In "Einstein’s Unfinished Revolution", Penguin Books, 2019, Lee Smolin introduces principles through which to develop fundamental physics. So, they are not mathematical or logical principles but founding elements for thinking about and then formulating physical theories.
Introduce five closely related principles for a future physics:
- The principle of background independence
- The principle that space and time are relational
- The principle of causal completeness
- The principle of reciprocity
- The principle of the identity of indiscernibles.
These are all aspects, claims Smolin, of what Leibniz called the principle of sufficient reason (PSR). he interprets the principle as follows:
Every time we identify some aspect of the universe which seemingly might be different, we will discover, on further examination, a rational reason why it is so and not otherwise.This is not quite standard but then, if we even go back to Leibniz, we have a number of versions. We shall examine the formulation and the five principles in light of their origin in the philosophy of Leibniz and then go on to discuss them as principles for developing physics especially in dealing with quantum mechanics and theories of space and time.
The promotion of the principle by LeibnizAlthough the PSR is most closely associated with Leibniz there is an earlier formulation by Spinoza
Nothing exists of which it cannot be asked, what is the cause (or reason) [causa (sive ratio)], why it exists.The version given by Smolin has an epistemic flavour while that of Spinoza is ontological. As Smolin is defending a realist view of physics an ontological formulation may be preferred. Leibniz provided a mixture of logical, ontological and epistemic formulations. The modern recovery of the reputation of Leibniz is based on his achievements as a logician and here is the version from the Monadology (not Leibniz's title)
31. Our reasonings are based on two great principles, that of contradiction, in virtue of which we judge that which involves a contradiction to be false, and that which is opposed or contradictory to the false to be true.
32. And that of sufficient reason, by virtue of which we consider that we can find no true or existent fact, no true assertion, without there being a sufficient reason why it is thus and not otherwise, although most of the time these reasons cannot be known to us.