Spinoza’s ‘Infinite Modes’ Reconsidered

II.1. Question 1: Does God cause necessary, eternal truths about God?

In his 15 April 1630 letter to Mersenne, the eternal truths Descartes mentions are those ‘mathematical truths you [Mersenne] call eternal’ (AT I.145). In the next letter to Mersenne, Descartes offers a specific example: the Euclidean common notion, the whole is greater than its part (AT I.151).²⁹ A longer list of eternal truths appears in the Principles. In addition to mathematical and geometrical truths, the class of eternal truths includes logical truths like it is impossible for the same thing to be and not to be at the same time, conceptual truths like he who thinks cannot but exist while he thinks, and (synthetic) a priori truths like what is done cannot be undone and nothing comes from nothing. Descartes does not give more specific examples here, and even says no additional examples need be supplied: so long as one is not blinded by preconceptions [nullis praejudiciis excaecamur], one will recognize eternal truths as eternal truths when one reflects on them (AT VIIIA.23–24; cf. AT VII.135).

A first question regarding the range of the Creation Doctrine is whether it is so unrestricted that even truths about God fall under its scope.³⁰

Sometimes Descartes implies that although truths concerning God’s nature are especially secure and must be true in any alternative scenario, such eternal truths are outside the scope of the Creation Doctrine. As Descartes writes to Mersenne,

You ask also what necessitated God to create these [eternal] truths; and I reply that he was free to make it not true that all the radii of the circle are equal—just as free as he was not to create the world. And it is certain that these truths are no more necessarily attached to his essence than are other created things. (27 May 1630, AT I.152)

God’s essence is an eternal truth (letter to Mersenne, 6 May 1630, AT I.150). Truths concerning God’s essence are necessarily ‘attached to God’s essence,’ so these truths are necessary, but not because they are created eternal truths God willed to be necessary.³¹

However, according to other passages, the Creation Doctrine looks completely unrestricted: all truths are the efficient causal effects of God’s free and indifferent will. In the Sixth Replies, Descartes writes,

it is contradictory [repugnat] to suppose that the will of God was not indifferent from eternity with respect to everything which has happened or will ever happen; for it is impossible to suppose that anything is thought of in the divine intellect as good or true, or worthy of belief or action or omission, prior to the decision of the divine will to make it so. I am not speaking here of temporal priority: I mean that there is not even any priority of order, or nature, or of ‘rationally determined reason’ as they call it, such that God’s idea of the good impelled him to choose one thing rather than another. (AT VII.431–432)³²

God’s indifferent will is indifferent because it is not conditioned by any antecedent ideas. The passage just quoted suggests there is no idea, no truth, in the divine intellect prior to God’s act of will—perhaps not even an idea, or truth, about God’s own essence and existence.³³

II.2. Question 2: Are laws of motion eternal truths?

A second question regarding the range of the Creation Doctrine is whether Descartes’s laws of motion—his law of inertia, law of rectilinear motion, and law governing the transfer of motion at collision—count among the eternal truths created by God.³⁴

Although Descartes does not name the laws of motion on his lists of eternal truths, one might think that he means to include them. For example, in The Treatise on Light, Descartes says the mathematical eternal truths and his laws of motion are such that we ‘cannot but judge them to be infallible when we conceive them distinctly, nor doubt that if God had created several worlds, they would be as true in all of them as they are in this one’ (AT XI.47. Cf. AT VI.43). The modal status of the mathematical truths and the laws of motion appear to be the same, which might lead one to think that their etiology is the same: they are all eternal truths that are not ‘necessarily attached’ to God’s essence, but are rather those created by God. Furthermore, Descartes includes motion in the Fifth Meditation discussion of the ‘true and immutable’ natures, or ‘immutable and eternal’ essences: ‘There are countless particular features regarding shape, number, motion, and so on, which I perceive when I give them my attention’ (AT VII.63–64, my emphasis). Fundamental laws describing how motion must be appear to be grouped with eternal truths about geometry and mathematics (see also Principles II, article 64, AT VIIIA.78–79).

But there is also evidence to suggest that we should not classify the laws of motion as created eternal truths.³⁵ In the Principles, Descartes elucidates the nature or essence of motion before he ‘proves’ the laws of motion. The nature of motion is ‘the transfer of one piece of matter, or one body, from the vicinity of the other bodies which are in immediate contact with it, and which are regarded as being at rest, to the vicinity of other bodies’ (AT VIIIA.53). According to Descartes, the essences of things are eternal truths (letter to Mersenne, 27 May 1630, AT I.152).³⁶ This suggests that the eternal truths concerning motion are not the laws of motion (which are presented as part of a discussion of the primary cause of motion, God), but rather truths like there is no motion without translation or there is no motion in a universe with only one body.³⁷

There is another apparent difference between the eternal truths and the laws of motion. Consider Descartes’s proof of the law that if a moving body A collides with another body B, and A’s power of continuing in a straight line is greater than the resistance of B, then A carries B along with it and loses a quantity of motion equal to what it imparts to B (AT VIIIA.65). This is proven not by appealing to a timeless divine decree, but rather by appealing to the ‘immutability of the workings of God,’ God’s conservation of the world ‘by the selfsame activity by which he once created it’:³⁸

…. since he conserves the world by the selfsame activity and in accordance with the selfsame laws as when he created it, he … conserve[s] motion as something which is mutually transferred when collisions occur. (AT VIIIA.66)

Bodies always have moved and always will move in certain ways because God continually acts in the same way. The mathematical eternal truths, in contrast, are not true because God is conserving anything: it is sufficient for God to simply create the eternal truths.³⁹

It also seems the eternal truths are truths about essential properties of extension, while laws of motion are not.⁴⁰ One cannot conceive of a wooden block unless one conceives of it as six-sided and as capable of motion, but one need not conceive of the block as actually in motion, or indeed as moving in ways required by Cartesian laws of motion.⁴¹

II.3. Question 3: Are any truths not necessary?

