Yesterday would have been his 118th birthday, and I didn't have time to wish him a happy birthday. I'm making them today, late, but the gift is for me. It is food for thought that I share with you. More than a century after his birth, the legacy of Kurt Godel, one of history's greatest logicians, continues to resonate powerfully in our present. In an era marked by the frantic search for absolute certainties in both science and politics, his work reminds us of the importance of accepting undecidability and uncertainty as unavoidable features of reality. Preserving and spreading this message is today more essential than ever to build a future characterized by critical thinking and open-mindedness.
Kurt Gödel's incompleteness theorems and the fall of absolute certainties
You know the famous ones incompleteness theorems by Kurt Gödel? I said “celebrated,” but don't be in awe. Not everyone knows them. I'll give you an example: there is a large puzzle (representing a mathematical system). Someone tells you that the puzzle is complete and that all the pieces fit together perfectly, without contradictions. Do you believe it? Kurt Gödel does not. Kurt demonstrated that in any sufficiently large and complex puzzle there will always be some pieces where it cannot be determined whether they belong to the puzzle or not. To be precise: it can neither be proven that these pieces fit perfectly, nor that they do not belong. Furthermore, one of these “undecidable” pieces is the very statement that says “this puzzle is complete and without contradictions”. In other words, it cannot be demonstrated, within the puzzle itself, that the puzzle is complete and coherent.
This discovery dealt a serious blow to the hopes of mathematicians like david hilbert e Bertrand Russell to construct a complete mathematics. A mathematics capable of demonstrating the truth or falsity of every single statement. It can't exist, David. It can never exist, Bertrand.
But Gödel's lesson goes beyond mathematics. He shows us that the search for absolute and incontrovertible truths has limits, and do you know why? Because reality is too complex to be contained in a fixed system of rules. Even in science and everyday life, we have to accept a certain degree of uncertainty and unpredictability.
Acceptance of uncertainty as the key to progress
Accepting uncertainty and complexity is not a limit, nor a failure. In order not to accept them, we have reduced ourselves like animals in the wild, defending everything by bias, with social media reduced to a dialogue between the deaf. Understanding that no one has the ultimate truth, and that a belief is not a truth proves to be an essential key to the progress of knowledge and society.
Kurt Gödel demonstrated it: it is precisely when we recognize the limits of our thought systems that we can open ourselves to new perspectives and a deeper exploration of reality.
In an increasingly complex and multifaceted world, where the challenges we find ourselves facing (from climate change to social inequalities) escape simple and unambiguous solutions, cultivating intellectual humility and the ability to deal with uncertainty and with others becomes an imperative. Only by embracing the complexity of reality, without giving in to the temptation of easy simplifications or pre-packaged answers, will we be able to find authentic paths for progress and innovation.
Those who are satisfied Gödel (I had to say it, sorry)
Let's take the case I was doing before. That of discussions on social media regarding complex topics such as climate change, moon landings or vaccinations. These discussions often polarize quickly. People take rigid and opposing positions, trying to affirm their opinion as the only absolute truth. Is it the fault of social media? Certain. But who writes on social media? We.
On the one hand, there are those who completely deny the existence of climate change or the effectiveness of vaccines, rejecting any evidence or argument to the contrary. On the other hand, there are those who consider these questions to be definitively resolved by science, without admitting any margin of uncertainty or doubt. Both of these attitudes are problematic and, in a certain sense, they do not take into account the teachings of Kurt Gödel. His lesson on incompleteness reminds us that even the most solid scientific theories can never be considered absolute and definitive truths, but are always subject to revisions, insights and refinements.
This does not mean that we should doubt everything or that all opinions are equally valid, but that we should approach these issues with an attitude of open-mindedness and intellectual humility. We should be ready to consider different evidence and arguments, to recognize the existence of uncertainties and aspects still to be explored, without giving up making decisions based on available evidence. If we applied the approach suggested by Kurt Gödel, we could instead approach these discussions in a more open and productive way. We might recognize that, while we have good reasons to support a certain position (for example, the reality of climate change or the importance of vaccinations), there are always margins of uncertainty and aspects to be explored further. This would allow us to dialogue in a more constructive way with those who have different opinions, trying to understand each other's reasons and find common ground, without sterile opposition.
Kurt Gödel's legacy for a future of critical thinking
Preserving Kurt Gödel's legacy is crucial. It means offering young people an example of courageous and curious thinking, which is not satisfied with pre-packaged answers but knows how to explore new horizons. It means transmitting the value of the passion for knowledge and the search for truth, while knowing that there are no absolute certainties.
In a world that often pushes us to seek certainties and easy solutions, Gödel's example reminds us of the importance of continuing to ask questions, of accepting complexity and of embracing uncertainty as an integral part of our human experience. Only in this way will we be able to build a future in which curiosity, open-mindedness and the ability to adapt to change are the keys to everyone's progress and growth.
We must carry Kurt Gödel's example in our backpack of the future. To never stop questioning ourselves, questioning our certainties and embracing the wonderful complexity of reality. Happy birthday, terrible old man.
