Spinoza and the Logical Limits of Mental Representation

I. The Consistency Thesis

The Consistency Thesis is a thesis about the content of all mental states—it says that it is necessarily consistent. The aim of this section is to clarify the Consistency Thesis by clarifying the operative notions of mental content and consistency. First, a mental state has content when it is about something. As Spinoza puts it, ‘the first thing which constitutes the actual being of a human mind is nothing but the idea of a singular thing…’ (E2p11).⁴ The content of a mental state is importantly distinct—at least conceptually—from that mental state’s object of representation.⁵ To speak somewhat loosely, the content is the pointing of the mind, whereas the object of representation is the thing pointed to (if it exists). Spinoza notes this distinction when he discusses the cause of ideas:

The formal being of ideas admits God as a cause only insofar as he is considered as a thinking thing, and not insofar as he is explained by another other attribute. I.e., ideas, both of God’s attributes and of singular things, admit not the objects themselves, or the things perceived, as their efficient cause, but God himself, insofar as he is a thinking thing. E2p5

The formal being of the human mind and the singular thing it represents have distinct causes. In other words, one is caused by God considered as thinking and the other is caused by God considered under some other attribute, viz. whatever attribute the singular thing which is the object of thought is a mode of. The formal being of the human mind includes its content (the act of judging that thus and so), whereas the thing caused by God under some other attribute is that content’s object. This distinction between content and object is implicit when Spinoza notes that ‘although the external bodies by which the human body has once been affected neither exist nor are present, the mind will still be able to regard them as if they were present’ (E2p17c, my emphasis). That is, when we regard an object as present we have a mental state which points to there being an object present. Whether that pointing is successful depends not on the content alone, but also on the existence of the object of representation and its correspondence with the content of the mental state (E1a6).

Let’s turn to the notion of consistency. The view that every object of representation of a mental state is consistent is entailed by the principle that no existing thing instantiates contradictory properties. Spinoza no doubt rejects the existence of contradictory objects, as do most philosophers.⁶ After all, he says that the square circle’s contradictory nature is the reason it doesn’t exist (E1p11d). So, the Consistency Thesis is not the uncontroversial claim that no mental state ever successfully represents an existing contradictory object. Rather, it is the more controversial claim that the pointings of mental states are consistent, i.e., that the objective reality of all mental states is consistent. In general, a mental state is inconsistent if its truth would entail that an inconsistent fact holds or inconsistent object exists. But it is important to note that there are two ways in which mental states might be inconsistent. The first is what I call multi-state inconsistency. This kind of inconsistency occurs when a mind has multiple mental states, the content of two or more individually consistent states logically conflict with each other, but there is no state whose content is the sum of the contents of each individual state. For example, a person who’s conflicted about getting married or staying single is experiencing multi-state inconsistency—they have two desires that are incompatible with each other, but no desire to be simultaneously married and single. This contrasts with what I call single-state inconsistency. It occurs when a single state, whether simple or composite, has inconsistent content. For example, a person with a desire to walk around in an Escher staircase experiences single-state inconsistency—they have a single mental state with inconsistent content, viz. a desire to walk around in an inconsistent scenario. I remain agnostic about whether Spinoza is committed to there being no multi-state inconsistencies.⁷ Instead, the Consistency Thesis should be read as the thesis that there are no single-state inconsistencies.⁸ Spinoza’s adherence to the Thesis will prove to be a departure from his Scholastic predecessors and therefore stands in need of explanation. In addition, the Consistency Thesis, together with Spinoza’s view that only minds have any intentionality, forces him towards the linguistic account of contradiction defended in the final section. That account, if truly Spinoza’s, has far-reaching consequences for how we understand his geometrical method.