One can also ask a third question: can Descartes even treat the eternal, necessary truths created by God as a special subclass of truths? Descartes does not want all truths to be eternal, necessary truths, but on one (at least initially attractive) way of reading the Creation Doctrine, it is hard to see how he can avoid saying that all truths are necessary.

In his 15 April 1630 letter to Mersenne, Descartes writes,

It will be said that if God had established these truths he could change them as a king changes his laws. To this the answer is: Yes, he can, if his will can change. ‘But I understand them to be eternal and immutable.’ —I make the same judgment about God. ‘But his will is free.’ —Yes, but his power is incomprehensible. (AT I.145–146; cf. AT V.166, AT VII.380)

Here we seem to get an explanation of the necessity of the eternal truths: they are necessarily true because they are created by God’s immutable will.⁴² As Menn puts it, ‘because God is immutable in his actions as well as his being, what he establishes as true at any moment he will establish as true at every moment’⁴³ (2002: 352).

Kaufman (2005) has dubbed this common interpretation the ‘Immutability Interpretation,’ and observes that the premises 1) God wills the eternal truths and 2) God’s will is immutable only yield the conclusion 3) the eternal truths are immutable if we assume that if God’s omnipotent will is immutable, effects of that will are also immutable.⁴⁴ Immutability is not equivalent to necessity, however, so yet another principle linking immutability to necessity needs to be assumed: for any x, if x is immutable, then x is necessary (2005: 7). Although this explains the necessity of the eternal truths, Kaufman argues that it only does so at the cost of necessitarianism.

The following is why necessitarianism is a risk. For Descartes, all things are effects of the immutable divine will: ‘there is always a single identical and perfectly simple act by means of which [God] simultaneously understands, wills, and accomplishes everything. When I say “everything” I mean all things’ (Principles I.23, AT VIIIA.14). Indeed, God

would not be supremely perfect if anything could happen in the world without coming entirely from him …. philosophy by itself is able to discover that the slightest thought could not enter into a person’s mind without God’s willing, and having willed from all eternity, that it should so enter.⁴⁵ (Letter to Elisabeth, 6 October 1645, AT IV.314)

Furthermore, God does not change his immutable will in response to petitionary prayers: we pray ‘simply to obtain whatever he has, from all eternity, willed to be obtained by our prayers’ (AT IV 315–316; cf. Conversation with Burman, AT V.66).

The truths concerning particular human actions, thoughts, and prayers could be immutable effects of an immutable will if they are indexed or ordered: God’s providence would then be God’s eternally and immutably willing an infinity of, say, temporally indexed truths. If, however, we assume the principle that immutable truths are necessary truths, then those indexed immutable truths turn out to be necessary truths.⁴⁶

And so a potential tension in the Cartesian system shows itself. If we adopt an (at least initially plausible) interpretation of the foundations of the necessity of the eternal truths, then it looks like Descartes is committed to all truths being necessary truths, a conclusion that conflicts with his assertions that some truths are contingent.⁴⁷

II.4. Question 4: What—and where—are eternal truths?

In the Fifth Meditation, Descartes points to two kinds of eternal entities. First, there is essentially eternally existing God: ‘it is quite evident that existence can no more be separated from the essence of God than the fact that its three angles equal two right angles can be separated from the essence of a triangle (AT VII.66). And, the Meditator says later, ‘after supposing that one God exists, I plainly see that it is necessary that he has existed from eternity and will remain [sit mansurus] for eternity’ (AT VII.68).⁴⁸ Second, there are true and immutable natures:

… I find within me innumerable ideas of things that even though they may not exist anywhere outside me, nonetheless cannot be called nothing; and although they can be thought in some manner at will, nonetheless they are not made by me [a me figuntur], but have their own true and immutable natures. Thus when, for example, I imagine a triangle, even if perhaps no such figure exists, or has ever existed, anywhere outside my thought, there is still some determinate nature, or essence, or form, immutable and eternal, which is not produced by me [a me non effecta est], nor depends on my mind [nec a mente mea dependet]. (AT VII.64)

Here Descartes distinguishes the true and immutable nature of a triangle and actual triangles in the world; the true and immutable nature is still something, even if there are no actual triangles (or no extra-mental extended world at all). But it also seems the nature does not exist only in the Meditator’s mind: this true and immutable nature is not produced by or dependent on his mind. True and immutable natures are eternal truths (AT I.152). One could read this passage as evidence that Descartes was a sort of Platonist: God’s eternal, necessary effects reside in a kind of (created) Platonic realm.⁴⁹

The exchange with Gassendi might also be taken as evidence of Descartes’s Platonism. In the Fifth Objections, Gassendi reveals that he takes the Fifth Meditation to concern entities with reality apart from human minds, as he objects to there being any true and immutable natures apart from God (AT VII.319).⁵⁰ Descartes does not contest this reading of the Fifth Meditation. That Descartes does not correct Gassendi suggests that Descartes was thinking of the true and immutable natures as having reality outside of human minds (AT VII.380).⁵¹

Elsewhere, however, Descartes’s view looks less Platonic.⁵² Consider Principles I.49:

When we recognize that it is not possible that something come from nothing, this proposition, nothing comes from nothing, is considered not as some existing thing, nor also as a mode of a thing, but as some eternal truth, which resides in our mind… (AT VIIIA.23–24; cf. Principles I.59, AT VIIIA.27–28)

Here Descartes could be read as implying that eternal truths exist only in human minds.⁵³ They are not things enjoying either eternal or non-eternal extra-mental existence, nor are they modes of extra-mental things.

