2013/01/29 by Fernando Sols, Sols, Fernando · 1 voice
Arts and Humanities · Mathematics · Physics and Astronomy · #Calculus (dental) #Character (mathematics) #Computer science #Decidability #Discrete mathematics #Epistemology #Gödel #Gödel's incompleteness theorems #Indeterminacy (philosophy) #Mathematical economics #Mathematics #Philosophy #Philosophy and History of Science #Pure mathematics #Randomness #Scope (computer science) #Sequence (biology) #Undecidable problem #physics.hist-ph
paper · pdf · doi:10.48550/arxiv.1301.7036
To be published in "Intelligible Design", M. M. Carreira and Julio Gonzalo, eds., World Scientific (Singapore, 2013). The last section has been revised to make it clearer
openalex publication_date 2013/01/29 · arxiv created 2013/04/09 · arxiv updated 2013/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The 20th century has revealed two important limitations of scientific knowledge. On the one hand, the combination of Poincaré's nonlinear dynamics and Heisenberg's uncertainty principle leads to a world picture where physical reality is, in many respects, intrinsically undetermined. On the other hand, Gödel's incompleteness theorems reveal us the existence of mathematical truths that cannot be demonstrated. More recently, Chaitin has proved that, from the incompleteness theorems, it follows that the random character of a given mathematical sequence cannot be proved in general (it is 'undecidable'). I reflect here on the consequences derived from the indeterminacy of the future and the undecidability of randomness, concluding that the question of the presence or absence of finality in nature is fundamentally outside the scope of the scientific method.