I realize you’re not interested in defining logical time or presumably the philosophical issues underlying time that would connect it to, but for what it’s worth I think “logical” is a weird thing to call this way of looking at time, but then this approach to time is almost entirely lacking in analytical philosophy as far as I have read so it lacks a good name at all. I’ve instead been calling things that look like this functional theories of time by analogy to functionalism since they treat time by what it does rather than what it’s made of, often because metaphysically it’s made of nothing, instead being a way of making sense of causality as observed from within the universe. That is, functional theories of time treat time as an observable phenomenon rather than a description of physics and make no assumption that time caches out metaphysically to anything that looks like time as it is experienced. Husserl, Heidegger, and Merleau-Ponty all wrote things suggesting we think about time in this way.
I agree that “functional time” makes sense, but somehow, I like “logical time” better. It brings out the paradox: logical truth is timeless, but any logical system must have a proof ordering, which brings out a notion of time based on what follows from what.
I realize you’re not interested in defining logical time or presumably the philosophical issues underlying time that would connect it to, but for what it’s worth I think “logical” is a weird thing to call this way of looking at time, but then this approach to time is almost entirely lacking in analytical philosophy as far as I have read so it lacks a good name at all. I’ve instead been calling things that look like this functional theories of time by analogy to functionalism since they treat time by what it does rather than what it’s made of, often because metaphysically it’s made of nothing, instead being a way of making sense of causality as observed from within the universe. That is, functional theories of time treat time as an observable phenomenon rather than a description of physics and make no assumption that time caches out metaphysically to anything that looks like time as it is experienced. Husserl, Heidegger, and Merleau-Ponty all wrote things suggesting we think about time in this way.
I agree that “functional time” makes sense, but somehow, I like “logical time” better. It brings out the paradox: logical truth is timeless, but any logical system must have a proof ordering, which brings out a notion of time based on what follows from what.