II. The Scholastic Background

At the time Spinoza wrote, much of the debate concerning the logical limits of mental representation occurred in the context of a debate over the ontology of what the Scholastics call ‘beings of reason’. Suárez defines beings of reason as those beings which lack ‘true being’ (DM 54.pro.1).⁹ True being consists in possible existence (DM 2.4.7) and so beings of reason, insofar as they lack true being, are impossible beings: ‘For in this [possession of true being and real essence] lies the distinction of creatures’ essences from imagined and impossible things…. In this sense, creatures are said to have real essences even though they do not exist’ (DM 31.2.2). Among the things that lack true being are those with a self-contradictory nature, such as the square circle, which Suárez and the Scholastics routinely call ‘chimaeras’.¹⁰ The standard seventeenth-century account, or family of accounts, of chimaeras, and beings of reason in general, is what I call the cognitivist account.¹¹ An account of beings of reason is cognitivist if it construes them as fundamentally mental entities. Suárez, for instance, writes:

[W]hat is normally and rightfully defined as a being of reason is that which has being only objectively in the intellect or is that which is thought by reason as being, even though it has no entity in itself. DM 54.1.6

An object exists objectively in the intellect when it exists as content.¹² Beings of reason, chimaeras included, exist objectively in the intellect insofar as they can be the content of ideas: ‘many things are thought which are impossible, and are fashioned in the manner of possible beings, for example, a chimera, which does not have any other being besides being thought’ (DM 54.1.7). By conceiving of self-contradictory beings as mental entities, the cognitivist is taking a stand on the logical limits of representation. More specifically, since we can represent chimaeras to ourselves, some forms of representation are not limited by classical logic.¹³

Spinoza was likely aware of the cognitivist account, including that of Suárez,¹⁴ and much of what he says about beings of reason is broadly cognitivist. For example, he explicitly says that beings of reason exist only in the intellect: ‘if anyone looks outside the intellect for what is signified by those words [‘beings of reason’], he will find it to be a mere nothing’ (G I 235/C I 301). In addition, Suárez’s whole motivation for discussing beings of reason lies in the fact that they are indispensable to human knowledge—’the cognition and knowledge of these [beings of reason] is necessary for human instruction’ (54.pro.1)—and so too Spinoza admits that beings of reason, though they exist just in the mind, are nonetheless epistemically useful: ‘[they help] us to more easily retain, explain, and imagine the things we have understood’ (G I 233/C I 299–300).¹⁵ However, the similarity with cognitivism largely ends there. For the cognitivist, contradictions are a subset of beings of reason and, as such, belong in the same ontological category, viz. as fundamentally mental beings. But Spinoza does not think beings of reason exhaust the category of non-being and he thinks we shouldn’t assume that a contradiction is a being of reason just because it’s not a real being. As he says, ‘it is easy to see how improper is the division of being into real being and being of reason’ (G I 235/C I 301).¹⁶ As a result, Spinoza rejects the Scholastic classification of chimaeras and instead reserves a unique ontological category for them. While beings of reason are mental in nature, chimaeras are merely linguistic:

[I]t should be noted that we may properly call a Chimaera a verbal being [ens verbale] because it is neither in the intellect nor in the imagination. For it cannot be expressed except in words. e.g., we can, indeed, express a square Circle in words, but we cannot imagine it in any way, much less understand it. So a Chimaera is nothing but a word, and impossibility cannot be numbered among the affections of being. G I 241/C I 307

The use of ens verbale is an obvious play on ens rationis.¹⁷ A being of reason exists only in the mind; a verbal being exists only in words, whatever that might mean.¹⁸ Because they exist only in words, contradictions cannot be expressed by either an intellectual idea or an imaginative idea. But intellectual and imaginative ideas are the only two kinds of ideas (E2p41–42). It follows that mental content is restricted by the law of non-contradiction. In other words, Spinoza has here explicitly endorsed the Consistency Thesis.

