Mathematical properties and physical properties are one and the same.
You clearly don't even understand what a "category" is, so I find it ironic that you would accuse someone else of making a category error.
Properties are just categorization. Suppose I categorize an apple as "round." Is that a mathematical property or a physical property?
An apple is clearly
not round in the same sense in which a sphere is round. Nothing in the physical universe is a perfect sphere. A sphere is a mathematical concept.
Wrong.
Mathematics is a way to describe reality. We use mathematics to describe behavior. In fact, it is the only way to fully describe behavior.
That is kind of the whole point of mathematics.
Clearly not spoken to many mathematicians, then.
The vast majority of mathematics has nothing to do with the physical world, and most pure mathematicians have no interest in the applicability of their ideas. Indeed, some of them find it quite irritating when some mathematical concept turns out to be useful in the physical world.
There is no "magic world of mathematics" floating around independent of reality. It is a description of reality and as such it is entirely dependent on reality. No reality, no mathematics.
This is sort of trivial to understand, since if there was no reality, there would be no humans, and if there were no humans, there would be no mathematics.
It's wonderful to see how the most subtle of concepts and the most intractable of mysteries can be swept aside by a few bold assertions.
Mathematics is not a description of reality. It is part of reality. The undiscovered digits of pi are part of reality every bit as much as the surface of Venus.
Completely irrelevant, and your claim to the contrary betrays how little you know.
Any behavior resulting from timing or biochemical processes can also be exhibited by networks of transistors.
Well, that's obviously wrong. Can a network of transistors produce a baby? One of the better-known biochemical processes.
If your tire went flat, and you couldn't find another tire, but some engineer came up and said "here, replace the wheel with this widget, it will behave just like the tire as far as your car is concerned," what would you tell him?
Would you stubbornly insist that the behavior of the tire isn't what allows the car to go? Would you insist that it is instead some magical property of an actual rubber tire that can't be exhibited by any other entity in the universe, and that no matter what his widget does the car won't be "going" at all?
I would not be foolish enough to believe that because some produces a "round " object, that it can replace the wheel. If I wanted to replace a particular component, it's never sufficient to find a property and duplicate it. It is necessary to find
all the essential properties for the role, and to duplicate all of them. This is exactly where the AI view of the brain is lacking. It treats the brain as a network of switches, and decides, on very little evidence, that all the other behaviour is irrelevant.
No, it is not obvious at all. There is no scientific reason why one could not replace a neuron in a brain with a suitably advanced cybernetic device programmed to emulate that neuron and have the brain function exactly as before. None.
If you can think of one, feel free to share it with us.
Replacing a neuron with something that does exactly the same thing will obviously be unlikely to make a difference. Replacing a neuron with something that does just one thing the same and does everything else differently - say for example a transistor - would be very likely to make a difference. Hence we don't replace damaged neurons with transistors.
Many of the theorems of mathematics and computer science seem silly to those who are not educated in the relevant subjects.
Luckally, "silly" doesn't mean squat in science. Sound mathematical descriptions do.
I am not proclaiming how smart I am. I am proclaiming how uneducated in this field you are.
If you want to establish that the substrate of consciousness might be limited to biological neural networks, then you will need to demonstrate that.
It's odd that even though you're happy to proclaim my lack of education, you seem unable to understand the simplest of concepts, no matter how often I repeat and repeat them. I have never insisted that consciousness is necessarily limited to biology. I'm simply stating that we don't know what biological process is responsible for consciousness. We don't know, for example, that it's equivalent to a network of transistors.
It is quite ironic that you are able to imagine how all these different systems in the universe might act as switches -- when it suits your argument -- yet you are completely unable to imagine how anything besides a biological brain might exhibit all the behaviors of consciousness.
I can imagine all sorts of things. I don't assume that because I can imagine something that it is necessarily true.
Perhaps because the latter doesn't suit your argument?