Indeed, it is possible to read the Fifth Meditation passage quoted above differently so that it does not sound so Platonic. Perhaps eternal truths and true and immutable natures are just the objectively real representational contents of innate ideas that only exist in human minds. Granted, there is a sense in which an innate idea does depend on the Meditator’s mind: anything that is objectively real depends on a mind in that objective reality is the reality ‘by which a thing exists in the intellect by way of an idea’ (AT VII.41). However, there is a distinction between ideas whose contents can be constructed and altered by the Meditator’s mind—‘factitious’ ideas like those of hippogriffs and sirens—and innate ideas whose contents are unalterable by the Meditator (AT VII.37–38). Both factitious and innate ideas can be thought of ‘in some way at will,’ but innate ideas cannot be modified at will.⁵⁴ So the true and immutable nature of a triangle, as the content of an innate idea, can be thought of at will and is, as an objectively real object, ‘not nothing’ (AT VII.41, AT VII.65), but it is not dependent on the Meditator’s mind in the sense that the Meditator did not construct that content.

However, it cannot be that all true and immutable natures are such that they are only the objectively real contents of innate ideas: the true and immutable nature of God is an objectively real object of an innate idea in the Meditator’s mind, but it is also a formally real something—that is, God himself—existing outside of the Meditator’s mind.⁵⁵

Some commentators, recognizing that Descartes’s texts pull in different directions, have suggested that perhaps Descartes subscribed to a ‘moderate’ Platonism: the eternal truths are created by God and external to human minds, but these truths are not external to God. These eternal truths can be understood as in the divine mind as objectively real contents of divine decrees.⁵⁶ They can still count as products of God’s causal activity, as a formally real mind can cause the objective reality of ideas within that mind (see AT VII.43–45).

But such moderate Platonic readings might not fit with Descartes’s claims that eternal truths are distinct from God.⁵⁷ Descartes says the eternal truths ‘are no more necessarily attached to [God’s] essence than are other created things’ (AT I.152); if eternal truths and true and immutable natures are in the divine mind, then they do seem more attached to God than ‘other created things.’

IV.1. E1p21

To begin, here is E1p21 and the beginning of its famously baroque demonstration:

1p21: All the things which follow from the absolute nature of any of God’s attributes have always had to exist and be infinite, that is, are, through the same attribute, infinite and eternal.

If you deny [that all things following from the absolute nature of any of God’s attributes are infinite and eternal], then conceive (if you can) that in some attribute of God there follows from its absolute nature something that is finite and has a determinate existence, that is, [determinate] duration, for example, an idea of God in thought.

At the beginning of the demonstration, we are asked to conceive that from the eternal attribute of thought there follows an idea that is 1) finite and 2) ‘has a determinate existence, that is, duration, for example, an idea of God in thought’ (idea Dei in cogitatione).

I propose that the ‘idea Dei in cogitatione’ assumed for reductio in E1p21d is the idea representing the true and immutable nature of God (under some attribute) in a finite, non-eternal thinking mind.⁷⁶ Note that this would have been a natural example for Spinoza to put forward: read this way, the idea assumed for reductio is an idea very much like that which plays a crucial role in Descartes’s Meditations.

In the Third Meditation, the Meditator uses his idea of God to prove God’s existence: the idea of God has infinite objective reality, and such infinite objective reality could only have been caused by a being with infinite formal reality—that is, God, an infinite, eternal, necessarily existing being (AT VII.47). Once the Meditator proves that God exists, the Meditator proves, from reflection on his own mind’s limited formal reality, that God must be the creator and sustainer of that limited formal reality (AT VII.48–50). The Meditator realizes that the idea of God—an idea of what Descartes says elsewhere is the ‘most eternal’ of eternal truths (AT I.150)—is innate, and remarks that it is ‘no surprise that God, in creating me, should have placed this idea in me to be, as it were, the mark of the craftsman stamped on his work’ (AT VII.51).

So, according to Descartes, God, who enjoys infinite, eternal formal reality, causes something infinite and eternal: an eternal truth with infinite objective reality. Yet Descartes’s God also causes something finite and non-eternal: the finite, non-eternal formal reality of the Meditator’s mind, in which there is a finite, non-eternal formally real idea that represents God.

Spinoza clearly thinks Descartes is wrong to believe God is transcendent (since God’s effects are modes of God). In this section, I suggest that Spinoza also thinks Descartes is wrong to believe that an infinite, eternal God causes anything with finite and non-eternal formal reality. Spinoza argues that if we cognize God properly, as the one and only substance, we will see that all of God’s effects are infinite and eternal modes. So Descartes’s contention that the Meditator’s finite formally real mind is caused by God must be rejected. Spinoza can also rule out the possibility, mentioned in Section II.4 above, that eternal truths caused by God reside solely in the finite and non-eternal minds caused by God, since such finite and non-eternal minds cannot be caused by an infinite and eternal God. At the end of the section, I explain why the possibility, also mentioned in II.4, that true and immutable natures and eternal truths reside solely as objectively real contents in a divine mind is also untenable, as well as why Spinoza might have said that ‘E1p21 and other things’ enable us to see that our mind ‘insofar as it understands, is an eternal mode of thinking’ (E5p40s).

E1p21d is broken into two main parts: the first part is supposed to establish that whatever ‘follows from the necessity of the absolute nature of an attribute itself must be infinite’; the second part is supposed to establish that what follows must be eternal. I take up each in turn.

…what follows must be infinite

After asking us to conceive of the finite idea Dei, the demonstration continues:

[1.a] Now since thought is supposed to be an attribute of God, it is necessarily (by E1p11) infinite by its nature. But insofar as it is the idea of God, [thought] is supposed to be finite.

Spinoza reiterates that thought, as an attribute of God, is infinite by nature. Being infinite is ‘an absolute affirmation of the existence of some nature’ (E1p8s1); thinking substance is infinite reality, or existence itself (E1p7, E1d8), conceived as thinking. Importantly, it does not make sense to conceive of thinking substance’s reality being diminished, nor does it make sense to conceive of thinking substance’s reality as admitting of augmentation or amplification. To do so would require thinking of substance’s reality in terms of units, but this would make substance posterior in nature to the constituent units and would render the infinity of substance mere indefinite infinity. Finite reality, in contrast, is that which can be limited by something of the same nature (E1d2), and it does make sense to think of such reality in terms of units: we can think that some existing finite thing would enjoy more or less reality if other things were there (or not there).

