Not being able to predict something for combinatorial or noise reasons is a more credible argument.
On a 32-bit computer, there are 2^32 bytes of memory or 256^(2^32)=2^34359738368 possible states. A program is something that takes you from one memory state to another and you want to figure out if the state transitions form a cycle?
Simplified a bit, the n-th busy beaver number is the number of 1s which can be written out by an n-state Turing machine.
For 2-symbols and n-states, the sequence goes: 6, 21, 107, >= 47176870, > 7.4×10^36534, > 10^10^10^10^18705353 — and those inequalities are because the numbers themselves cannot be computed directly, you have to run the program to see what it does.
[1] https://en.wikipedia.org/wiki/Transcomputational_problem
Although I personally believe hypercomputers are not physically possible, I'm not aware of any general proof that they are physically impossible. I've seen papers that suggest physical models for hypercomputers. Notice that there is a hierarchy of hypercomputers of varying powers and some of them can solve the Halting Problem.
Do you have a link discussing physical models for hypercomputers?
https://oronshagrir.huji.ac.il/sites/default/files/oronshagr...
https://link.springer.com/article/10.1007/s11047-009-9114-3
https://sci-hub.do/10.1142/S0129626412400105
An overview is in A. Syropoulos: Hypercomputation: Computing Beyond the Church-Turing Barrier. Springer 2008, chapters 8-9.
Gotta love the subsection headline in the third paper mentioned above: "A CTC Based Relativistic Hypercomputer That Actually Works Without Problems." ;-)
That's the ultimate problem, internally you can't notice if you're going to terminate, and a machine of the same power can't either. It's gotta be stronger.
Since contradiction proofs are arguments that operate in connection with the structure of proofs in general rather than exclusively in terms of the specific problem, then the entire argument may collapse on a technicality like "very large" vs "infinite". It's almost like the truth status of the argument is sharply discontinuous: you can't modulate the argument slightly and arrive at sensibly related assertions.
Whereas if the argument were made solely in terms of the problem itself (without the added meta-layer argument from the contradiction proof), but still used the halting problem, then we might consider the fact that in reality our computers have finite state so are technically exempt, but the argument still holds for all intents and purposes because of how large the finite state is.
Or is there another reason these arguments are generally bogus?
If you imagine you have a lot of inputs to a predicate, then the topology of their truthiness tells you something — and we can talk about “smooth” logic models, where being a little wrong in our assumption means we’re a little wrong in our conclusion. We can then apply tools from analysis, like bifurcation theory.
The “halting problem schema” has a bifurcation at the finite/infinite boundary, which isn’t particularly uncommon for high level functions.
But it’s important to know, when writing proofs.
And generally speaking, places bifurcations can happen are regimes where your model is going to struggle. In the business world, knowing the “logic faults” of your model and keeping yourself in a “smooth regime” is important.
Current AI which probably doesn't fit either of our definitions of intelligence can design novel untrained strategies. See for example AlphaGo Zero.
It's not even clear exactly how our brains work so its hard to imagine that they couldn't be implemented with a sufficiently powerful computer but more broadly a computer doesn't necessarily mean a silicon chip any more than it meant a vacuum tube. If silicon chips prove an insufficient mechanism there is no particular reason we couldn't somehow use a biological substrate or indeed even one we haven't thought of.
Perhaps you simply need to acknowledge our limited understanding of the brain AND expand your definition of the term computer.
Not commenting on what OP said, but I don't think this is correct. Even in principle, how can any computational process produce conscious experiences, which are by nature subjective and unquantifiable?
The Wikipedia definition of "computation" is "any type of calculation that includes both arithmetical and non-arithmetical steps and which follows a well-defined model". But this only makes sense in the context of a designer or observer external to the computation who can identify what that model is and thereby make sense of the output. So you can't say that brain processes are computational, much less life itself, without committing some variation of the homunculus fallacy.
John Searle (famously known for his Chinese Room thought experiment) made this argument in a paper called "Is the Brain a Digital Computer?" [1] He points out that "if we are to suppose that the brain is a digital computer, we are still faced with the question 'And who is the user?'"
