# Spinoza and the PSR

## The Principle of Sufficient Reason

To understand Spinoza’s arguments it is important to appreciate that he, like Leibniz, endorses the “Principle of Sufficient Reason” (PSR).

Exactly what one means by a “sufficient reason”, and exactly to that which it is supposed to apply (e.g. objects, facts, events, etc.) is not always clear. One can have different versions of the principle. Here’s a somewhat generic formulation of the PSR:

For every fact F, there is a metaphysically sufficient explanation (or reason) why F, rather than not F, is the case

The notion of explanation (or “reason”, or “ground”) is usually (but not always) taken to have the following three features:

1. Irreflexivity: if r explains s, then r ≠ s. (Alternatively: nothing can explain itself.)

2. Asymmetry: if r is explains s, then s does not explain r.

3. Transitivity: if r is a reason for s, and s is a reason for t, then r is a reason for t.

There are three features of the PSR that are generally agreed to by its defenders (at least historically speaking):

1. For whatever domains that are governed by the PSR, there is nothing within those domains that is brute, or unexplained. Thus, the generic version of the PSR ranges over all facts—i.e. there are no brute facts. This is consistent with the PSR being limited to only some ontological categories, and thus there being bruteness within a domain not governed by the PSR (though typically in the Modern period the PSR was endorsed in a completely unrestricted form by those who endorsed it at all).

2. The explanandum (i.e. thing explained or the effect) is metaphysically necessitated by the explanans (i.e. the explainer or cause): a full, or complete, explanation metaphysically necessitates that which it explains.

3. The PSR is or entails a form of “determinism”.

It’s important to distinguish between determinism as it is typically construed and a related yet distinct view called “necessitarianism.”

Determinism
every fact or state of affairs is necessitated by antecedent states of affairs together with the laws of nature.
Necessitarianism
every truth is necessarily true.

Both of these doctrines can be formulated in multiple ways, depending upon interests and context. Note also that necessitarianism → determinism, but not vice versa. This is because a state might be necessitated by a previous state that was not itself necessary. For example, perhaps the universe might have begun with any number of different configurations of mass and energy. Assuming determinism, once one of those configurations occurred, everything after is necessitated. But things could have gone differently if the initial state had been different. In contrast, if necessitarianism is true, there is only one way things can go, and the “initial state” (if there is one) is itself necessarily the case.

One way in which the PSR can vary in strength concerns the extent of its reach or application. Is the principle “unrestricted” in the sense that it applies to everything, or is it “restricted” in some way, applying only to a subset of what there is (or could be).

Finally, different varieties of the PSR can be generated depending upon precisely how one interprets it:

1. Is the notion of “reason” or “ground” ontological or epistemological?

2. i.e. is the principle concerned merely with that through which something is what it is, or that through which one can understand or explain something? (or, in some cases, both? – for Spinoza it seems to be both)

3. Is the PSR a constitutive principle or a regulative principle?

4. i.e. is the principle the basis of how things are, or just how we might endeavor to understand things?

## Spinoza on the PSR

Spinoza says a variety of things in the first book of the Ethics that commit him to endorsing the PSR.

For every thing a cause or reason must be assigned either for its existence or for its non-existence. For example, if a triangle exists, there must be a reason or cause which prevents it from existing, or which annuls its existence. Now this reason or cause must either be contained in the nature of the thing or be external to it. (E1p11d2)

…[I]f a fixed number of individuals exist in Nature, there must necessarily be a cause why those individuals and not more or fewer, exist. (E1p8s2)

That which cannot be conceived through another thing must be conceived through itself. (E1a2)

From a given determinate cause there necessarily follows an effect; on the other hand, if there be no determinate cause it is impossible that an effect should follow. (E1a3)

Recall our discussion of the scope of the PSR. Does Spinoza mean to limit the PSR to the ontological category of things, as E1p11d2 would seem to imply? What counts as a thing for Spinoza? Is there a distinction, for Spinoza, between things (e.g. a red ball) and facts (e.g. the ball is red)?

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