# What are the limits of human knowledge?

This is an interesting philosophical question.What can we know? (And what not?)

A great deal could be written about this, because the philosophers of antiquity have already thought about it.The most famous of these is Plato. With his cave parable, he laid the foundation for the idea that we, as human beings, are confronted with a fundamental separation between the visible-seeming (what we can perceive with our senses) and the spiritual (the ideas, the truth).The prisoners in Plato’s cave know nothing of their limitations, as they know nothing but captivity. They believe that the shadows they see on the walls are the reality.

This idea has been taken up time and again and today finds itself in a more acute form, especially in so-called radical constructivism, an epistemological school of thought that completely rejects the possibility of objective knowledge.From this perspective, we as human beings are doomed to live in an image *completely constructed* by our senses, without even having the chance to look “behind the scenes”.After radical constructivism, it is impossible for us to decide whether the world that represents our senses really exists, or whether it is a mere illusion or simulation.

Modern science has partly embraced the constructivist view, but assumes that there really is a world that is independent of human senses.But so-called critical rationalism contains the precautionary principle: we can learn about the world, but we will never be able to say with complete certainty whether it is true (or illusion).So we will only be able to approach the truth. This approach to the truth can be imagined, for example, as the child’s play “Point-Connecting”, in which a lot of points are connected by lines according to a certain rule until a meaningful picture emerges. Science draws lines (theories) and then checks whether they fit into the picture or not (falsification). If not, it removes the lines again. Some lines are also drawn twice and three times, whenever a theory has been re-examined and not refuted. Thus, gradually, an image emerges, which may be a fairly accurate reflection of the truth, which we can never fully experience.

Mathematics occupies a special status.Since it does not depend on sensory perception, but only operates with rational calculation, it has a very concrete concept of truth. In mathematics, conjecture can be proved. Until the 20th century, it was assumed that *all* conjectures could be proved in mathematics and that mathematics was a coherent, logical, complete system.However, G枚del’s incompleteness set provided a delicate blow to this assumption.Because G枚del proved (with mathematical precision) that she is wrong. Inspired by the so-called liar paradox, he constructed the statement that any “sufficiently powerful, recursively enumerable formal system” (i.e. a system of signs and rules in which mathematical statements can be proved) “is either contradictory or incomplete”. Put simply, logically flawless sentences can be made, such as “Jacob says he is a liar.” Or: “The smallest natural number that cannot be defined in less than fourteen words.” (The sentence has thirteen words, mind you.)

This made it clear that mathematics is not capable of bringing the unequivocal and unambiguous truth to light.Mathematics, too, is subject to formal weaknesses that cannot be remedied even with the greatest effort and the most brilliant mind.

We find a similar problem in computer science.The P-NP problem divides questions, roughly speaking, into those that can be answered by algorithms with a manageable or manageably increasing effort (polynomial – P) and those that can only be answered with overly growing effort (exponential – NP) . The NP problems include, for example, the so-called Hamilton circleproblem.So far, no algorithm has been found to solve this comparatively simple problem with non-exponential increasing effort. The computer scientists are arguing whether no one has yet made it, or whether there is a general impossibility of finding algorithms with non-exponential effort for these kinds of problems. An answer to the question is not foreseeable at this time.

All these different limits to our knowledge show that we human beings are endowed with the amazing gift of measuring our own spiritual capacity.So our spiritual capacity is enough to recognize where it is limited.

In the novel Solaris by Stanislaw Lem, the human actors are confronted with a being that seems capable of a far greater realization than humans.As a reader, one asks oneanother: What is it like for a fruit fly to communicate with a human being? Would such communication succeed at all? Would the fruit fly have any chance of understanding anything of what has been said? The example, of course, is already encased in language.

Dier philosopher Ludwig Wittgenstein formulated the sentence: “The limits of my language are the limits of my world.” If something cannot be expressed with the possible formal means, it cannot be thought of.If we can’t think of something, can we know?