A related problem is qualia. There is no computational process that will produce the sensations of colour or sound or touch. At best you will have some representation that requires having actually experienced those sensations to understand it. So a computational process cannot be the basis of or an explanation for those sensations, and therefore consciousness generally.
[1] https://philosophy.as.uky.edu/sites/default/files/Is%20the%2...
I mean, there's nothing physically stopping us from simulating a brain, right? It's a finite object with a finite amount of physical ingredients, and therefore with a finite amount of computing power we can simulate what it does. To me personally, that's a computational process. Maybe that's an overly broad definition of computation, but I think these debates tend to be about whether there is something fundamentally different about "life" (by which I assume you include consciousness). But maybe that's not what you're saying.
> He points out that "if we are to suppose that the brain is a digital computer, we are still faced with the question 'And who is the user?'"
What does that question even mean? I think it seems deep because we humans have a tendency to ascribe some sort of supernatural aura to our lived experience. Life is something incredible but that (at least to my knowledge) is not uncomputable...
> There is no computational process that will produce the sensations of colour or sound or touch.
Got one: the brain!
> At best you will have some representation that requires having actually experienced those sensations to understand it.
Why does a computer not "experience" something?
Searle: "Thus for example the wall behind my back is right now implementing the Wordstar program, because there is some pattern of molecule movements which is isomorphic with the formal structure of Wordstar. But if the wall is implementing Wordstar then if it is a big enough wall it is implementing any program, including any program implemented in the brain."
That's why Searle asks "who is the user?" At some point things have to stop being observer relative and have an intrinsic meaning or essence of their own.
> Got one: the brain!
That's circular reasoning. The point is that qualia are not something which, in principle, can be the subject of computation. There is no way to represent the fullness of sensation itself, like the redness of red or the softness of silk, as information. So how can our brains be "computing" it?
Its like saying that some deficits in computability prevent us us from doing arithmetic and therefore from launching rockets successfully at distant targets.
I might never know the exact pattern in my brain of the "redness of red" as experienced by you but it seemed to work well enough for my brain to form a pattern similar enough to communicate thoughts just as the incompleteness or inherent lack of precision of measurement don't prevent the rocket from being launched successfully.
As far as I know, the only thing limiting us from perfectly understanding the brain is our limitations with measuring it. I don't know of any scientific studies that claim the brain exists outside of physical space.
Let's assume the brain doesn't exist purely in physical space. Free will exists. There is something immeasurable and outside of matter and energy that experiences the color red. Sensations are impossible to define because they exist only in this immeasurable world.
I heard about a guy that claimed it was obvious that the origin of lightning and earthquakes were from the gods themselves. I try not to think like that guy.
A sequence of neurons firing is not equivalent to the sensation of red. It doesn't even tell you anything about the nature of the sensation of colour more broadly, or why the sensation of red looks the way it does and not like, say, the sensation of blue or yellow instead.
All you have is a material correlate -- a merely descriptive physical "law".
Have you seen videos where people perform experiments on people's brains while they're awake? The subjects experience sensations that are inseparable from their neurons firing.
I would say the sensation of red and neurons firing are the exact same thing to the person experiencing it. It's like saying a flashlight that is on is different than photons traveling away from a light bulb with a battery and a current. They're the same thing to the observer. The sensation of red is caused by and is only possible by neurons firing. The neurons firing causes and only results in the sensation of red. The observer does not know the difference.
> It doesn't even tell you anything about the nature of the sensation of colour more broadly
I don't think seeing red tells us about the sensation of color more broadly either. I think that's a concept created through human discussion, not by our senses.
> or why the sensation of red looks the way it does and not like, say, the sensation of blue or yellow instead.
I was talking to your point of "but whether that experience of redness itself is information". I don't know why red looks the way it does, but I imagine the reason exists in the physical world and we could find out if we understood the brain.
I do think in the future we could activate someone's neurons and have them experience red, blue, and yellow in any combination we want. And we could give someone else the same experience (hypothetically we perfectly understand the brain) by activating neurons in their brain. I think that is perfectly communicating color.