[1.b] But (by E1d2) [thought] cannot be conceived to be finite unless it is determined through thought itself.

We have assumed for reductio that there is a finite formally real idea of God. As Spinoza reminds us in [1.b], to be conceived as finite, its reality must be limited or determined by something that is also thought (E1d2). In this demonstration, we are supposing that the only things that exist or are formally real are the infinite thinking substance and the finite idea of God.⁷⁷ These are the only things available to do any limiting, so in order for the finite idea of God to be conceived as finite, it must be limited either by itself or by thinking substance.

[1.c] But [thought can] not [be determined] through thought itself, insofar as it constitutes the idea of God (for to that extent [thought] is supposed to be finite). Therefore, [thought must be determined] through thought insofar as it does not constitute the idea of God, which nevertheless (by E1p11) must necessarily exist.

‘Thought itself, insofar as it constitutes the idea of God’ can be taken to be thinking substance only insofar as it is the idea of God, the mode we are assuming enjoys finite formal reality. So understood, ‘thought itself, insofar as it constitutes the idea of God’ cannot determine the idea of God for a simple reason: the finite mode cannot determine itself to be finite.⁷⁸ So it must be determined by something else, or ‘through thought insofar as it does not constitute the idea of God’:

[1.d] Therefore, there is thought which does not constitute the idea of God, and on that account the idea of God does not follow necessarily from the nature [of thought] insofar as it is absolute thought (for [thought] is conceived as constituting the idea of God and as not constituting it). This is contrary to the hypothesis. So if the idea of God in thought, or anything else in any attribute of God (for it does not matter what example is taken, since the demonstration is universal), follows from the necessity of the absolute nature of the attribute itself, it must necessarily be infinite. This was the first thing to be proven.

Here is one reconstruction of Spinoza’s reasoning in [1.c] and [1.d].⁷⁹ The entity that limits the finite idea of God must 1) not be the finite idea of God itself (because the idea cannot limit itself), 2) be understood under the attribute of thought (from E1d2), and 3) be finite (since, in limiting the idea of God, it will also be limited by the idea of God, and so is finite, by E1d2). Since we are assuming that the finite idea follows from thinking substance alone (without the assumption of any other modes), the only candidate entity that could do any limiting would be thinking substance (since again, the finite idea cannot limit itself). But if thinking substance limits the finite idea, then thinking substance would have to be finite, which is absurd. So something that is finite cannot follow from the absolute nature of a divine attribute; what follows must be infinite.⁸⁰

So reconstructed, this demonstration generalizes to other attributes. The demonstration does not hinge on anything particular to the attribute of thought, but just requires that we consider the idea of God as a finite, formally real mode of substance considered under an attribute. However, this reconstruction does not clearly explain why Spinoza adds that the thought that does not constitute the idea of God nevertheless ‘must necessarily exist’ (by E1p11) at the end of [1.c]. This, somewhat perplexingly, is a common oversight, so common that I have not yet found a reconstruction of E1p21d that explains why Spinoza brings in E1p11 here.⁸¹

Another potential difficulty with this reconstruction is that the absurdity is that substance is both finite and infinite; it is not clear how this maps onto Spinoza’s claim that thought is conceived both ‘constituting’ and ‘not constituting’ the idea of God. But perhaps we can accommodate this language in the following way: thought is conceived as constituting the idea of God when we conceive of the finite idea of God, and conceived as not constituting it when we conceive of what must be posited to limit that idea so that it is finite. However, this is not, in itself, absurd. It is only absurd if we supplement this claim with the claims that only what is finite can do the limiting, that the only potential limiter of the finite idea is substance, and that that substance is necessarily infinite. The text, however, suggests the argument to absurdity is more direct: the assumption leads us to conceive of (the same) thought both as constituting and not constituting the idea of God.

I would like to propose an alternative reconstruction, one that generalizes to other attributes, incorporates E1p11, and gets to the absurdity directly. Return to this portion of the demonstration:

[1.c.i] But [thought can] not [be determined] through thought itself, insofar as [quatenus] it constitutes the idea of God (for to that extent [thought] is supposed to be finite).

Above we interpreted ‘thought itself, insofar as it constitutes the idea of God’ to be the assumed finite formally real idea of God: the ‘insofar as’ was supposed to focus our attention on the mode of substance. But a mode cannot limit itself, so must be limited by something else. The reconstruction above emphasizes that this limiting thing must also be finite; absurdity results because substance, which is infinite, cannot play that role.

Yet it is also possible to read ‘thought itself, insofar as it constitutes the idea of God’ not as the finite formally real idea of God, but rather as the substance on whose formal reality the mode depends for its formal reality. On this reading, thinking substance constitutes, in the sense of makes or causes, the mode; the ‘insofar as’ focuses attention on thought as the immanent cause of its own mode. While it is true that a finite thing cannot limit itself, that is not the reason we must appeal to something else. The problem, rather, is that to say that thought is determined through the thinking substance insofar as it constitutes, or causes, the finite mode is just to restate what we have already supposed for reductio.

[1.c.ii] Therefore, [thought must be determined] through thought insofar as it does not constitute the idea of God, which nevertheless (by E1p11) must necessarily exist.

Again, thought can only be limited by thought (by E1d2), so the assumed idea of God must be limited by something that is also thought. We have already ruled out the possibilities a) that the idea of God limits itself and b) that what does the limiting is the thinking substance on which the idea of God depends for its formal reality (‘thought itself, insofar as it constitutes the idea of God’).⁸² So what is doing the limiting must be thought that is external to both the assumed finite mode and the substance that constitutes that mode. However, this is just to posit another thinking substance: thought that ‘nevertheless (by E1p11) must necessarily exist.’ There is just one infinite, necessarily existing thinking substance.⁸³ So the one thinking substance is conceived both ‘as constituting the idea of God and as not constituting it.’ This is absurd, and so we can assert the contrary of our hypothesis. Only a non-finite idea, a thing whose formal reality does not require positing an external limiter, can follow from thinking substance; such a non-finite idea is, of course, just an infinite idea.

