Penrose proposed that intellect is an understanding that involves consciousness. Penrose argues that understanding is not computable. As proof, he uses Gödel's incompleteness theorem and concludes that conscious thinking has a non-computable component. It is easy to disprove this statement. It is clear that the work of the brain involves many processes that we are not conscious of. It is certain that we are not conscious of the opening and closing of ion channels, work of neuroreceptors, spread of nerve impulses, transport of neurotransmitters, etc. However, it is these processes that are closely related to thinking. Thus, it cannot be excluded that some thinking processes are not conscious. If we are not conscious of something, then we cannot prove it. But this does not mean that the truth is obtained in some uncomputable way! Truth is just innate.
See for details Melkikh A.V. 2019. Thinking as a quantum phenomenon. Biosystems. 176. 32-40.
Article Thinking as a quantum phenomenon
RE: If we are not conscious of something, then we cannot prove it. But this does not mean that the truth is obtained in some uncomputable way!
True enough. But neither does it mean that what we cannot prove is unprovable. Do you not think that anything that is computable is also provable?
I think yes. But this is not the most important question about thinking. The most important that the work of our brain is fully innate.
I don't understand what you mean by "innate". First you say "Truth is just innate." Do you mean a priori knowledge by that? Then you say "the work of our brain is fully innate." Does that mean the evolved or genetically programmed abilities or functions, which may include computational capacities?
Yes, I mean apriori knowledge and programmed (not necessarily genetically) abilities and functions.