Physics and science: the art of taking a stance about undecidable questions

Abstract: In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this existential crisis may appear to be new, we develop the view that it has a long history and that, in fact, providing closure to undecidable questions is a defining feature of scientific practice and development. We support our claim with historical and contemporary examples and suggest that the crux of many instances of undecidability in science is a form of invalid induction. Finally, we use our thesis to discuss the place of mathematics in the sciences, and to assess whether or not certain perspectives in the philosophy of mind might provide us with closure.