So reconstructed, the demonstration incorporates the mention of E1p11 in [1.c.ii] and gets to the absurdity directly. It also generalizes to other attributes: we could run the demonstration with a finite body, but we would again be forced to posit more than one formally real substance (this time under the attribute of extension).

…what follows must be eternal

I will quote the second stage of the demonstration in full:

[2.a] Next, what follows in this way from the necessity of the nature of any attribute cannot have a determinate [NS: existence, or] duration. For if you deny this, then suppose there is, in some attribute of God, a thing which follows from the necessity of the nature of that attribute—for example, idea Dei in cogitatione—and suppose that at some time [this idea] did not exist or will not exist.

[2.b] But since thought is supposed to be an attribute of God, it must exist necessarily and be immutable (by E1p11 and E1p20c2). [2.c] So beyond the limits of the duration of the idea of God (for it is supposed that at some time [this idea] did not exist or will not exist) thought will have to exist without the idea of God.

[2.d] But this is contrary to the hypothesis, for it is supposed that the idea of God follows necessarily from the given thought. Therefore, the idea of God in thought, or anything else which follows necessarily from the absolute nature of some attribute of God, cannot have a determinate duration, but through the same attribute is eternal. This was the second thing [NS: to be proven]. Note that the same is to be affirmed of any thing which, in some attribute of God, follows necessarily from God’s absolute nature.

Spinoza reintroduces the reductio assumption: namely, that the idea of God exists for some limited time [2.a]. Spinoza reminds us that the attribute of thought exists necessarily (E1p11) and is immutable (E1p20c2) [2.b]. The situation we are assuming, then, is one in which we have a necessarily existing, immutable substance and a mode that only endures for some time. This means that there are times at which the mode does not exist [2.c].

However, this leads to absurdity. Spinoza does not make his reasoning explicit, but I think we are supposed to remember E1p20c2’s point that it is absurd to suppose that the essence of substance could change. Spinoza reminds us that it is supposed that the mode follows with necessity from the necessarily existing essence of thinking substance [2.d]. For the mode to not follow, which is the case at all of those times at which the mode does not exist, we would have to suppose that the essence of substance is different at those times.

We can thus deny our assumption: the idea of God cannot exist for some limited time. Its existence is necessary (in virtue of substance’s essence being necessary), and thus eternal.⁸⁴ This will apply to anything following with necessity from the absolute nature of God.

It is sometimes argued that this second stage establishes the everlastingness of (certain) modes.⁸⁵ While this is a possible reading of the language of E1p21—’all the things which follow from the absolute nature of any of God’s attributes always had to exist’ (semper existere debuerunt)—I do not think this language forces us to conclude that the things enjoy sempiternal reality, rather than reality that is timelessly eternal. In E1p19, Spinoza said that God’s ‘existence, like his essence, is an eternal truth.’ In E1p17s, Spinoza had drawn a parallel between the infinity of things following from the divine nature and what follows from the essence of a triangle. Such a geometric essence is a paradigm case of a true and immutable nature, an eternal truth.⁸⁶ In this context, it is reasonable to suppose that Spinoza is arguing that the propria following from the divine essence (whether that essence, or attribute, is extension, thought, or some other attribute), like the propria following from the true and immutable nature of a triangle, also enjoy the reality of eternal truths or true and immutable natures. From the perspective of someone reasoning in time, the true and immutable nature of a triangle always exists, even if the nature’s eternal reality is not reality that can properly be said to be enduring. Perhaps in saying that the things which follow from the absolute nature of God’s attributes always had to exist, Spinoza is just making a similar point. If a substantial essence (attribute) is eternally real, then, from the perspective of someone reasoning in time, that essence, as well as all of that essence’s propria, always exists, but this does not mean that it is apt to say that the eternally real entities themselves endure over time.

One might protest that making the effects timelessly eternal makes modes too much like substance, and that this is reason enough to suppose that the effects under discussion in E1p21 are sempiternal. But had Spinoza wanted to signal that God’s nature is the only nature that is timelessly eternal, we should expect him to announce this.⁸⁷ Furthermore, even if both substance and modes enjoy the timelessly eternal reality of eternal truths, this does not mean that we cannot identify a key difference between them. In E1p24, Spinoza points to just such a difference: unlike God’s own essence, the ‘essence of things produced by God does not involve existence’ (E1p24).⁸⁸ There is, just as we expect from modes, ontological dependence: modes have the reality they because they inhere in their immanent cause, the eternal substance.⁸⁹

Before I turn to E1p22, I want to point to one upshot of the reconstruction of E1p21d I have provided. On most reconstructions of E1p21d, Spinoza employs the same strategy for reductio twice: that is, in order for the idea Dei to be limited either in reality (i.e., be finite) or be limited in duration (i.e., be non-eternal), we must already assume that there is already some limited (and limiting) thing; but in that case, what follows does not follow from the absolute nature of substance, because it does not follow from substance alone, and that is contrary to hypothesis. So interpreted, it seems Spinoza has been confusingly prolix. The demonstration can be streamlined without distortion.

On my view, the demonstration cannot be condensed because the strategy in each stage’s reductio is different. In the first stage, the absurd consequence is that the same thing—substance—is both P (constituting the idea of God) and not-P (not constituting it). In the second stage, the absurdity is that we must posit a change in a necessarily existing essence (viz., substance’s). If this is how the demonstration goes, then, although we might complain that Spinoza could have made his reasoning more perspicuous, we cannot complain that he has repeated himself unnecessarily.

IV.2. E1p22

E1p22 is an extension of E1p21:

E1p22: Whatever follows from some attribute of God insofar as it is modified by a modification which, through the same attribute, exists necessarily and is infinite, must also exist necessarily and be infinite.

