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Is it there any computer or cellular automaton or model of the brain where they could compute logically impossible things and incomputable things?

For example, if we wanted to compute/simulate/think about a universe where 1+1=3 (which would gives as result a universe where literally everything could happen, possible or impossible things; where we could do logically impossible things like drawing a line that intersects a circle at three points, factorizing number 181 or finding a solution to Russell's Set, defined as a list of things that both contains itself and does not contain itself at the same time, without resorting to weird definitions of list/contain/etc, i.e. in the context of naive set theory) we would find immediately important problems:

If 1+1=3, everything equals everything at the same time. Everything is also unequal to everything at the same time. If you hold that as a general assumption, then everything is inconsistent. What this means is that given an algorithm and an input, there is no one output. There are infinitely many outputs. In some contexts infinite possible outputs is not an issue (subject to whether or not you assume the axiom of choice) if those outputs fall on a computable distribution. But in the event that we have exploded logic, there is no such computable distribution. Which means that everything both is and isn't an appropriate output. "1+1=apple".

So could there ever be some computer/cellular automaton/brain that could compute these? Is it there any model of such machine/brain? Even if it is physically impossible given the physics that we have in our universe, is it there any model of that?

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closed as unclear what you're asking by David Richerby, Evil, Yuval Filmus, Thomas Klimpel, Thinh D. Nguyen Oct 19 '18 at 15:32

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ I don't see how such a model would be valuable. If, according to our axioms like the Peano axioms, under which 1+1=2 holds true, someone were to prove 1+1=3, that would invalidate those axioms. However, before math was axiomatized, 1+1=2 was already true, there just was no underlying formalism from which it could be deduced. A follow-up question might thus be "Does 1+1=2 show that all of math is inconsistent or just that our axioms and deduction have failed us?." $\endgroup$ – cadaniluk Sep 27 '18 at 16:23
  • $\begingroup$ On another note, if the entirety of math were to be shown inconsistent, that would make a model infeasible. A model relies on deduction and reasoning to predict future events and to expose properties of the modelled object in a consistent way. Computation relies on decidability and the notion of an algorithm. Inconsistency to such an extent you described would render all that non-existent. There is the notion of nondeterminism as opposed to determinism, in which there is not one but multiple states an object (or automaton) can assume. However, this is nowhere near inconsistency. $\endgroup$ – cadaniluk Sep 27 '18 at 16:29
  • $\begingroup$ @cadaniluk I don't really care if "1+1=3" invalidates the axioms of maths, which in fact, it does violate this, but if there is or if there could be any computer/cellular automaton/brain that could compute this and thus simulate what would happen in a universe where 1+1=3 (possible and impossible things could happen, like factorizing 181 even though it is a prime number, drawing a line that intersects a circle in three points or finding a solution to Russell's Set paradox as it is defined in the main body of my question $\endgroup$ – minnafotter Sep 27 '18 at 16:30
  • $\begingroup$ @cadaniluk the problem with trying to compute this (such simulation), is that given an algorithm and an input, there is no one output. There are infinitely many outputs. In some contexts infinite possible outputs is not an issue (subject to whether or not you assume the axiom of choice) if those outputs fall on a computable distribution. But in the event that we have exploded logic, there is no such computable distribution. Which means that everything both is and isn't an appropriate output. So is it there or could there be anything (cellular automaton/computer/brain that could compute this? $\endgroup$ – minnafotter Sep 27 '18 at 16:33
  • $\begingroup$ I do understand your question, but I think it is self-contradictory. To illustrate, why would you think that "[t]here are infinitely many outputs"? If "everything is inconsistent" as you say in your question, how can you ever describe what an algorithm or infinity is? Is infinity = 42? No, it's not. But it is, yes. If you really want somebody to answer this, you have to be more specific about what your model of inconsistency is. A propos "model," that would have to be described in some sort of meta-language, which must be consistent, otherwise its description would be inconsistent as well. $\endgroup$ – cadaniluk Sep 27 '18 at 16:43
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This question is just playing with words. According to Ludwig Wittgenstein, "whereof one cannot speak, thereof one must be silent". OK, I don't know what that quote means. Well, I do not know what this question means either. Or, possibly, I know exactly what this question means even better than OP.

What does not it mean by "everything impossible can happen?" This sounds like a beginner philosopher just starting his journey or a seasoned philosopher in search of unknown territories. It sounds like the merging of waves and particles but many times crazier.

What cannot happen in reality could happen in virtual reality. What cannot happen in virtual reality could happen in pure mind. (Please notice I am stealing the concepts.) Everything impossible happens right here. I mean, it is happening right there inside that sentence.

Does human mind work logically? Does the current question indicate a new passage to new knowledge? Is there anything here that can salvaged just like the negative number, irrational number, imaginary number?

Enough (playing with words) is enough. Let us get down to the ground truth. Suppose some "computer or cellular automaton or model of the brain where they could compute logically impossible things and incomputable things". Can you imagine a way in which that computing thing could bear some positive influence on our world and our understanding of the world in ordinary ways? That request/question is the most reasonable answer to your question, as I see it. All those once "illogical" but not eliminated creations have practical applications, as for example, negative numbers helps us solve equations with positive numbers and for example, some aspects of the world is better described by the imaginary or complex numbers.

(This question and this reply belongs possibly to Philosophy Stack Exchange)

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  • $\begingroup$ Thank you for your question. Please don't get offended but I did not understand you answer. Besides, from what I understood, it is a philosophy-based answer. My question it is related to philosophy in some ways (since it is related with human cognition, possibility, impossibility, existence, non-existence...etc). But I put this question in this site because I need a scientific answer. Is it there any cellular automaton (or computer or anything else or a highly evolved brain) that could compute all of this I said in my original question? Just that. $\endgroup$ – minnafotter Sep 27 '18 at 20:35
  • $\begingroup$ Let me use an example. Suppose I look at you and ask you "can you be a tree?" One of your first reactions might be "What the heck does that suppose to mean?" Then I insist that I really mean what I mean and that it is possible that you are a tree. Then you might start to wonder, "OK, let me assume that in another world/model/minds, I am a tree. Does that matter to me now? " That is the kind of question I was asking at the end of my reply. Basically, I am asking you to make some meaning out of your question since, as I suspect, people will just say what you are asking does not make any sense. $\endgroup$ – Apass.Jack Sep 27 '18 at 20:53
  • $\begingroup$ Just in case the above explanation is still sort of opaque to you, then here is my simplified simple answer to you: no, there is not. (To others, I may or may not give a different answer.) $\endgroup$ – Apass.Jack Sep 27 '18 at 20:55
  • $\begingroup$ so you are advising me that I should ask if there are any cellular automata, computer, brain...etc that could compute impossible things that would have practical applications to our universe, right? That, since what I am asking would not have any real/useful/practical application, most of the people here would tell me that what I am asking it is nonsense, right? @Apass.jack $\endgroup$ – minnafotter Sep 27 '18 at 21:21
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    $\begingroup$ @minnafotter What you are asking boils down to "Is there an X which does not have properties that X must possess?" $\endgroup$ – rus9384 Sep 28 '18 at 23:02

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