What does "inseparable" mean? That the sensation occurs at the same time that the neurons fire? That may be true, but it doesn't make them equivalent.
> It's like saying a flashlight that is on is different than photons traveling away from a light bulb with a battery and a current.
They're not the same, for what it's worth. The term "flashlight" conveys a certain intent and structure that "photons traveling away from a light bulb with a battery and a current" does not.
> The sensation of red is caused by and is only possible by neurons firing. The neurons firing causes and only results in the sensation of red. The observer does not know the difference.
The fact that two different phenomena are closely coupled via a cause and effect relationship does not make them the same phenomena.
If you push two magnets together, the fact that the same force causes them to attract or repel does not mean that the motion of the first is literally equivalent to the motion of the second, or that the force itself is literally equivalent to either motion. They are closely correlated, but ultimately distinct.
You just can't avoid the fact that qualitative phenomena do exist in their own right. They can't be explained away using a physical model that assumes from the get go that they don't exist.
Erwin Schrodinger said:
> Scientific theories serve to facilitate the survey of our observations and experimental findings. Every scientist knows how difficult it is to remember a moderately extended group of facts, before at least some primitive theoretical picture about them has been shaped. It is therefore small wonder, and by no means to be blamed on the authors of original papers or of text-books, that after a reasonably coherent theory has been formed, they do not describe the bare facts they have found or wish to convey to the reader, but clothe them in the terminology of that theory or theories. This procedure, while very useful for our remembering the facts in a well-ordered pattern, tends to obliterate the distinction between the actual observations and the theory arisen from them. And since the former always are of some sensual quality, theories are easily thought to account for sensual qualities; which, of course, they never do.
Can a sensation exist without neurons firing? The root of our conversation is the question if a sensation purely exists in the physical world. If it does, then it is possible to measure it. If it doesn't, then that breaks our scientific understanding of the world and would be exciting news.
> They're not the same, for what it's worth. The term "flashlight" conveys a certain intent and structure that "photons traveling away from a light bulb with a battery and a current" does not.
Yes there is no strict definition of a flashlight. Let's use your definition of a flashlight. Is it possible in your mind to separate the concept of a flashlight and your definition? Without "your definition here", the flashlight no longer exists. My point was without firing neurons, the sensation does not exist.
> The fact that two different phenomena are closely coupled via a cause and effect relationship does not make them the same phenomena.
My wording was not the best. My point was that the sensation of red is physically equivalent to neurons firing. How do we measure a sensation? If we cannot measure a sensation, does it exist in the physical world? If it doesn't exist in the physical world, then what does it existence mean to the scientific community?
> If you push two magnets together, the fact that the same force causes them to attract or repel does not mean that the motion of the first is literally equivalent to the motion of the second, or that the force itself is literally equivalent to either motion. They are closely correlated, but ultimately distinct.
I agree that these forces are distinct. We can measure the force of each magnet separately and we can define the motion of one magnet without referencing the motion of the other.
> You just can't avoid the fact that qualitative phenomena do exist in their own right. They can't be explained away using a physical model that assumes from the get go that they don't exist.
What is a qualitative phenomena? I couldn't find information on this term.
If we can't measure a qualitative phenomena in the physical space, what does it mean to exist?
With the right algorithm, could interpret the randomly moving particles in a gas as computing conway's game of life or anything else, if the algorithm just disregards everything about the particles and contains instructions that generate the expected results from conway's game of life. In that extreme case, I don't think it's useful at all to claim that the gas particles are simulating conway's game of life.
In an opposite extreme, you could say that the randomly moving particles in a gas are computing the motion of the random movements of particles in a gas. The interpretation algorithm is just "look at the particles at time t. Their locations represent the particles' locations at time t.". It's clear here that the system being interpreted is in fact doing all the computation and that nothing is hidden in the interpreter's work.
One interesting way to try to differentiate these two cases is that if you want the results of a longer-running simulation, then in the latter case, you let the actual system run longer, and the work to interpret it doesn't increase at all. In the former case, if you want to get the results of running conway's game of life for 2000 steps instead of 1000 steps, then it doesn't matter how long you let the gas particles go on for, but you do have to do more work on the interpreting side.