E1p22’s demonstration is short: it ‘proceeds in the same way as the demonstration of the preceding one [E1p21d].’

This demonstration does not usually get attention, but I will propose a reconstruction of it here. Like E1p21d, it proceeds in two stages. For the first stage, assume that something finite, N, follows from an infinite mode M. Again, the reality of finite things is such that it is limited and limiting (E1d2). Infinite, or non-finite, reality is different: it cannot do any limiting or be limited. The infinite mode M cannot limit N, ensuring its finitude, unless M is itself finite. So if N does follow from the infinite mode M, M is finite. As was the case in the first stage of E1p21d, the absurdity is that the same thing (M) is both P (infinite) and not-P (finite).

For the second stage, note that Spinoza equates eternal existence and necessary existence (E1d8).⁹⁰ For reductio, assume that a non-necessary non-eternal thing K follows from a necessary, eternal mode J. There are times at which K does not exist. However, J exists necessarily and is eternal; that is, J is immutable. But J cannot cause K to be or not to be unless J itself exists in one way at one time and then in another way at another time. There cannot be a change in what follows from J’s essence unless there is a change in J’s essence. But J’s essence exists necessarily and is eternal, and so is immutable. In order for J’s essence to be different, God’s essence (whence J follows) must be different. But this is absurd, and is the same absurdity seen in the second stage of E1p21d.

From E1p21 and E1p22, we can conclude that what is non-eternal and non-infinite cannot follow from what is infinite and eternal; all the things following either immediately or mediately from the infinite and eternal essence of God—that is, each and every one of the infinity of things following from the divine nature (E1p16)—are infinite and eternal. The infinity of things may differ in their essences, as the essence of a triangle differs from the essence of a circle, but their eternal reality is, as what is non-finite, such that it cannot limit or be limited by anything else.⁹¹ Sub specie aeternitatis, everything following from the divine nature is on ontological par: any essence, conceived to be eternally real, ‘contained in God and to follow from the necessity of the divine nature’ (E5p29s), is as eternally real as any other.⁹²

Before turning to E1p23, I want to briefly point out that on my reconstruction, E1p21–22 can be taken to target a claim Descartes makes about the idea of reality that is finite and limited (either in time or in space). For Descartes, the idea of the infinite—that is, God’s infinite reality—is not generated by starting with the idea of our own finite reality and then just removing limits on that reality: that only gives us the indefinite. Instead, the idea of the infinite is prior to the idea of the finite or limited.⁹³ Descartes sometimes suggests that the idea of the finite is the idea of a limitation, or negation, of this prior idea of the infinite:

I say that the notion I have of the infinite is in me before that of the finite because, by the mere fact that I conceive being, or that which is, without thinking whether it is finite or infinite, what I conceive is infinite being; but in order to conceive a finite being, I have to take away something from this general notion of being, which must accordingly be there first. (Letter to Clerselier, 23 April 1649, AT V.356)

As I have read E1p21–22, Spinoza would say that we need to be more careful. Spinoza agrees with Descartes on the general point that the idea of the infinite is the idea of the reality that must be presupposed whenever we consider the reality of any of God’s effects, but he will insist that the reality of these posterior effects is also infinite and eternal reality—as he will point out later, each mode has its infinite and eternal reality in virtue of its cause (substance), not in virtue of its own essence.⁹⁴ For Spinoza, to think that substance’s reality could admit of limits is to misapprehend substance’s reality; properly understood, that reality cannot be understood as limiting or limited. A finite, non-eternal thing cannot be understood as substance’s reality with limits imposed, or something ‘taken away.’⁹⁵

IV.3. E1p23

Where E1p21 and E1p22 can be read as a priori arguments—given what the cause is like, we know what its effects must be like—E1p23 can be read as an a posteriori argument. That is, given an effect, we know what the cause must be like:

E1p23: Every mode which exists necessarily and is infinite has necessarily had to follow either from the absolute nature of some attribute of God, or from some attribute, modified by a modification which exists necessarily and is infinite [and eternal].

The reasoning of the demonstration appears to be this. Whatever is, is a mode inhering in God, the one and only substance, and nothing can be or be conceived without God (E1d5, E1p15). If something is conceived to enjoy infinite and necessary [i.e., eternal, by E1d8] formal reality or existence, it is an infinite and necessary [eternal] mode of a substance. A mode is a way its substance is modified, so this mode conceived to have infinite and necessary [eternal] reality is a mode inhering in the infinite and necessary [eternal] substance; the mode is a way eternal formal reality, or ‘existence itself’ (understood under an attribute) is modified (E1d6, E1p19). We know from E1p21 and E1p22 that whether a thing follows immediately or mediately from the divine nature, it will enjoy infinite, eternal reality; all the things following from the divine nature are infinite and eternal. So if we have an infinite and eternal mode, we know that it either followed immediately or mediately from the divine nature.

IV.4. A Spinozan Meditator

According to my reconstruction of E1p21d, the idea assumed for reductio is the kind of idea Dei that would have been familiar to Cartesian readers: it is the idea of God at the center of Descartes’s Meditations, the idea a finite, limited human mind has of the true and immutable nature of God.⁹⁶ From reflection on this idea, Descartes’s Meditator proves the existence of God, which in turn enables the Meditator to secure other important conclusions, including that God is the creator and sustainer of his being and that all his clear and distinct ideas are true. Spinoza agrees with Descartes that human minds have an idea of the ‘most eternal’ of eternal truths: ‘the human mind has an adequate cognition of God’s infinite and eternal essence’ (E2p47). Of course, Spinoza disagrees with Descartes on the nature of God and God’s relation to creation. To draw out the implications of reading E1p21–23 as I have, it helps to consider what careful reflection on the Spinozan idea Dei secures.

