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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?

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    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. – Conifold 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? – Delforge Dec 3 '19 at 13:49
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    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. – Conifold 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")? – Delforge 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. – Conifold Dec 3 '19 at 18:32
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Let's start with a reference, then think things through indepenently:

Leibniz presents the Principle of Sufficient Reason as holding universally within the created world. He gives us various formulations of it; examples are 'Nothing is without a reason', and 'Nothing takes place without a sufficient reason, that is, nothing happens without its being possible, for someone who knew enough about things, to give a reason which would suffice to determine why it is thus and not otherwise'.1 Ultimately, he thinks, this leads us to seek a sufficient reason for the existence of the world itself, and to find it in God's choice of the best. For any particular object or event, there will be a less ultimate explanation to be found as well: the sun is shining because there is a gap in the clouds. But any such explanation is incomplete. Filling it out leads us in due course to fundamental statements about the world we live in, and the question becomes why that world (a world governed by these laws, and with those initial conditions) exists. The answer is that the actual world has been chosen by God because it is the best of all possible worlds.

This naturally raises the question what sufficient reason there is for God's choice, or for the existence of God himself. Leibniz recognizes the danger of this regress. He has to show that the regress must terminate here, or at least that there is nothing arbitrary about our stopping the quest for reasons here. Most people think there is no way of satisfying this ideal of an absolutely complete explanation, in which the regress is terminated. I want to show that there is nothing wrong in principle with the idea that the regress can terminate, and terminate with God. Whether it can be made to do so in practice is another matter, and on that I shall do no more than indicate where an argument lies.

First, however, more needs to be said about the Principle of Sufficient Reason itself, because it may seem to be just an outdated metaphysical assumption. It cannot be outdated altogether, because what it says is that whatever happens has an explanation, and an explanation which we could in principle recognize as such. As a methodological assumption this is as indispensable now as it was to Leibniz, though we may have lost his confidence that there will always be an explanation to be found. In assuming that whatever explanations we do find are recognizable as such, we inevitably rely on criteria of simplicity or neatness, criteria which determine what constitutes a best, or an adequate, explanation in any particular case. What is more (and just as vital), we cannot satisfy ourselves with a mere exhortation to look for such explanations. We may not agree with Leibniz that such explanations are always to be found, but we think not only that they are always to be sought: we agree with him also in believing that where we do find them, they give us the truth about the world. We rely on that assumption every time we judge that something before us continues to exist when we are not perceiving it; we rely on it in every inductive inference. From the observation that grass has always been green in the past we move to the prediction that it will be green tomorrow, but what mediates that is the idea that this is the simplest hypothesis; the prediction that grass is in general green (within our part of the universe at any rate) is the best explanation for the observed uniformity, and it entails the prediction. (Ralph Walker, 'Sufficient Reason', Proceedings of the Aristotelian Society, New Series, Vol. 97 (1997), pp. 109-123: 109-10.)

Looking at things for ourselves, all that the principle of sufficient reason holds is that (very roughly) if an event occurs there must be a sufficent reason why that event rather than another - or nothing at all - occurred. This neither logically imposes nor probabilistically suggests anything about the nature of the sufficient reason. At the start we saw it traced to the will or choice of God, an unlikely agent of mechanistic determinism.

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