The PSR, Spinoza and Hudde

I shall presuppose that:
(1) The true definition of each thing contains nothing beyond the simple nature of the thing defined.
From this it follows that
(2) No definition involves or expresses any multiplicity or any definite number of individuals since it involves or expresses nothing but the nature of the thing, as it is in itself.
For example, the Definition of a triangle contains nothing but the simple nature of the triangle, not some definite number of triangles, just as the definition of the Mind, that it is a thinking thing, or the definition of God, that he is a perfect Being, contains nothing but the nature of the Mind, or of God. It does not contain a definite number of Minds or Gods.
(3) There must necessarily be a positive cause of each existing thing, through which it exists.
(4) That this cause must be affirmed to exist either in the nature and definition of the thing itself—because existence pertains to its nature, or its nature necessarily contains existence—or outside the thing.

From these presuppositions it follows that [A] if some definite number of individuals exists in nature, there must be one or more causes which were able to produce precisely that number of Individuals, neither more nor fewer. For example, if twenty men exist in nature—to avoid all confusion I shall suppose that they exist together and without predecessors in nature—it will not be sufficient, to give a reason why the twenty exist, to investigate the cause of human nature in general. [B] What must also be investigated is the reason why neither more nor fewer than twenty men exist. For (according to the third hypothesis) concerning each man a reason and cause must be given why he exists. But (according to the second and third hypotheses) that cause cannot be contained in the nature of the man himself, for the true definition of man does not involve the number of twenty men. Therefore (according to the fourth hypothesis), the cause of the existence of these twenty men, and hence of each of them separately, must exist outside them.--Spinoza to H [Hudde], Letter 34, Voorburg, 7 January 1666. Translated by E. Curley, The Collected Works of Spinoza, Vol. II, (Princeton 2016), pp 25-26. [Emphasis added.]

This post is triggered by an invite from Karolina Hubner and Justin Steinberg to write on the Spinoza and Hudde (1628 – 1704)) exchange. If we only had the second quoted paragraph above, and not the earlier part of the letter, we might infer that the third hypothesis is a causal principle in the spirit of “ex nihilo, nihil fit” (“from nothing, nothing comes”). What's notable is that rather than using what we may call its negative formulation (ex nihilo, nihi) 'from nothing, nothing...', Spinoza opts for what we may call a positive formulation: "(3) There must necessarily be a positive cause of each..."

The positive formulation of Hypothesis (3) echoes Axiom 11, from Spinoza's (1663) The Principles of Cartesian Philosophy,:

Nothing exists of which it cannot be asked, what is the cause, or reason, why it exists. See Descartes’ Al.
Since existing is something positive, we cannot say that it has nothing as its cause (by A7). Therefore we must assign some positive cause, or reason, why [a thing] exists—either an external one, i.e., one outside the thing itself, or an internal one, i.e., one comprehended in the nature and definition of the existing thing itself. (Curley (1985), Vol 1, p. 246; emphasis in original)

It is worth noting that Spinoza here is explicitly riffing on Descartes' Replies to the Second Objections (of the Meditations), and in the context of his treatment of the Cogito; and that Spinoza does so, as he tells us, because it is "impossible for" him "to think that something may come from nothing." (PCP, Vol 1, p. 242) 

In their SEP entry, Yitzhak Melamed and Martin Lin claim that Axiom 11 is "Spinoza’s earliest statement of the PSR." (They omit the causal principle on p. 242 perhaps because it's possible to read it as Spinoza attributing it to Descartes.) It's worth mention that there is a version of the PSR in the Short Treatise, which may well date from before 1663. (I thank John Grey and Daniel Schneider for alerting me to this.) In part 1, Chapter 6 (the one on predestination), paragraph 4, Spinoza writes:

Regarding our second question: whether there is any thing in Nature of which one cannot ask why it exists? our saying this indicates that we must investigate through what cause a thing exists. For if that [cause] did not exist, it would be impossible for this something to exist.
We must seek this cause, then, either in the thing or outside it. But if someone asks what rule we should follow in this investigation, we say it does not seem that any at all is necessary. For if existence belongs to the nature of the thing, then certainly we must not seek the cause outside it. But if existence does not belong to the nature of the thing, then we must always seek its cause outside it. And since the former is true only of God, this shows (as we have already proven before) that God alone is the first cause of everything. (Curley (1985), VOL 1, p. 86)