If one has an adequate idea of God’s infinite and eternal essence, one understands that God is the one and only infinite, eternal, immutable, necessarily existing substance in which everything else inheres as modes and which can be conceived through different attributes (E1p1–15, E1p19–20). One sees that divine causation does not involve a will that is free by being perfectly indifferent, since the essences of all things simply follow with necessity from the divine essence (E1p16–17). One sees that God’s effects are not modally diverse: all of God’s effects are necessary.

Furthermore, given what God’s formal reality is (infinite and eternal), one sees that the formal reality of all of God’s effects must enjoy reality that cannot be understood as either limiting or being limited (E1p21–22). While some essences following from the divine nature (as in E1p16) presuppose other essences, as eternal truths presuppose other eternal truths,⁹⁷ all of these essences enjoy infinite and eternal reality, albeit only because God causes them to have that reality (E1p24). Furthermore, there cannot be some other cause, besides God, of some necessary, eternal, infinite thing: any such thing is a mode caused by and inhering in the one and only infinite and eternal substance, God (E1p23). One sees that an infinite and eternal God’s effects are not ontologically diverse.

One sees that God is the cause of the essence of things (E1p25; see E1p16), and, since all essences follow with necessity from God’s necessarily existing nature, in causing himself to have eternal, infinite reality, God immanently causes all things to have eternal, infinite reality as modes. One perceives, then, that God is the cause of all things ‘in the same sense in which he is called the cause of himself’ (eo sensu, quo Deus dicitur causa sui, etiam omnium rerum causa dicendus est, E1p25s, my emphasis).

By Spinoza’s lights, Descartes’s Meditator got it wrong: had the Meditator had the right conception of God, then reflection on his idea Dei would have revealed that his own mind is causally sustained as a mode of God enjoying infinite and eternal formal reality (considered under the attribute of thought), not as a finite formally real thinking thing created and conserved over time and existing apart from God. Once the Meditator understands that (a Spinozan) God must exist, he can see that all of God’s effects are infinite and eternal modes of God.⁹⁸

There is more that the Meditator can grasp. If the Meditator sees that there is no true and immutable nature that is not in, conceived through, and caused by God (E1p23), then he will see that an idea of any true and immutable nature is an idea of an infinite and eternal mode of God. Since cognition of an effect depends on and involves cognition of its cause (E1a4), he will see that an idea of any true and immutable nature is a cognition of God; all of God’s effects are, in this sense, eternal and necessary ideas about God.⁹⁹

Importantly, with the right Spinozan idea of God, the Meditator will also see that the true and immutable nature of some body (e.g., of a circle), considered as an objectively real content of an adequate idea, and that true and immutable nature, as something formally real, are one and the same thing considered under different attributes (E2p7). Furthermore, he understands that the objectively real content of his idea and his idea, considered as a formally real idea, are one and the same thing considered under the attribute of thought (E2p20–21). So, if he is able to adequately represent a true and immutable nature, like that of a circle, that means that what is doing the representing—his formally real idea—is also a true and immutable nature.¹⁰⁰ The Meditator will realize, that is, that his having an idea of a true and immutable nature—an idea of any eternal, infinite mode—indicates his mind, insofar as it has this idea, is a mode of God with infinite, eternal formal reality.

The Meditator thus recognizes that his experiences of contemplating true and immutable natures and eternal truths are experiences of his own status as an eternally real thing: he ‘feel[s] and know[s] by experience’ that he is eternal; ‘for the mind feels those things that it conceives in understanding no less than those it has in the memory’ (E5p23s). He comprehends that ‘insofar as [his mind] understands,’ or has adequate ideas of properties of things, eternal truths, or true and immutable natures, his mind ‘is an eternal mode of thinking’ (E5p40s). He realizes his understanding mind is part of the infinite intellect of God, which is all of the essences following from the divine essence (E1p16), conceived as infinite and eternal modes under the attribute of thought, or natura naturata (E1p29, E2p11c, E2p43s, E5p40s).¹⁰¹

Perhaps the Meditator had thought that true and immutable natures and eternal truths created by God were merely objectively real in the divine mind.¹⁰² Now he can see that such a view is mistaken. These effects are not merely objectively real contents in God’s infinite intellect, since they are also formally real. And these effects are not merely in God’s infinite intellect, if that intellect is understood to be ontologically distinct from human minds: the adequate idea of a true and immutable nature or eternal truth in a human mind is the adequate idea of that true and immutable nature or eternal truth in God’s infinite intellect.¹⁰³

V.1 Letter 64

A first objection is that my interpretation is incompatible with what Spinoza writes to Schuller in his 1675 letter (Ep. 64). Schuller asked for some examples of the entities Spinoza discusses in E1p21 and E1p22, and Spinoza replies,

… the examples for which you ask are of the first kind [the kind discussed in E1p21] in Thought, absolutely infinite intellect; in Extension however motion and rest; of the second kind [discussed in E1p22], the face of the whole Universe [facies totius Universi], which although varying in infinite ways, remains however always the same, on which see scholium of lemma 7 … (G IV.278; cf. KV I.ix.2–3, G I.48)

This is obscure, and Spinoza does not offer further clarification beyond the reference to the ‘Physical Digression,’ the short treatise on body and motion in Part II of the Ethics.

This letter is often cited to defend a view of the infinite modes according to which they are laws of nature; this is suggested by ‘motion and rest.’ More generally, it is cited in support of the view that the infinite modes are just a subclass of God’s modes. If Spinoza had wanted to say that all modes are, in fact, infinite modes, he would have just said so here.

However, I do not think the examples are incompatible with what I’ve suggested above.

The essence of any body is a ratio of motion and rest (E2lemma5). Now, to understand a ratio of motion and rest, one need not conceive of anything determined to be what it is by anything actually in motion. However, to understand any ratio of motion and rest, one does need to conceive of extension as that which can always be conceived in terms of “motion and rest,” regardless of what the specific terms might be. This, I take it, is a basic eternal truth concerning the nature of extension, or what follows “from the absolute nature” of extension (E1p21).¹⁰⁵

The scholium of lemma 7 makes the point that there is an unchanging—that is, immutable—ratio of the infinity of individual bodies’ ratios of motion and rest. In other words, there is a true and immutable nature of the system of all things, of all the essences following from the divine nature (E1p16). Granted, Spinoza does not say that any particular ratio is also a true and immutable nature enjoying eternal and infinite reality as a mode of substance, but I do not think what he does say is incompatible with this being so.

