# What is the relationship between computation and Gödel's incompleteness theorems? [closed]

In what way do Godel's incompleteness theorems impact computers/hypercomputers? Do they somehow prevent them from being capable of computing everything (of computing literally all uncomputable/undecidable/illogical/logically impossible things)?

To ask this in another way, if Gödel's theorems "vanished" or otherwise did not hold, would that mean that computers/hypercomputers would be able to compute literally all uncomputable/undecidable things?

To take it a step further: Is it only Gödel's theorems that stop us from computing illogical/logically impossible things? For instance, without Gödel's theorems, could we compute things that are (logically) impossible to depict/describe/compute/conceive (like a circle cutting a straight line in 3 points in Euclidean geometry, which is impossible to draw/depict)? Could we compute illogical/logically impossible things that are (logically) impossible to depict/describe even by words?

• "If Gödel's theorems vanished or did not hold ... would computers/hypercomputers be able to compute all undecidable things ?" As stated, the answer is trivial : YES. If there is no death, we will live forever. – Mauro ALLEGRANZA Apr 29 at 10:50
• Gödel’s Incompleteness Theorems is a Mathematical theorem that applies to consistent formal systems with some "minimal" expressive capabilities. Assuming that a real compueter is the physical implementation of a formal system, then also a computer is subject to the theorem. Having said this, what are "impossible things" ? Obviously a real computer compute "possible computations". – Mauro ALLEGRANZA Apr 29 at 10:54
• If Euclidean geometry is consistent, there are no circles cutting a straight line in 3 points (irerspective of G's Th) and thus no computer whatever can compute three distinct intersection points, because there are only two. – Mauro ALLEGRANZA Apr 29 at 10:56
• This is probably the third time this question has been asked. Can someone tell me what is driving this question? Is it some current philosopher's work? Why would a computer be able to transcend reality? Who says they can? – Richard Apr 29 at 11:32
• @Richard A version of Gödel's theorems have passed into popular culture, but in the popular imagination, they are a mystical force, capable of defeating science, mathematics and computing, like a holy relic warding off a vampire. And conversely, without that relic standing in their way, computers would become all-powerful. – Chris Sunami Apr 29 at 16:23