Though the CM passage will form the textual starting point for my interpretation, there are two particular worries with attributing the Consistency Thesis to Spinoza on the basis of this passage. The first is that the CM is an immature work, an appendix to the Principles of Cartesian Philosophy, a work intended as an exposition of the Descartes’ Principles. If the claim that chimaeras are merely verbal is nothing but Spinoza’s view on what Descartes thinks, then the attempt to explain the Consistency Thesis within the context of Spinoza’s more mature system will prove misguided from the start. But we can reject the anti-cognitivism of the CM as an account of Descartes’ position if we can plausibly read Descartes as a cognitivist. It is true that Descartes thinks that a certain species of representation is logically consistent, viz. that of clear and distinct perception. After all, clear and distinct perception that p entails that p is true and there are no true contradictions (AT VII 62/CSM II 43). As Descartes writes in the Second Replies: ‘self-contradictoriness in our concepts arises merely from their obscurity and confusion; there can be none in the case of clear and distinct concepts’ (AT VII 152/CSM II 108). But the fact that one species of representation is necessarily consistent doesn’t entail that all are (which the Consistency Thesis requires). So we cannot attribute the Thesis to Descartes on basis of the fact that clear and distinct perception is consistent. More importantly, there is evidence that Descartes thinks that some forms of representation can be inconsistent. First, right before the passage quoted above, Descartes seems to admit that representation can be inconsistent, albeit not clear and distinct representation: ‘all self-contradictoriness or impossibility resides solely in our thought, when we make the mistake of joining together mutually inconsistent ideas’ (ibid.). Second, he routinely refers to ideas of chimaeras. For example, in the Second Meditation he writes ‘[s]ome of my thoughts are as it were the images of things, and it is only in these cases that the term “idea” is strictly appropriate—for example, when I think of a man, or a chimaera, or the sky, or God’ (AT VII 37/CSM II 25). If we can form an idea of a chimaera, a contradictory being, then mental representation is not necessarily consistent. Now one might worry that Descartes is using ‘chimaera’ here in a rather loose sense, e.g., to refer to things that don’t exist rather than to things that can’t exist due to an internally contradictory nature. But Descartes is clearly aware of the more technical use of the term—as it is used to mean self-contradictory being—because in a letter to Clerselier in which he discusses the origin of falsity, he says that ‘not even chimeras contain falsehood in themselves’ (AT V 354/CSM III 376). The presence of ‘not even’ makes sense only if chimaeras are understood to be necessarily non-existent, for he is saying that even an idea of a necessarily non-existent being is not false prior to a judgment that such a being is possible. So Descartes’ view seems to be similar to that of Suárez: we can conceive of logically inconsistent objects as potential subjects of judgment. Insofar as conception is a form of mental representation, Descartes rejects the Consistency Thesis.

There is a second reason to think that the CM is not merely a restatement of Descartes’ views. In the TdIE, a work written at roughly the same time as the CM, Spinoza argues that we cannot feign logical impossibilities but can only put them in words:

We cannot feign, so long as we are thinking, that we are thinking and not thinking; in the same way, after we know the nature of body, we cannot feign an infinite fly, or after we know the nature of the soul, we cannot feign that it is square, though there is nothing that cannot be put into words. G II 22/C I 26¹⁹

In addition, later in the TdIE he describes what occurs in the mind when a person utters a contradictory sentence: ‘if by chance we should say that men are changed into beasts, that is said very generally, so that there is in the mind no concept, i.e., idea, or connection of subject and predicate’ (G II 24/C I 28). That is, when a person says ‘men are changed into beasts,’ there is no mental act that corresponds to the form of the sentence. This denial stands in stark contrast to the way Suárez (and Descartes) thinks we can unite contradictories in the mind:

There is a third cause [of beings of reason] resulting from a certain fecundity of the intellect, which can construct figments from true beings, by uniting parts which cannot be combined in reality. In this way it fashions a chimaera or something similar. DM 54.1.8

Though the TdIE is an immature work that was never finished, it is clearly a work that Spinoza considered his own. So, the fact that he makes claims similar to those in the CM should be taken as evidence that the CM is an expression of his own ideas, at least on the topic of chimaeras.

The second worry with using the CM as the starting point for my argument is that Spinoza might have accepted the Consistency Thesis in his early work, but rejected it in his mature work. In the next sections I hope to show that he’s committed to it by key doctrines associated with his mature works. But for now I will simply highlight a few late texts in which he make claims in the neighborhood of the Consistency Thesis. First, in the TTP Spinoza admits that the intellect’s powers of expression are limited relative to the powers of images and words:

Since the Prophets perceived God’s revelations with the aid of the imagination, there is no doubt they were able to perceive many things beyond the limits of the intellect. For we can compose many more ideas from words and images than we can by using only the principles and notions on which our whole natural knowledge is constructed. So now it’s clear why the Prophets perceived and taught almost everything in metaphors and enigmatic sayings. G III 45–46/C II 92