However, for a practical claim, it is probably impossible to formally prove that an interpreter function is both bijective between a physical system and a computation (it maps absolutely every possible state of the physical system to exactly one step of a computation).
However, it's important that the following argument can be made: if the evolution of a physical system is isomorphic to a computation of a particular algorithm for solving the traveling salesman problem, and if the phsyical system needs ~1 second for each step, then the system can't go from state A to state B in less than X seconds, where X is the number of steps required by that algorithm to reach those same steps. The actual interpretation of the algorithm or its purpose is not relevant here, the mathematical limits of how the computation happens remain relevant regardless.
That is because you can't find 2 different isomorphisms between the same physical system and 2 different computation that are not isomorphic to each other, if these are actual proper isomorhpisms (bijective) and not just hand-wavy analogies.
This is completely wrong. The opposite is true: computation is a mechanical process, it does not depend on an observer giving it meaning. It's true that the same mechanical process can be interpreted as different computations, but they will have the exact same computational properties (e.g. complexity), only the result will be interpreted differently.
In particular, it is extremely unlikely that the wall is implementing Word Star, because WordStar is a highly structured computation. The wall MIGHT be implementing some very simple additions, and essentially any process is implementing any one step computation.
I see what you're saying, and maybe I am misunderstanding your point, but to me it seems like you've gotten yourself bogged down in wordplay when there is something much simpler going on: say I have a human named Bob from Des Moines, and next to him is a machine constructed to approximate Bob to arbitrary accuracy (this is possible because Bob is a made up of a finite number of particles/wavefunctions). Are you arguing that there's something special about Human Bob? If so, what is your argument for that? The two are "indistinguishable" and by that I mean whatever threshold you have for two things to be "indistinguishable" (practically speaking), you can technically make a reproduction of Bob that satisfies that threshold.
> That's circular reasoning. The point is that qualia are not something which, in principle, can be the subject of computation. There is no way to represent the fullness of sensation itself, like the redness of red or the softness of silk, as information. So how can our brains be "computing" it?
I would argue this is circular reasoning. "There is no way to represent the fullness of sensation itself" -- yes I would argue there is: whatever time-dependent set of physical states make up this "realization" in your brain.
This is true even of a chess program that attempts to model the current and possible states to the chess board in a fashion as to bring about a goal by way of selection of moves.
Suppose we take a very precise process and produce an exact physical copy of you. For being artificial it ought to experience the same sorts of experiences as you. The same ought to be true of a computer simulation of same. The same ought to be true for a variety of increasingly large modifications of the original design. After all if billions of humans can pop out divergent versions of humans who are all conscious it seems hard to argue that you are a unique configuration. In fact if we imagine working for the next 1000 years on producing a better human being that we ought to be able to produce beings who no longer regard us as truly human because we lack both subjective experiences they regard as essential and computational capability. Maybe they can hold a million times more data in their head at once and they regard us as squirrels.
These beings might regard our workings as completely explicable and replicatable in many substrates while regarding their own workings at the far limit of their own understanding as inherently beyond all possible understanding.
Both you and they are probably wrong. Searle was an asshole.
It is disturbing that a philosopher who writes books about these concepts does not understand even this elementary fact about computation. The whole point of developing computer theory was in fact to rid mathematics of the need for human ingenuity, to find simple mechanical rules that can be followed even by a machine to arrive at the same results that a mathematician would.
Related to qualia and the Chinese room experiment and so on, those are arguments about something we perceive, but they do not describe something that we know for sure is fundamental about the world. They may well be descriptions of an illusion we have. You can't assume the existence of qualia as proof that something can't be computational, it mostly goes the other way around: you would have to prove that qualia are real to prove that something can't be computational.
Dunno, don’t care, just want a functional machine. If it gets from A to B, “swimming” is irrelevant.
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As a matter of philosophy, the typical response is qualia happens to everything, but we only recognize it in things with dense computation and self-awareness similar to ours.