Be that as it may, let's return to the first letter to Hudde. Let's stipulate, for the sake of argument that Spinoza's conclusion, which I labelled [A], follows from the four 'hypotheses.'* My interest is in the final clause, "neither more nor fewer." That [A] includes 'neither more nor fewer' [nec maiorem, nec minorem] looks, at first glance, a kind of redundant exactitude requirement. To count as a proper explanation (or ground, etc.) the cause of the existence of some entity (or group) may not overshoot or undershoot. I call it 'redundant' because Spinoza already has stated 'precisely' [in Latin: illum iuste].+ [A] anticipates a principle we find in the Ethics, “if a certain number of individuals exists, there must be a cause why those individuals, and why neither more nor fewer, exist.” (E1p8s2) 

But in the letter to Hudde, from the exactitude requirement in [A] Spinoza infers the requirement/demand [B].++ And [B] seems to demand that the cause X of some entity (or number of entities) Y also explains the omissions of possible entities (Yn) such that only Y. If you think that my gloss on [B] is too strong, fair enough. But it is not wholly improbable interpretation because later, in the Ethics, Spinoza articulates an even stronger version of this principle: “For each thing there must be assigned a cause, or reason, both for its existence and for its nonexistence”. (E1p11dem). And so it looks like [B] anticipates some such demand for providing causes of nonexistence(s).

I should note that depending on how one thinks of what a cause or reason is, it's not silly to think that an explanation for Y simultaneously helps rule out why all kinds of not Ys do not obtain. If I can show why a projectile with a particular velocity breaks a particular window at a particular time, I can probably also show why given that velocity it is only breaking that window (and not other windows) at that time. If you agree with Spinoza that a definition is a kind of (formal) cause you can run this example through properties of triangles (and which help explain why it's not a hexagon).

So, crucially, then, compared to the Short Treatise and the Cartesian Principles of philosophy, in the letter to Hudde, Spinoza starts packing quite a bit more into what counts as a proper causal explanation of things existing in nature and so also starts developing a heavier duty version of the PSR to be used in explanations of nature.

The foregoing also helps explain why Hudde was confused in the first place. His question to Spinoza was (according to Spinoza) to provide "a demonstration of the Unity of God from the fact that his Nature involves necessary existence." In the Cartesian Principles of philosophy, at the end of his demonstration to proposition 11 ("there is not more than one God") Spinoza had added the following remark:

It should be noted here that it follows necessarily from the mere fact that some thing involves necessary existence from itself (as God does) that it is unique. Everyone will be able to see this for himself, provided he meditates attentively. I could also have demonstrated it here, but not in a way perceptible by everyone, as has been done in this proposition. (Curley (1985), p. 255)**

Spinoza returns to this material in Chapter 2 of the Appendix. And he says somewhat cryptically, "I advise the Reader that by right we infer God’s Unity from the nature of his existence, which is not distinguished from his essence, or which necessarily follows from his essence." (Curley (1985), p 319)

Clearly Hudde -- himself a very accomplished mathematician and natural philosopher [not to say eventually one of the most powerful people in Amsterdam and Holland [and so Europe]] --- had tried to meditate attentively, but had failed in seeing it for himself. And the reason why he had failed in this is, I submit, that Spinoza had actually not yet articulated [A] and [B].

For without such precification or extension of the causal principle it is not obvious how one can even begin to rule out multiple Gods. (I am not suggesting that Spinoza has successfully done so here. Clearly some folk think even the Ethics version fails.) This is especially so if one thinks, not implausibly, that the cause of (a) God can itself be not limited in particular ways  (since it it is powerful enough to cause God and neither involves any multiplicity or any definite number of individuals).

 

*I probably would have translated 'onderstelling' with 'supposition.' But 

+In Latin [A] reads: quod si in natura certus aliquis individuorum numerus existat, una pluresve causae dari debeant, quae illum iuste nec maiorem, nec minorem individuorum numerum producere potuerunt.

In Latin [B] reads: sed etiam ratio investiganda est, cur nec plures, nec pauciores, quam viginti homines existant. 