I also do not think what Spinoza says about thought in Letter 64 is incompatible with my interpretation. The ‘absolutely’ in ‘absolutely infinite intellect’ is, I think, just a way of signaling that this ‘intellect’ is the most basic eternal truth about thought, or the most basic property of substance considered under the attribute of thought: whatever else characterizes ideas, they are representations. Here, in using the word ‘intellect,’ Spinoza also means to signal the truth of whatever this intellect represents. So truly representing is prior in nature to any particular true idea; it is a way that thinking reality must be in order for there to be any particular true ideas at all. The (true and immutable) nature of thinking reality is such that it can always be conceived in terms of true representations.

As Spinoza explains in the first half of Ethics Part II, true ideas represent properties of bodies—and some true ideas represent the essences of bodies, or ratios of motion and rest. A longstanding puzzle in Spinoza interpretation is why Spinoza does not list a ‘mediate infinite mode’ for the attribute of thought.¹⁰⁶ Here is a suggestion: Spinoza did not think he needed to because he was confident Schuller would see the parallel. What corresponds to the ‘face of the whole universe’—the ratio of all ratios—is the true representation of that true and immutable nature. It is the ratio considered not as enjoying the formal reality of bodies, but as enjoying the objective reality of objects of thought.¹⁰⁷

Again, nothing Spinoza says here is obviously incompatible with my proposal that all the modes immanently caused by God are eternal, infinite modes.

V.2. A more serious problem?

As I mentioned in Section I, other scholars, seeing that E1p21–23 commits Spinoza to the view that God’s effects are infinite, have invoked one or more ‘infinite modes’ to explain God’s causation of the limited, actual things described in E1p28. Perhaps God causes finite things by causing infinite modes that are pervasive features of the enduring world required for any finite thing to come into being. Or perhaps God causes finite things by causing the infinite mode that is the sempiternal individual that is the entire transitive causal nexus of finite things considered as a whole. According to my reading, these strategies for making sense of Spinoza’s system cannot work: the reality of such pervasive features, or the sempiternal individual, is not the kind of unlimited, infinite, eternal reality that God, properly conceived as the one Spinozan substance, causes.

Much of the Ethics—arguably much of Part II and most of Parts III and IV—concerns what is manifestly not eternal or infinite: things that are affected—even destroyed—by other things. One could complain that my reading renders Spinoza’s system inconsistent. All there is is the one substance and its modes; if all modes are infinite and eternal, then everything that is actual, or real, in the way familiar non-eternal and finite things are actual, does not have a place in the system. God is the cause of all things, but if each and every one of God’s effects is real as an infinite and eternal mode, then God does not cause the reality of ordinary things—the actual, always-in-some-respect limited (and limiting) reality in which we and other actual things strive to endure (E3p6–7).

I do not think my reading renders Spinoza’s system inconsistent, but I do think we need to reexamine the fundamental structure of that system.¹⁰⁸

Spinoza holds that in order for causation to be intelligible, it must be within an attribute. This is a causal-explanatory ‘barrier’ between attributes.¹⁰⁹ I do not think this is the only such barrier in the system: 1) an infinite and eternal God’s immanent causation of infinite and eternal modes and 2) transitive causation of things with ‘finite and determinate existence’ (E1p28) are similarly sequestered, even when the causal relata are considered under the same attribute. Properly conceived under any of its attributes, substance enjoys infinite, eternal formal reality, and can only be coherently cognized as immanently causing effects that also enjoy infinite, eternal formal reality; what enjoys infinite, eternal formal reality can only be coherently cognized as immanently caused by substance. These are conclusions I understand to be established in E1p21–23. Finite and non-eternal things can only be coherently cognized as transitively causing (and caused by) finite and non-eternal things. I understand this to be the main point of E1p28. As I read Spinoza, neither finite, non-eternal things nor indefinite, sempiternal things can be cognized both as enjoying the kind of formal reality they do and as immanently caused by and inhering in substance.

God’s essence can only be properly conceived as enjoying, necessarily, infinite and eternal formal reality. Importantly, however, the infinity of essences following from the divine essence do not involve existence. One and the same essence can be considered either as enjoying formal reality as an infinite and eternal mode, in which case its reality can be understood to be immanently caused by an infinite and eternal God, or as enjoying formal reality as a non-eternal and finite thing, in which case its reality cannot be understood as immanently caused by an infinite and eternal God.¹¹⁰ So, God is the cause of all things and all things are modes; it is just that we cannot coherently cognize things as modes of God when we consider them as real in the way the jostling bodies and impermanent minds of ordinary experience are taken to be real.¹¹¹

I cannot provide more defense of this proposal here.¹¹² I will just end by noting that if this is the basic structure of Spinoza’s monist system, then it can be understood as providing alternatives to three Cartesian views concerning causation. The first is the view I focused on in this essay: the doctrine of God’s creation of the eternal truths. The second is the view, alluded to in Section IV.4, that an infinite, eternal God can be understood as creating and conserving finite (or indefinite) non-eternal (or sempiternal) things. The third is the view that minds and bodies causally interact. That Spinoza replaces the third view with what he sees as a more intelligible monist alternative is universally accepted, although there are—as with anything Spinoza—a variety of ways to understand the alternative Spinoza furnishes. However, the extent of Spinoza’s departure from the other two views has not, to my mind at least, received enough attention.¹¹³ I hope I have shown here why we may want to pay more attention: once we do, we may realize that common ways of reading certain propositions—or understanding Spinoza’s system as a whole—need to be reconsidered.¹¹⁴