Like a cat or a dog or a whale.
We can maybe see hints of it in birds, insects (colonies), etc.
We’re starting to discover some of the complex signaling pathways in, eg, old growth forests — but they’re so out of scale and unlike us, we have trouble comprehending whatever experience, eg, the giant fungus under Oregon might have.
The magical thing you think is beyond comprehension just isn't real.
Until we start understanding how the brain encodes and 'computes' thought, we can't really claim to know if it is or isn't simply a computer.
Even if we knew that a person saw red when such and such neurons fired, the neurons firing would still just be a material correlate. It would be in no way equivalent to or explain anything about the sensation itself.
But I am talking about a much more in-depth understanding of the working of the brain, similar to the level of understanding we have of a microprocessor all the way from transistors to the algorithms running on it. If we could understand human thought at a similar level, we MIGHT find out that "the feeling of red" is not fundamentally different than "the understanding that 1 + 1 = 2", and we could come up with quantifications of it in different ways, from the physical representation in the brain to a certain "bit pattern" in the abstract model of the human brain computer.
Note that the argument for qualia is not one that proves the existence of qualia - it is essentially only a definition. We have no reason to believe that the thing which the term qualia describes actually exists in the world, beyond our own personal experience, which is circular in a way. The argument goes "I feel like this thing I'm experiencing is a qualia, therefore I assume that things similar to me also have qualia", which sounds logical enough. But then, "things similar to me" is actually defined in such a way that it basically assumes qualia exist, since an AGI whose internal state we could probe precisely enough to prove that qualia do not exist for it is then assumed to be outside of "things similar to me".
I guess the idea is that an abstract concept like "the understanding that 1 + 1 = 2" would be easier to "quantify" in the relevant sense than "the feeling of red", but I don't think that's true.
The very concept of a representation presumes an intellect in which that representation is mapped to the underlying concept. No particular physical state objectively signifies some abstract concept any more than the word "dog" objectively signifies that particular type of animal. But our mental states must be able to do so, because denying this would be denying our ability to engage in coherent reasoning and therefore self-defeating. So those mental states can't be "implemented" solely using physical states.
This argument was actually proposed by the late philosopher James Ross and developed in greater detail by Edward Feser. [1] A similar argument -- though he didn't take it as far -- was made by John Searle (of Chinese Room fame). [2]
But in any event, I would reject the notion that any representation of "the feeling of red" is equivalent to the sensation itself.
> Note that the argument for qualia is not one that proves the existence of qualia - it is essentially only a definition. We have no reason to believe that the thing which the term qualia describes actually exists in the world, beyond our own personal experience, which is circular in a way.
Well, I think it is self-evident that qualia exist for me, and that those same qualia demonstrate that there are physical correlates of qualia. I also think there is good reason to think that qualia exist in others because we share the same physical correlates.
Can I completely prove or disprove that others have qualia? No -- not you, not a rock, not an AGI. But I still have the physical correlates, which gives me some basis to draw conclusions.
[1] http://edwardfeser.blogspot.com/2017/01/revisiting-ross-on-i...
[2] https://philosophy.as.uky.edu/sites/default/files/Is%20the%2...
I have read the entire paper - thank you for the link! - and I find it either false or trivial (to use a style of observation from Chomsky). Searle is asserting that computers don't do anything without homunculi to observe their computation, which is patently false. If I create a robot with an optical camera that detects if there is a large object near itself and uses an arm to open a door if so, the system works (or doesn't work) regardless of any meaning that is ascribed to its computations by an observer. It is true that the computation isn't "physical" in the sense that there isn't a particle of 0 or 1 that could be measured, but it is also impossible to describe the behavior of the system without ultimately referring to the computation it performs. So, if Searle is claiming that such a system only works (opens the door) in relation to some observer, then he is obviously wrong. If he is claiming that the physical processes that occur inside the microprocessor and actuators are the real explanation for how the system behaves, not the computational model, then he is in some sense right, but that is trivially true and no one would really contest it.