**I am assuming that unity and uniqueness here mean the same thing. Wiep van Bunge (in Dutch) also assumes this passage prompted Hudde's question.

Comments

[JVC]

Dear Eric,

Some free thoughts on your super interesting piece.

Note 1:

ES: “in the letter to Hudde [1666], from the exactitude requirement in [A] Spinoza infers the requirement/demand [B]. And [B] seems to demand that the cause X of some entity (or number of entities) Y also explains the omissions of possible entities (Yn) such that only Y. […] later, in the Ethics, Spinoza articulates an even stronger version of this principle: “For each thing there must be assigned a cause, or reason, both for its existence and for its nonexistence”. (E1p11dem). And so it looks like [B] anticipates some such demand for providing causes of nonexistence(s).”

Perhaps we might already find a version of [B] also in the Short Treatise [ca. 1662-63]. It’s part of a rather technical discussion; I omit the details here, and just give the relevant passage:

“As for the second, if that cause were not more determined to produce the one rather than the other, i.e., either to produce this something, or to omit producing it, then it would at the same time be impossible both that it should produce it and that it should omit producing it. This is an outright contradiction.” (Spinoza, KV, I, Ch. 6, p. 86 in Curley Vol. I)

Here too Spinoza seems to be saying that there must always be a reason why a cause is determined to produce the one rather than the other.

So I would propose this as a rebuttal of your claim that: ”crucially, then, compared to the Short Treatise and the Cartesian Principles of philosophy, in the letter to Hudde, Spinoza starts packing quite a bit more into what counts as a proper causal explanation of things existing in nature and so also starts developing a heavier duty version of the PSR to be used in explanations of nature.”

Note 2:
Hudde: how do we get from God as ‘a necessary existing being’ to ‘God as a singular necessary existing being’?
Spinoza: we necessarily infer God’s Unity from the nature of his existence; this is self-evident for those who properly meditate

However, this is far from evident, ES explains: “For […] it is not obvious how one can even begin to rule out multiple Gods. (I am not suggesting that Spinoza has successfully done so here. Clearly some folk think even the Ethics version fails.) This is especially so if one thinks, not implausibly, that the cause of (a) God can itself be not limited in particular ways (since it it is powerful enough to cause God and neither involves any multiplicity or any definite number of individuals).”

To be honest, I find this very difficult to understand. How can I have the idea of multiple necessary existing beings? That seems logically impossible right?

Regardless, I was wondering: isn’t it so that this abovementioned refutation [viz. ‘the idea that the cause of God itself cannot be limited’, and therefore that we cannot exclude multiple productions of ‘Gods’- or something like that] only makes sense if one considers Spinoza’s particular conception of the substance-attribute relation in the Short Treatise? As many have noticed, Spinoza there defines the attributes as substances. Some therefore have read Spinoza as positing God as a kind of “supra-substantial Being constituted by an infinite number of substances-attributes” (quoted from F Di Poppa, ‘Spinoza’s concept of substance-attribute: a reading of the Short Treatise’, p. 921). So in the Short Treatise we seem to be confronted precisely with a definition of God as a being that seems to be unifying other substances, entailing all kinds of questions. So would it not be possible that is was the Short Treatise that caused Hudde to ask these questions?

[Eric Schliesser]

Hi Jo,
That's very interesting and helpful.
1.) So, in context Spinoza is discussing contingent causes (not all causes), so it's a bit hard to say if he treats it as a general account on causation and explanation. Having said that, I agree with you that he is clearly already discerning that in a causal explanation one is simultaneously in a position to explain an omission/absence. But the point is not developed and it is not yet articulated in full generality as a demand. So, I agree with you that it's wrong to start the narrative with the first letter to Hudde, but I don't think the Short Treatise quite gets at a robust PSR yet.
2. I don't see why there couldn't be multiple necessary beings. (Why does that involve an incoherency?)
I also don't see why the point presupposes the Short Treatise metaphysics.
Given Hudde's interests and stature I think it is very likely he would have been interested in and have knowledge of the Cartesian Principles. (This text was known in the wider republic of letters.) It really is a much larger step to assume he would have knowledge of the Short Treatise (and somehow be in Spinoza's circle of students/intimates), and I don't think that's required by the considerations you offer.