<p>There's a serious science of the theoretical limits of representation / information processing in CS, in complexity theory &amp; computability theory. You can pull some of that stuff across to cognitive science, the question 'what level of the complexity hierarchy does language sit at' has a decent track record of productivity, it's not totally crazy to ask the same thing of cognition in general.</p>

<p>For me, there's a satisfying answer in <a href="https://mitpress.mit.edu/sites/default/files/sicp/index.html" rel="nofollow noreferrer">https://mitpress.mit.edu/sites/default/files/sicp/index.html</a>, although if you start at the beginning, it takes a little while to get there. In the lecture videos, it's the bit where he puts on the wizard hat. Because if you're going to answer a question as profound as this one, it's best to wear a cool hat when you do.</p>

<p>This is not the only answer, some folks believe in literal quantum cognition, so you could go chat to them too. They're kinda fringe at the moment, and I'm not a subscriber, but they are very smart people and the only game in town if you want think about going beyond Church-Turing.</p>

CC BY-SA 4.0
2018-08-25T19:30:53.373Z
what are the theoretical limits of representation / information processing in CS, in complexity theory & computability theory? @steveLangsford
Forsete
CC BY-SA 4.0
2018-08-25T20:28:09.153Z
There's a complexity hierarchy defined by the resources needed, eg time and space requirements. Turing machines are at the top, they can compute anything that can be computed using infinite time and space. The halting problem and the completeness/consistency of arithmetic are beyond Turing machines, so is computing Chaitin's constant. Chaitin's constant is probably a good entry point to this stuff, there's some good popsci writing about it, including a nice pop-math book by Chaitin himself, which is a lot of fun if you don't mind a ton of ！ marks. arxiv.org/pdf/math/0404335.pdf
steveLangsford
CC BY-SA 4.0
2018-08-10T15:14:41.447Z
2018-08-10T15:14:41.447Z
steveLangsford
<p>There are things that we cannot imagine because they are impossible (like a solution to Russell's set theory, since it is impossible to reach that solution because it is illogical.)</p>

<p>Some months ago, discussing with a user in this site, he said that although no one has reached that notion, it could be the case that someone in the future could achieve it, but he did not know the topic well enough to make any meaningful conclusion. (<a href="https://chat.stackexchange.com/transcript/73718/2018/2/28">https://chat.stackexchange.com/transcript/73718/2018/2/28</a>)</p>

<p>Maybe someone here could help me</p>

<p>So could we develop a notion of conceivability that would allow us to imagine all of these things? Even all things that do not exist or cannot exist or are impossible like a solution to Russell's set problem or a thing that is illogical but at the same time is logical or inventing a new logic (or illogic) system...etc? What would be needed to reach such notion of conceivability? A change in the laws of physics? Or just biological evolution in our brains??</p>

CC BY-SA 4.0
2018-08-09T02:09:42.847Z
The question is too speculative for this (science-based) site. Try philosophy.SE.
got trolled too much this week
CC BY-SA 4.0
2018-08-09T15:13:47.650Z
@Fizz Why is it too speculative? I was looking for a science based answer for this question (even if it is hypothetical)
Forsete
<neuroscience><evolution><brain><thought>
Could we develop a notion of conceivability that would allow us to imagine impossible/inconsistent/illogical things?
Forsete
# Could we develop a notion of conceivability that would allow us to imagine impossible/inconsistent/illogical things?

(Asked by: username_0 on 2018-08-09)

There are things that we cannot imagine because they are impossible (like a solution to Russell's set theory, since it is impossible to reach that solution because it is illogical.)

Some months ago, discussing with a user in this site, he said that although no one has reached that notion, it could be the case that someone in the future could achieve it, but he did not know the topic well enough to make any meaningful conclusion. (<https://chat.stackexchange.com/transcript/73718/2018/2/28>)

Maybe someone here could help me

So could we develop a notion of conceivability that would allow us to imagine all of these things? Even all things that do not exist or cannot exist or are impossible like a solution to Russell's set problem or a thing that is illogical but at the same time is logical or inventing a new logic (or illogic) system...etc? What would be needed to reach such notion of conceivability? A change in the laws of physics? Or just biological evolution in our brains??

**Tags:** neuroscience, evolution, brain, thought

> **Comments:**
> **username_1**: The question is too speculative for this (science-based) site. Try philosophy.SE.  
> **username_0**: @Fizz Why is it too speculative? I was looking for a science based answer for this question (even if it is hypothetical)  

---

## 1 answers

### Answer by username_2 on 2018-08-10. Score: 2

There's a serious science of the theoretical limits of representation / information processing in CS, in complexity theory & computability theory. You can pull some of that stuff across to cognitive science, the question 'what level of the complexity hierarchy does language sit at' has a decent track record of productivity, it's not totally crazy to ask the same thing of cognition in general.

For me, there's a satisfying answer in <https://mitpress.mit.edu/sites/default/files/sicp/index.html>, although if you start at the beginning, it takes a little while to get there. In the lecture videos, it's the bit where he puts on the wizard hat. Because if you're going to answer a question as profound as this one, it's best to wear a cool hat when you do.

This is not the only answer, some folks believe in literal quantum cognition, so you could go chat to them too. They're kinda fringe at the moment, and I'm not a subscriber, but they are very smart people and the only game in town if you want think about going beyond Church-Turing.

> **Comments:**
> **username_0**: what are the theoretical limits of representation / information processing in CS, in complexity theory & computability theory? @username_2  
> **username_2**: There's a complexity hierarchy defined by the resources needed, eg time and space requirements. Turing machines are at the top, they can compute anything that can be computed using infinite time and space. The halting problem and the completeness/consistency of arithmetic are beyond Turing machines, so is computing Chaitin's constant. Chaitin's constant is probably a good entry point to this stuff, there's some good popsci writing about it, including a nice pop-math book by Chaitin himself, which is a lot of fun if you don't mind a ton of ！ marks. arxiv.org/pdf/math/0404335.pdf  

---