Furthermore, there likely is no way to actually give an accurate, formal physical model of this entire system that does not also include some kind of computational model of the algorithm it performs to interpret the photons hitting the sensor as an image, to detect the object, to determine if the object is large enough that the door should be opened, to control the actuator that opens the door etc.
Basically, you can look at human beings as black boxes that take in inputs from the environment and produce output. Searle and I both agree that there exists some formal mathematical model that describes how the output the human being will give is related to the input that it gets (including all past inputs and possibly the entire evolutionary history). However, he seems to somehow believe that computation is not necessary as a part of this formal model, which I find perplexing.
His claims that cognitivists believe that if they successfully create a computer mimicking some aspect of human capacity that the computers IS that human capacity seems completely foreign to me, I have never seen someone truly claim something this absurd. At most, I have seen claims that if we have successfully created a computer system mimicking a human capacity, that this constitutes proof against mind/body dualism at least for that particular capacity, which is I think relatively correct, though more formally this should be called evidence against the need for mind/body dualism rather that actual proof.
> because denying this would be denying our ability to engage in coherent reasoning and therefore self-defeating. So those mental states can't be "implemented" solely using physical states.
I don't think this holds water. A computer (the theoretical model) is, be definition, something that can perform coherent reasoning without any special internal state. A physical realization of a Turing machine can "think about" any kind of computational problem and come up with the same answer that a human would come up with, at least in the Chinese room sense. Yet we know that the Turing machine doesn't have any qualia, so why should we then believe that qualia are fundamental to reason itself?
To me, computer science has taken out all of the wind from any kind of qualia-based representation of the human mind.
> But in any event, I would reject the notion that any representation of "the feeling of red" is equivalent to the sensation itself.
This I agree with in some sense - the map is not the thing. Let's assume for a moment that we have an AGI which uses regular RAM to store its internal state. Let's also assume that the AGI claims that it is currently experiencing the feeling of seeing red. We could take a snapshot of its RAM and analyze this, and even show it to another AGI, which could recognize that some particular bit pattern is the representation of the AGI feeling of red. Still, that second AGI would not be feeling "I am seeing red" when analyzing this bit pattern. It could though feel "I am seeing red" if it copied the bit pattern into the relevant part of its own memory, even if its optic sensors were in no way receiving red light.
Whether the system "works" or "doesn't work" is dependent on what the machine was designed to do, which is not an objective physical fact about the machine. Perhaps the machine was not meant to open the door when an object is detected, but to close it instead, or to do something else entirely; only the designer would be able to tell you one way or the other.
The same is true for all computation, and that is Searle's point.
> A computer (the theoretical model) is, be definition, something that can perform coherent reasoning without any special internal state.
Computers don't actually engage in reasoning, though, for the same reason. A machine is just a physical process, and physical processes do not have determinate semantic content.
Ross and Feser then argue that because thoughts do have determinate semantic content, they are necessarily immaterial, and I think they are correct.
(This argument is unrelated to qualia; I don't think qualia are fundamental to reason itself.)
This property of determinacy seems ill defined as well. It's basically defined from the assumption that the human mind is immaterial. If a machine and a human both arrive at the same result when posed a question (say, they both produce some sound that you interpret as meaning '42'), by what measure can you claim that one had semantic meaning and the other did not?
The idea of cognitivism is that there is no fundamental difference (even though of course it is very likely that the process by which this particular machine arrived at that result is different from the process by which the human did).
If I stand by a door and open it when big objects come into my field of view, how is that different from a machine doing the same?
And then, if I had a Machine that could converse and act just like a human (including describing its feelings and internal sensations) while doing nothing fundamentally different from our current PCs, by what measure would you say that this machine is 'simualting' a mind and is not in fact a mind in itself? (though of course it would be a different mind than a human would have).
Thanks for the discussion! :)
Good example, because the vast majority of people don't understand that. I tried and I still don't, nevermind someone who doesn't even care.
I mean, I know the theory, I know the individual parts, but can't quite fully understand how a complete processor works.