This passage does not explicitly commit Spinoza to the Consistency Thesis, but it does echo the notion of there being different degrees of expressive power that Spinoza uses to state the Consistency Thesis in the CM (words can express things that imagination and intellect can’t). Second, in the Ethics, Spinoza warns that ‘people either completely confuse these three—ideas, images, and words—or do not distinguish them accurately enough’ (E2p47s). In his explanation of the confusion he writes that ‘those who confuse words with the idea, or with the very affirmation which the idea involves, think they can will something contrary to what they are aware of, when they only affirm or deny with words something contrary to what they are aware of’ (ibid.). For example, one might understand that p but nonetheless utter that not-p. This echoes an earlier passage in the KV:

It is, of course, true that we can…indicate to others, either by words or by other means, something other than what we are aware of. But we shall never bring it about, either by words or by any other means, that we think differently about the things than we do think about them. That is impossible, as is clear to all, once they attend to their intellect, apart from the use of words and other symbols. G I 83/C 124, my emphasis

In both passages Spinoza is describing how we can utter what we don’t have an idea of. What’s relevant here is that Spinoza is again highlighting the fact that the expressive power of words is greater than that of ideas—we can express in words what we can’t express in the intellect. None of these passages is definitive proof that Spinoza subscribed to the Consistency Thesis in his mature work. But they do show that the concern with the greater power of linguistic expression is a concern throughout Spinoza’s career. Insofar as the Consistency Thesis is stated in terms of expressive powers, these passages are evidence that the Consistency Thesis is not simply a view that the early Spinoza entertained and then later set aside.

III. Imaginative Representation

Unfortunately, Spinoza doesn’t tell us why we cannot express contradictions in ideas, whether imaginative or intellectual. So, there is interpretive work that needs doing. To start, it is important to note that there is theoretical space for Suárez and Descartes to allow for the existence of inconsistent content partly because they both deny that content needs to be the object of an assertoric attitude. For example, Suárez says that ‘in these conceptions, however, the intellect is not in error, since it does not affirm those things to be such in reality as it conceives them by a simple concept—so there is no falsity’ (DM 54.1.8). Descartes echoes this when he says, in the already quoted letter to Clerselier, that ‘not even chimeras contain falsehood in themselves’ (AT V 354/CSM III 376). For both Suárez and Descartes, we can conceive of a chimaera without also conceiving it as true or as existing. They help themselves to this distinction between merely conceiving a chimaera and judging a chimaera to exist because they both think there are separate faculties of the mind—one for conceiving and one for judging. But Spinoza denies that the mind has two separate faculties. Rather, an idea is necessarily a judgment: ‘in the mind there is no volition, or affirmation or negation, except that which the idea involves insofar as it is an idea’ (E2p49) and ‘the will and the intellect are one and the same’ (E2p49c). In other words, there is no such thing as a non-assertoric representation.²⁰ Seemingly non-assertoric representations, such as mere conceivings, are really just assertoric representations of some sort or other, e.g., weaker assertoric representations outweighed by stronger assertoric representations (E2p49cd). So, within Spinoza’s system there can be inconsistent content only if there can be inconsistent assertoric content of some kind or other. In this and the following sections, I offer a two-step argument for why there is no such content in Spinoza’s system, including inconsistent assertoric content that is overruled by stronger ideas and content about inconsistent essences. The first step of the argument focuses on the imagination, while the second focuses on the intellect.

Spinoza is explicit that the imagination need not include images in a literal pictorial sense. Rather, to imagine x is simply to cognize x on the basis of changes that objects produce in the body. ‘the affections of the human Body, whose ideas present external bodies as present to us, we shall call images of things, even if they do not reproduce the figures of things [a]nd when the Mind regard bodies in this way, we shall say it imagines’ (E2p17s, emphasis mine). So, when we ask whether Spinoza allows for inconsistent imaginative content, we are not concerned with whether he thinks something like a mental picture can be inconsistent.²¹ Rather, the question is whether there can be a single-state inconsistency that results from changes in the body, i.e., whether a single mental state that results from changes in the body can have P and not-P as content. Let us suppose, for argument’s sake, that such a mental state is possible. A true idea agrees with its object (E1a6), and since there can be no contradictory or inconsistent object to render the imaginative idea true, it follows that an inconsistent imaginative idea is false. So far, this is not a huge surprise. Inconsistent representations of external bodies are false representations (no external body is inconsistent).²² But Spinoza also says that false representations are false only because they are incomplete representations, i.e., representations which leave out information about the thing being represented: ‘falsity consists in the privation of knowledge which inadequate, or mutilated and confused, ideas involve’ (E2p35). Spinoza is denying here that false ideas have some intrinsic feature which could be identified with their falsity.²³ In his own words, ‘there is nothing positive in ideas on account of which they are called false’ (E2p33). For if there were such a feature, it would have to be a feature which is a mode of God (E1p15) and there could be no such mode of God because ‘all ideas, insofar as they are related to God, are true’ (E2p32). One consequence of this view of falsity is that a false idea can retain its intrinsic features and be true if it is considered relative to a knowing mind, because the knowing mind has that extra information that renders the false idea true. Spinoza offers an example of this transformation at the beginning of Book IV of the Ethics:

