It's simply a very complex one. Also your brain doesn't so much project reality as take the signals that you have coming in and force them in to a model that you have already decided is correct come hell or high water.
6 talking about emergence and ignoring how discoveries actually happened please stop
Like this is all so. Terrible? For one the chain of being they have for sciences. Ecology < Biology < chemistry < physics < math < nothing is just. That's not how things developed. That's how we view things now but what's important to determining if the mind is a machine or not is to look at how things were discovered rather than how we view them in the moment.
By and large our first science would be botany or medicine though the process for determining what was good and bad was..iffy to say the least. For one, as rudimentary as it is, we gained an understanding that if you put seeds of a plant in the dirt they grow up in to crops you can eat, and you can keep doing this for a VERY LONG TIME. Two, for most of our history plants were our primary medicine. The effectiveness varied but people did have that understanding of nature at the very least.
So from a biological origin you then move on to chemical as you get bronze smelters and later iron smelters and then alchemy and everything else under the sun until we get here today.
If the origin was from nothing, then wouldn't our first knowledge have been physics, then chemistry, then biology, then ecology, then evolution? Isn't the more likely scenario the idea that the brain is looking out for its survival and as such first learns what makes it food and then goes from there? And if you can say "survival is generally what drives the brain in pre-historical humans" then what you're actually just saying is the mind is a biological organ like anything else and it obeys the exact same laws as any other organism on the planet.
tl;dr this whole piece is a steaming pile of garbage. The person who wrote this doesn't seem to have the faintest clue about the history of technology or math or science or...well. Anything really? Like most of us they have set up a worldview and they will attempt to get any and all information to fit in to that model because that is how we function.