If someone from as early as 1920 would find an advanced robot that is a combination of some Boston Dynamics model and offline/autonomous Google Assistant (so it could walk, listen/talk/reply, and maybe pick stuff up), they would not be able to figure out how its "brain" works. At best they'd have a general idea/theory.
Same thing with our brains and current understanding of it. I believe it is possible to reverse engineer it completely, but not with today's tools.
The most common belief is that consciousness is simply the self-introspection of a sufficiently powerful computer that can form models of other agents. That is, this computer is able to infer what other agents may do using a model of their inner state, such as beliefs about the world and desires; then, if it applies the same model to itself, it comes up with a similar image of an agent which it calls its own consciousness. Qualia and such are then just illusions, theoretical properties of these models, not fundemantal properties of this world (somewhat equivalent to saying that in fact we are all philosophical zombies, no one has any qualia).
I am not claiming that we know for a fact this is true. But we also don't know anything that can conclusively disprove these hypotheses for now, certainly not something as simple as the idea of qualia.
We don't need to know. It suffices to expand "reason" to include not just inference, but properly those things which inference depends on, namely, conceptualization+abstraction and judgement. You could never infer that "all triangles have angles adding to 180 degrees" unless you were in possession of the signified concepts. And here is where the temptation to frame brains in terms of computers becomes plainly, let's say, problematic. Concepts like "triangularity" or "the color green" are abstract in that they do not exist as concrete things in their own right. You can have concrete green triangular objects in the world, but not triangularity or green as such...except in a mind that is able to abstract universals from particulars. So images (including the vulgarized CS sense) won't help you because they're always concrete impressions (one green triangle at the expense of all other possible green triangles). Formal structures expressed in what amounts to some notation won't help you either because they only get their meaning from an interpreting mind. Often, it seems attributions of intelligence to computers stem from a tacit failure to remove ourselves from the picture, projecting our capacities onto a hunk of cleverly arranged metal.
> If silicon chips prove an insufficient mechanism there is no particular reason we couldn't somehow use a biological substrate or indeed even one we haven't thought of.
Computation is a formalism independent of substrate. You can implement a Turing machine using anything that can maintain the appropriate interpretive correspondence. But even then, a computer is not an objective kind of thing like a tree. Unlike a tree, a computer is only a computer because the observer has chosen to interpret it as such, or to use it as such. (The naive materialists in the room might try to expand that claim to encompass anything, but in the very act they've made things worse. The mind's capacity to comprehend the world is severely crippled if not destroyed, and now you have to explain this mind that somehow can entertain the existence of wondrous things like trees and elephants that the rest of the universe is unable to evince, thus making the mind even more mysterious than it was before the reductionist took to his hatchet.) So if substrate makes a difference, then it's the substrate that matters, not some correspondence with a computational formalism.
> You need to start by proving that brains and all idealized computers we can build are inherently on different levels.
The burden of proof is on those claiming minds and computers are the same thing.
I never understand this argument. IMHO the rest of your argument seems to obfuscate something rather simple... your brain is a physical object. The atoms that make up the neurons, glial cells, etc. are real and are governed by physics. Are you saying that what you think of as "you" is made up of more than these physical ingredients? To me that would be invoking something "magical" and would thus bear the burden of proof.
> You can have concrete green triangular objects in the world, but not triangularity or green as such...except in a mind that is able to abstract universals from particulars
Why can a sufficiently powerful computer not conceptualize these things? How is that fundamentally different than what goes on in your brain?
At first blush the mind is just an emergent property of the powerful biological computer in your skull. If you think its animated by a spiritual component its on you to provide that that even exists.
And note that it is not that hard, at least in principle, to construct a system that can detect its own incompleteness.
As far as we know today, the most likely theory is that our brains are Turing-equivalent computers. There is no other known model of computation, and no scientific argument that would show our vrains/thought processes can't be computers (that is not to say we have proven either of these, they are just the most likely statements, like P!=NP).
The fact that you can recognize some paradoxes means exactly nothing about your computational power. There is a sufficiently large lookup table that contains the correct answers to any question you might be able to read during your lifetime. Evaluating it requires nothing more than a finite automaton.