For example, when we look at the sun, we imagine it to be about 200 feet away from us. In this we are misled so long as we remain ignorant of its true distance. But when its distance is learned, the error is removed, not the imagination, i.e., the idea of the sun that explains its nature only insofar as the body is affected by it. And so, although we come to know its true distance, we shall nevertheless imagine it as near to us. For as we have said in 2p35s, we do not imagine the sun to be near just because we are ignorant of its true distance but because the mind conceives the sun’s size insofar as the body is affected by the sun. Thus, when the rays of the sun falling upon the surface of the water are reflected toward our eyes, we imagine it just as if it were in the water, even if we know its true place. E4p1s

The imaginative idea of the sun doesn’t change when we do some astronomy, but we now know that its content is simply a reflection of how the human body is affected in certain circumstances. In the same way, to use an example from E2p35s, consciousness of our actions in the absence of knowledge of its causes leads us to believe we are free. After learning about determinism, the feeling doesn’t disappear, but we recognize it as a feeling that arises due to ignorance of specific causes.

This is where the trouble lies. If there could be an inconsistent imaginative idea, then it must be possible for it to be a true idea of God’s. A false idea is rendered true by adding more information—i.e., by removing the privation of knowledge from the mind whose idea it is. So, if there could be an inconsistent imaginative idea, then it must be possible to render it true by adding more information to the mind whose idea it is, such as information about how the human body works. But no amount of additional information can remove a [P and not-P] error because a [P and not-P] error is not an error due to being incomplete. Rather, it is an error that exists because its logical form is impossible. An inconsistent imaginative idea would therefore be an idea whose falsity is grounded in an intrinsic or positive feature of the idea. So there can be no such idea in Spinoza’s system.

One might object that a mind, whether God’s or our own, could have a true idea with inconsistent content in the following sense. Recall that the idea of the sun as 200 feet away becomes true when it is recognized for what it is, namely a response of the human body to certain perceptual stimuli (E4p1s). Perhaps the same is true of inconsistent imaginative ideas—it’s a feature of the human body that sometimes it takes contents that are individually consistent and combines them into an inconsistent idea. Consider the waterfall illusion. When one experiences it, a single object appears both stationary and moving. But we know why this happens—the visual system experiences some lag when it transitions from focusing on a moving object (e.g., a waterfall) to a stationary one (e.g., a nearby rock). As a result, the object looks to be both moving and stationary simultaneously, at least to those who experience the illusion.

But the waterfall illusion is controversial. In fact, there are, to my knowledge, no uncontroversial cases of inconsistent perceptual experiences. For example, it is possible to interpret the waterfall illusion as a case of vacillation between incompatible visual representations, or as a case of ambiguity of the kind present in the duck-rabbit.²⁴ In fact, Spinoza considers some putative cases of inconsistent imaginings, or ‘feignings,’ and attempts to explain them away in just this fashion.²⁵ He focuses on the putative case of imagining a candle that is both burning and not burning:

[Consider someone who says:] “Let us suppose that this burning candle is not now burning, or let us suppose that it is burning in some imaginary space, or where there are no bodies”. Things like this are sometimes supposed [to be feigned], although this [candle] at last is clearly understood to be impossible. But when this [utterance] happens, nothing at all is feigned. G II 21/C I 26

