Does the principle of sufficient reason imply mechanistic determinism?

The principle of sufficient reason states that any fact has a cause (https://plato.stanford.edu/entries/sufficient-reason). To some authors, this principle led to extrapolated mechanistic determinism a.k.a. the Laplacian determinism (https://hal.archives-ouvertes.fr/hal-01610331/document).

From a personal point of view, "sufficient" is subjective and depends on one's own appetite for a specific kind of causal explanation, eventually beyond an efficient and prior mechanistic cause. Hence, in the absence of credible mechanistic explanations, God may serve as a sufficient reason for a highly unexpected/unexplained event, as well as a statistical distribution that assumes a random process, e.g., regarding a dice rolling. These simple viewpoints seem to fulfill the principle of parsimony stating that reasons should not be multiplied unnecessarily, which may be the problem when searching for sufficient causes in high dimensional mechanics.

Then, are "God" or a "statistical distribution" a manifestation of the principle of sufficient reason or a negation of it? Can I define the principle of sufficient reason as an axiomatic need for explanation, whatsoever the explanation? Is this view supported by any philosopher? Is it commonly accepted?

• No, it does not, and Laplacian determinism was derived from classical mechanics and the uniqueness theorem for solutions to differential equations, not the principle of sufficient reason. Even if we identify reasons with causes those causes need not be mechanistic, and God can be directly cited as a sufficient cause only if it is demonstrated that he actually did directly intervene and caused a miracle, not as a fallback for whenever the cause is unknown. See SEP for non-causal PSR that has more to do with explanations. Dec 3 '19 at 13:07
• @Conifold Thank you for your answer. However, I don' know what do you mean by "non-causal PSR" (can we say that reason and cause are synonyms as the principle is often referred to as the principle of sufficient cause?) and how it relates to the SEP entry paper? Dec 3 '19 at 13:49
• For non-causal PSR see section 6 of the SEP article. Not all explanations are causal, so no, we can not identify reasons with causes. In the modern context "cause" usually means what Aristotle called efficient cause, while the name "principle of sufficient cause", when used, refers to all Aristotelian causes, a much more broad notion. Using only efficient causes is characteristic of the mechanistic explanations. Dec 3 '19 at 14:00
• Thank you, the fact that the principle relies on Aristotelian causes is a sufficient answer to me. Then, I assume that a statistical model can be a sufficient reason. However, as a curious scientist interested in philosophy, I still wonder if a statistical distribution would be considered as sufficient formal cause (the static shape of the possible outcomes, "the account of what-it-is-to-be”) or a sufficient efficient cause (since it involves a stochastic process, "the primary source of the change or rest")? Dec 3 '19 at 15:09
• Statistical distribution can be a reason, but I doubt it can be a sufficient reason, as it does not determine the outcome. And if it reflects mere correlations it may not even be a reason. Dec 3 '19 at 18:32