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Liebniz as a scientific thinker is known as a codiscoverer of the Calculus, along with Newton; as a philosopher he is also known for his phrase 'best of all possible worlds', which was apparently an attempt by him to solve the theodical problem of evil, and a phrase parodied by Voltaire in Candide.

Is there any connection between this aspect of his philosophy and his philosophy of the physical world, or nature?

Consider, that Newtonian Mechanics in its Hamiltonian formulation posits the dynamics of a system as the 'best' trajectory in phase space; and there are corresponding perspectives in Relativity and field theory - classical and quantum; and this is genealogically related to the principle of shortest time by Hero of Alexandra, Ibn Haytham and Fermat.

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  • math.purdue.edu/~eremenko/bernoulli.html has some interesting comments on the history of the physics side of this.
    – Dave
    Jun 25, 2015 at 16:33
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    Classical trajectories are not exactly the "best", it was already known in 19th century that they do not necessarily represent maximum or minimum of action, only a stationary value. However, that was after Leibniz's time, and "the product of mass, velocity and distance is mathematically the equivalent of the integral of live force over time. Leibniz had already shown that this quantity is likely to be either minimised or maximised in natural phenomena". So likely yes.
    – Conifold
    Jun 25, 2015 at 17:50
  • @dave: your link says, and paraphrasing: that the variational calculus in the 18C, for the reasons I listed above, was considered as a proof of God. This was what I was looking for - but unfortunately no reference. Thanks.
    – Mozibur Ullah
    Jun 26, 2015 at 8:57
  • @conifold: Where is your quote from? Which physical quantity is the product of mass, velocity and distance, i.e. of momentum and distance? How does it relate to the action from the variational principle of least action?
    – Jo Wehler
    Jun 28, 2015 at 20:36
  • @jo wehler The quote is from here en.wikipedia.org/wiki/…
    – Conifold
    Jul 3, 2015 at 0:32

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Without going into the details of Leibniz's philosophy, the general trend for that whole era (Descartes, Newton, etc...) was that science was just the elucidation of God's design. Taken in that context, the connection between Leibniz's physics and his attempt to solve the problem of evil is almost trivial.

Moreover, the physics (and general scientific mindset) of the time were the precursors to the determinism that led Laplace to claim that everything that will every occur can be predicted based on the initial state of the universe. With that determinism in mind, one could argue that we are living in the best of all possible worlds, and the laws of physics along with the initial configuration of the world were specifically chosen such this world was the predetermined.

My main point is that even if Leibniz didn't explicitly draw the connection between his physics and his theology, he thought that the connection would have been obvious enough that he didn't need to spell it out.

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