Re:Mathematical axioms for consciousness - 2007/07/04 20:39Well...no, they are not the input to M. M takes the universe as input, and gives an altered universe as output. However, this one Turing machine can be taken to be composed of several sub-units. One Turing machine, S, will take the universe as input and give an approximation to the universe as output. Another sub-unit I would take the input as S(UM) and the output as the string of symbols - a "thought". After, T(S(UM)) would be given as input to sub-unit B, with an altered version UM' of the original universe. M is a composition of these 3 other Turing Machines.
I did consider taking the model to be a real Turing Machine, or an oracle, and so forth. However, when I examined the Hodgkin-Huxley equations of neurons, along with several other of the basic equations found in the study of the brain, it seemed as though they all could be exactly simulated on a standard Turing Machine. Now, although I realize that neurology as it stands may be quite a way off from giving highly significant results about the fundamental nature of sentience, but any deviations from Turing-machine computability would have to have some sort of physical explanation. Besides, all the fundamental limitations on Turing machines would not - in my opinion - impose drastic limitations on the mind. It is my belief that an even simpler computational system may one day be shown to contain the full class of conscious behavior, perhaps something resembling cellular automata, but the Turing machine has the most research already done on it, thus making an easier structure to deal with when proving theorems. Anyway, as I have said earlier, many of these assumptions may prove to be slightly flawed in a technicality - but the main purpose of the current model is just to see if such logic is useful at all to the defining of the mind. Which of the assumptions do you think are most likely to be altered by future discoveries?
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Raúl
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Re:Mathematical axioms for consciousness - 2007/07/06 16:43Well, it is not the core of my research, but there are some authors that advocate for a nature of sentience based on quantum mechanics. See this thread for details:
If they are in the right direction, that would mean that a Turing machine computation scheme wouldn’t suffice to replicate the quantum processes taking place in the brain. And they believe that these processes are the ones that produce consciousness. However, there are other authors who think there is a way to simulate quantum processes on top of a Turing machine like computer. For instance, Javier Montserrat [1] advocates for the search of an heuristic ontology on quantum neurology that could be simulated on a Turing machine.
[1] Monserrat, J. "Neural networks and quantum neurology: a speculative heuristic towards the psychism architecture". IWINAC 2007 Invited Speaker.Raúl Arrabales Moreno. conscious-robots.com/raul
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Plato Demosthenes
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Re:Mathematical axioms for consciousness - 2007/07/07 19:07As I explain in my post on the quantum consciousness theories, I do not really see such ideas as undermining a Turing-Machine based approach. If the approach is wrong, I would imagine that the reason why it wouldn't would a large amount of continuous factors involved in the so-called TOE. Turing machines are fundamentally non-continuous, so it would pose a problem. However, the majority of the researchers at this point believe that all properties are at some level discrete, supporting the Turing-machine approach. Besides that possibility, what do you think is the weakest link in the argument? Many assumptions were made, and some of them are clearly more unlikely than others.
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Raúl
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Re:Mathematical axioms for consciousness - 2007/07/09 18:55Well, I think the hardest problem in a theory of consciousness is phenomenology. Other aspects of consciousness (such as attention) can be explained in a functional way. Or even if we don’t have a plausible explanation, one can intuitively see that a functional explanation is possible. Here, by functional I mean computable in terms of a Turing machine. That would mean that the replication of consciousness in an artificial machine is a matter of time. It would consist in the task of designing an algorithm.
But when it comes to phenomenology, how could you functionally explain qualia? The question itself is nonsense. The problem is whether or not to consider qualia as mere epiphenomena. If you consider that the phenomenal dimension of consciousness is actually epiphenomenal, then you tend to think it is a side effect produced in the natural hardware. That is why the theory of quantum consciousness could explain something that cannot be explained in mere functional terms.
What could be then the weakest argument in a pure mathematical account for consciousness? I think phenomenology is definitely one problem in this arena. If you think of qualia as produced by a side effect in nervous system, how could you explain it in mathematical terms?Raúl Arrabales Moreno. conscious-robots.com/raul
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Plato Demosthenes
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Re:Mathematical axioms for consciousness - 2007/07/23 04:45Perhaps, however, any computational system has the qualia of its input. I see no way that it could be falsified, so it may not be a highly scientific concept, but the idea might prove of value. Can you see any ways with which to test this, through either a thought experiment or a physical one?
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Raúl
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Re:Mathematical axioms for consciousness - 2007/07/24 17:03I think the test for phenomenal consciousness is an unsolved problem (as discussed in the Test for consciousness forum [1]). However, we could think about a functional test in which you test the functionality of consciousness but not the related qualia. It would be something like the heterophenomenology method proposed by Dennett. Anyhow, I think heterophenomenology don’t give you any empirical proof or tool to escape from epiphenomenalism.
I haven't had time yet to read much, but it is related to the mathematical roots of mind. This is an excerpt from the introduction:
The Book of Paragon is a web site that offers one solution to the centuries old philosophical conundrum of how minds relate to bodies. This site shows that the perspective simplex, or perspex, is a simple physical thing that is both a mind and a body.
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Re:Mathematical axioms for consciousness - 2008/02/15 13:30So it took me quite a while, but I finally finished reading the book I Am a Strange Loop by Douglas Hofstadter. I think I am now in much better condition to understand your points. So I think I should review again your proposal about the mathematical axioms for consciousness, now under the light of fairly understanding what a strange loop is.
I think I can see much clearer now the point you made with the abstract formulation of mathematical axioms. Could we just say that you’re trying to find a mathematical definition for a strange loop? Then, what is different here from what Gödel did with Russell and Whitehead’s Principia Mathematica? And, how can be these mathematical symbols grounded so to be applied to real subjects?Raúl Arrabales Moreno. conscious-robots.com/raul
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