Creative and geometric times in physics, mathematics, logic, and philosophy

We distinguish two different concepts of time that play a role in physics: $\mathit{\text{geometric}}\mathit{\text{time}}$ and $\mathit{\text{creative}}\mathit{\text{time}}$. The former is the time of deterministic physics and merely parametrizes a given evolution. The latter is instead characterized by real change, i.e. novel information that gets created when a non-necessary event becomes determinate in a fundamentally indeterministic physics. This allows one to give a naturalistic characterization of the present as the moment that separates the potential future from the determinate past. We discuss how these two concepts find natural applications in classical and intuitionistic mathematics, respectively, and in classical and intuitionistic logic, as well as how they relate to the well-known A- and B-theories in the philosophy of time. We acknowledge that we do not offer here a unified concept or a new philosophy of time. However, we contend that none of the existing philosophical accounts fully integrate both the geometric and creative concepts of time.