Monadology, Information, and Physics, Part 2: Space and Time (revised)

In Part 2, drawing on the results of Part 1, I will present my own interpretation of Leibniz’s philosophy of space and time. As regards Leibniz’s theory of geometry (Analysis Situs) and space, De Risi’s excellent work appeared in 2007, so I will depend on this work. However, he does not deal with Leibniz’s view on time, and moreover, he seems to misunderstand the essential part of Leibniz’s view on time. Therefore I will begin with Richard Arthur’s paper (1985), and J. A. Cover’s improvement (1997). Despite some valuable insights contained in their papers, I have to conclude their attempts fail in one way or another, because they disregard the order of state-transition of a monad, which is, on my view, one of the essential features of the monads. By reexamining Leibniz’s important text Initia Rerum (1714), I arrived at the following interpretation. (1) Since the realm of monads is timeless, the order of state-transition of a monad provides only the basis of time in phenomena. (2) What Leibniz calls “simultaneity” should be understood in two, related ways, first as (a) a timeless 1-to-1 correspondence of the states of different monads, and second (b) as temporal simultaneity definable on that basis. (3) With this understanding, whatever is correct in Arthur’s and Cover’s interpretation can be reproduced in my interpretation. On this basis, (4) we can introduce a metric of time based on congruence of duration. (5) Leibniz connected time with space in Initia Rerum by means of motion, and introduced the notion of path (which is spatial) of a moving point; thus the congruence of duration can be reduced to congruence of distance. (6) Then, I can show both classical metric and relativistic metric can be reconstructed on the same basis, depending on the coding for phenomena. (7) The relativistic metric can be combined with Leibniz’s idea of internal living force, suggesting a relation of mass with energy. (8) However, since Leibniz has never shown the ground of constant speed of an inertial motion, there may be a vicious circle. (9) In order to avoid this, we can extend the notion of path to whole situation, thus yielding a trajectory of the whole phenomenal world. (10) Then, by applying optimality to possible paths, we may arrive at the law of motion, without vicious circle. A comparison of Leibniz’s dynamics with Barbour’s concludes Part 2. A Synopsis is added