Computability

On the Mathematical Computability of Human Thought

The progressing digitalization and automation of our world increasingly nourishes the fear that human consciousness might be conquerable by machines. This concern stems from the observation that we have already begun to formalize human actions to an extent that questions our freedom and thus also our responsibility.

The idea of a fully algorithmized existence raises profound ethical and philosophical questions that are of central importance in the context of »Digital Humanism«.

A fundamental problem that questions the idea of a complete algorithmization of humans is the Halting Problem in computer science. It proves that it is fundamentally impossible to develop an algorithm that can decide for any arbitrary computer program and any arbitrary input whether the program will ever terminate. Although the Halting Problem specifically applies to computer programs, it illustrates a fundamental limit of computability. It shows that there are certain types of unpredictability that escape algorithmic capture. This unpredictability is an essential aspect of human Deliberation.

The incompleteness theorems of Kurt Gödel provide another important contribution to this discussion. They show that in any sufficiently powerful formal system, there are true statements that cannot be proven within that system, and that no consistent formal system can prove its own consistency. Gödel's theorems set limits on the ability of formal systems to fully capture the complexity of truth and human knowledge.

Two important facets of the debate become evident through the following considerations:

• I am not Brain (Markus Gabriel): The philosopher Markus Gabriel, a proponent of New Realism, emphasizes in his approach of Neo-Existentialism that our subjective feelings and consciousness cannot simply be reduced to the physical processes in the brain. This perspective underscores the importance of the first-person perspective and the challenge of fully objectifying subjective experience.

• Practical Reason and Non-Algorithmicity (Julian Nida-Rümelin): The philosopher Julian Nida-Rümelin refers in his theory of Practical Reason, among other things, to Gödel's theorems to emphasize the non-algorithmicity of human Deliberation. The unpredictability of human decisions, an aspect closely related to the Halting Problem, poses a significant challenge to the idea of a complete algorithmization of human thought.

Other Important Thinkers and Perspectives:

The discussion about the limits of algorithmization of humans is influenced by a variety of thinkers and disciplines. They include:

• Philosophical Perspectives: Thomas Nagel, David Chalmers, John Searle

• Neuroscientific Perspectives: Antonio Damasio, Gerald Edelman

• Logical and Mathematical Considerations: Roger Penrose

Conclusion

The debate over the limits of algorithmization of humans is of crucial importance, even if at first glance it may seem distant from everyday life. However, the life practice of many people is already heavily shaped by rule-based approaches. If we are to live in an increasingly algorithmized world in the future, where human Deliberation is replaced by automated systems, we must confront fundamental questions of freedom and responsibility.

The idea that people are held accountable in an order prescribed by algorithms, without the opportunity to incorporate their own considerations, raises disturbing scenarios reminiscent of dystopian visions like George Orwell's »1984«. It is therefore essential to vigorously pursue this discussion to ensure that the development of technology aligns with the values of »Digital Humanism« and respects human dignity and autonomy.