What does a clock show? What does it mean to say that this iteration is prior to that? If we reject mathematical models as inadequate for exhaustively answering empirical questions, I am afraid that an answer can only be provided by gesturing, tautologically, towards some sort of unfolding. Tautologically because, of course, our notion of unfolding is already informed by the notion of periodic processes. — SophistiCat
I don't want to reject mathematical models, far from being a mere philosophical point; if I thought that I would have to change job! Specifically, I think mathematical models really do allow us to find things out about nature. What I was trying to highlight was that the use of time in mathematical models doesn't really tell us much about it, as any smooth bijective function of time could be used to parametrise them.
All that really says is that the time parameter in mathematical models is often rather arbitrary, and when thinking about what ontological commitments to form based on mathematical models, we should be very careful with attributing existence to something which may be chosen so freely.
In terms of the Lotka Volterra example earlier, the relevant dynamic the equations seek is the reciprocal dependence of predator numbers on prey numbers. Predator numbers and prey numbers are something it makes sense to have a commitment about, and the rate of change of one with respect to the other is the
target of the model. It's what the equations try to capture.
Time in the model, in that regard, is a useful independent parameter that you can evaluate both populations at. I'm not saying we should do away with it.
So when you ask yourself, "What is time?" you can point to periodic processes or to theoretical models, but then if you ask, "What validates those explanations?" you still have to go back to the phenomenology (including, of course, the phenomenology of clocks), because what else would we go back to? That doesn't mean, of course, that we have to hang on to every prejudice and intuition, but our explanations have to be true to something, or else they just hang free, like abstract mathematical entities. — SophistiCat
What I have in mind is a few procedures for giving an account of the unified concept of time.
(A) One takes the plurality of rates, synthesises that through some phenomenological considerations, and outputs a concept of time which is necessary in
our understanding.
(B) One takes the time variable, synthesises that through some phenomenological considerations, and outputs a concept of time which is necessary in
our understanding.
(C) One takes the plurality of rates, synthesises that through our capacities of understanding more generally, and outputs a time concept which is tied
speculatively to time
in nature.
(D) One takes a time variable, synthesises that through our capacities of understanding more generally, and outputs a concept of time which is tied
speculatively to time
in nature.
You can see that (A,B) and (C,D) are grouped structurally, I don't really care which approach is taken within (A,B) or (C,D), they denote the development of a phenomenological understanding of time indexed to humans and a
use of whatever that time concept is to understand time in nature.
What I'm trying to point out here is that we should not take answers from the (A,B) group of questions as answers to the (C,D) group of questions. Even if one has, like in Kant, linked the unity of the time concept to the sensory manifold and the transcendental unity of apperception, one still has the independent branch of questions about time in nature; like what Riemann and Einstein and even Bergson aimed at; that cannot be given answers in this way. (C,D) questions are possible to address, and are of philosophical merit. They just require a different workflow to address than the 'link to a priori structure of experience' machine, as there is time in nature irrelevant of experiential temporality.
The problems posed by (C,D) do influence how we should think of experiential temporality - perhaps it is not 'primary' in all senses, humans evolved in the presence of a time which is not our own, and in that regard the 'merely ontic' notion of time targeted in (C,D) is primary. But here what really matters is that they're different question groups with different methodologies to attack. (C,D)
weaponise experiential temporality to 'carve nature at its joints'.
My love of the chain rule example is that it suggests one way to exploit the arbitrarity of the time variable to 'internalise' it to other concepts; of differentials of unfolding. While time and unfolding are probably interdependent, time is often seen as unitary whereas unfolding is a plurality of links which we know have affective power in nature. It invites an immanent thought of time, whereas the times thought in (A,B) and the hypostatised 'indifferent substrate' of time are both marred by their transcendental character.
Edit-imprecise summary: time is something empirically real, not just something transcendentally ideal. The empirically real component requires different methodology to attack than the usual Kantian/phenomenological interpretive machines, and is still of philosophical interest.