His first attempt to explain the imagining as consistent involves occlusion: ‘in the first case I have done nothing but recall to memory another candle that was not burning (or I have conceived this candle without the flame), and what I think about that candle, I understand concerning this one, so long as I do not attend to the flame’ (ibid.). The resulting representation is logically consistent: that thing in front of me is not burning. Of course, ‘that thing’ is in fact burning, but I have occluded it from my representation. So, I am not actually imagining the existence of anything that is F and not-F. The second explanation involves equivocation or ambiguity:

In the second case, nothing is done except to abstract the thoughts from the surrounding bodies so that the mind directs itself toward the sole contemplation of the candle, considered in itself alone, so that afterwards it infers that the candle has no cause for its destruction. So if there were no surrounding bodies, this candle, and its flame, would remain immutable, or the like. G II 21-2/C I 26

In this case, one imagines a candle that is burning in the sense that there is a flame on the tip of the wick (‘burning₁’) and then imagines that the candle is not burning in the sense that the flame never destroys the wick (‘not burning₂’). The representation is therefore of a candle that is both burning₁ and not burning₂. But this representation is no more inconsistent than my representation that my friend is both warm (in terms of personality) and not warm (because she forgot her coat). So, Spinoza has reason to reject the possibility of inconsistent imaginative ideas, as well as resources to explain away potential counterexamples.²⁶

IV. Intellectual Representation

It remains to be seen whether there can be intellectual representations with inconsistent content.²⁷ Clearly there can’t be intellectual representations that an inconsistency exists. There are no inconsistencies and all intellectual representation is true and therefore agrees with its object (E2p41s, E1a6). But it might nonetheless be possible to represent an inconsistency in a different way, such as when one represents the essence of a thing as inconsistent. Spinoza seems at times to countenance such representation when he talks about the essences of square circles (E1p11d). If there are such things, then it would seem that we, or some mind, could think about them. Not surprisingly, there are at least two views in the literature which posit ideas of the essences of contradictions. As a result, they allow for intellectual ideas of inconsistences. I will argue that both of these views fail.

On the first view, which I call the ‘standard view,’ a thing’s formal essence is akin to an eternal blueprint for existence (as opposed to its actual essence, which is its striving (E3p7)).²⁸ Just as a blueprint for a house can exist without the house existing, so too can there be a formal essence of a thing without there being the actual thing itself: ‘the human Mind cannot be absolutely destroyed with the Body, but something of it remains which is eternal’ (E5p23). The primary motivation for this view comes from Spinoza’s claim that we can think about non-existents by thinking of these formal essences: ‘the ideas of singular things, or of modes, that do not exist must be comprehended in God’s infinite idea in the same way as the formal essences of the singular things, or modes, are contained in God’s attributes’ (E2p8, my emphasis).²⁹ The standard view provides a simple framework for the intellectual cognition of inconsistencies: we have ideas of square circles insofar as there are formal essences of square circles and we think about them.

But there are both textual and philosophical reasons to reject the existence of contradictory formal essences. The most important text occurs in Spinoza’s proof of the impossibility of self-destruction.³⁰ That doctrine, which forms a crucial part of the proof of the more famous conatus doctrine, states that ‘no thing can be destroyed except through an external cause’ (E3p4).³¹ In the proof of the impossibility of self-destruction, Spinoza claims that there could be no essence of a self-destructing thing because:

The definition of any thing affirms, and does not deny, the thing’s essence, or it posits the thing’s essence, and does not take it away. So while we attend only to the thing itself, and not to external causes, we shall not be able to find anything in it which can destroy it, q.e.d. E3p4d

