The clock indicates the moment . . . . but what does
     eternity indicate?

— Walt Whitman • Leaves of Grass

A One-Dimensional Universe (concl.)

It might be thought an independent time variable needs to be brought in at this point but it is an insight of fundamental importance to recognize the idea of process is logically prior to the notion of time.  A time variable is a reference to a clock — a canonical, conventional process accepted or established as a standard of measurement but in essence no different than any other process.  This raises the question of how different subsystems in a more global process can be brought into comparison and what it means for one process to serve the function of a local standard for others.  But inquiries of that order serve but to wrap up puzzles in further riddles and are obviously too involved to be handled at our current level of approximation.

Observe how the secular inference rules, used by themselves, involve a loss of information, since nothing in them tells whether the momenta are changed or unchanged in the next moment.  To know that one would have to determine and so on, pursuing an infinite regress.  In order to rest with a finitely determinate system it is necessary to make an infinite assumption, for example, that for all greater than some fixed value   Another way to escape the regress is through the provision of a dynamic law, in typical form making higher order differentials dependent on lower degrees and estates.

Resources

• Differential Logic and Dynamic Systems
• Differential Logic • One-Dimensional Universe

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