Of course, this is just a bare assertion that there are no essences of self-destroying beings (including contradictions) and Spinoza hasn’t provided a reason for their non-existence.³² Garber (1994: 59–60), for instance, considers Spinoza’s view that an essence must be consistent to be arbitrary and stipulative. Even worse, it might appear in this passage that Spinoza is unjustifiably sliding from a claim about the impossibility of X (a self-destroyer) to a claim about the impossibility of an essence of X. But there are actually good reasons for Spinoza to deny the existence of inconsistent formal essences, reasons which he could have easily called upon at this point in the Ethics. Essences, whether formal or otherwise, are modes of God and so must be conceived through God’s nature: ‘modes can neither be nor be conceived without substance…they can be in the divine nature alone, and can be conceived through it alone’ (E1p15d).³³ The way that formal essences are conceived through God’s nature is as logically consistent ways that God can be.³⁴ For example, my formal essence is contained in God’s attributes of Thought and Extension as a way that God can be. Some formal essences are contained in God’s attributes as logically consistent ways that God can be but isn’t, due to the order of nature. For instance, even if there are no perfect hexagons, there is nonetheless a formal essence of a perfect hexagon insofar as a perfect hexagon is a way that God, as extended, can be but isn’t (due to the order of nature).³⁵ But a self-destroyer, such as a square circle, expresses a way that God’s self-affirming nature cannot be, not even if the order of nature got out of the way. The upshot is that there can be no formal essences of contradictions. If there are no formal essences of contradictions, then there can be no intellectual idea with inconsistent content, because an intellectual idea is always true and a true idea must have some object which it agrees with. Outside of objects and their essences, there do not seem to be any candidates for what a true idea agrees with.

Laerke (2017), however, offers a second, non-standard account of the cognition of non-existents which has the potential to explain the possibility of inconsistent intellectual content without positing formal essences of contradictions. Laerke agrees with the standard view that the cognition of non-existents occurs through the cognition of formal essences that are contained in God’s attributes. But he denies that there are any formal essences of non-existents. Rather, we cognize non-existents by thinking about the formal essences of their causes of non-existence. His account is motivated in part by Spinoza’s claim in E1p11d that there is a cause both for each thing’s existence and for its non-existence:

Now, since for a thing to exist for Spinoza just means that the divine attributes are modified in such a way so as to produce this thing, one implication of the causal principle in E1P11D2 could seem to be that, just as existent things are contained in the attributes as existing in virtue of some external cause, non-existent things must be not contained in the attributes of substance as existing in virtue of a given external cause or reason. Such nonexistent things are not just absent from existence, but positively excluded from existence by other, existent things. And when they are thus excluded from existence, this means that the unique substance is thus modified so as not to produce them. Those things simply do not exist. If, I suggest, Spinoza nonetheless holds that the formal essences of non-existing things are somehow contained in the attributes, it is because, even if non-existing things are not contained in the attributes qua existing, they are nonetheless contained in the attributes qua non-existing. They are modes presently excluded from existence by that which exists and thus contained in the attributes in a determinate way qua excluded from existing. It is in virtue of such determinate causes or reasons of non-existence that we can say that the formal essences of non-existing things are actually contained in the attribute qua non-existing. Laerke 2017, 30

For example, we can think about my non-existent 2018 dog by thinking about the causes which preclude its existence, e.g., my current desire not to have a dog. On this account, then, we can think about a contradiction, such as a square circle, by thinking about what keeps it out of existence. Since square circles fail to exist due to the nature of squares and circles, we can think about square circles by thinking about the essences of squares and circles. Since the essences of squares and circles unproblematically express God’s nature, Laerke’s account avoids the result that there are essences of self-destroyers which express God’s nature.

There is the following problem with Laerke’s account, however. There is an important distinction between (i) conceiving of two things and (ii) conceiving of them as conjoined. For example, I can think of my next two papers without thinking of combining them (a fact which future reviewers are no doubt grateful for). The same distinction applies when the two things in question are jointly contradictory. That is, there is an important difference between (i) conceiving of the essence of a square and the essence of a circle and (ii) conceiving of the essence of a square circle. The difference is one that Spinoza describes in at least two places. First, in a passage from the TdIE already quoted, he says ‘if by chance we should say that men are changed into beasts, that is said very generally, so that there is in the mind no concept, i.e., idea, or connection of subject and predicate’ (G II 24/C I 28).³⁶ In other words, an English speaker who utters the sounds ‘men are changed into beasts’ may perhaps have an idea whose content includes men, beasts, and perhaps the phenomenon of change, but the idea has no unity. It is merely a mental lump or list which lacks anything corresponding to the grammatical structure of the utterance. Second, in the CM Spinoza uses the example of two independently thinkable things whose conjunction is merely linguistic:

If we were to conceive the whole order of nature, we should discover that many things whose nature we perceive clearly and distinctly, that is, whose essence is necessarily such [i.e. clear and distinct], cannot in any way exist. For we should find the existence of such things in nature to be just as impossible as we now know the passage of a large elephant through the eye of a needle to be, although we perceive the nature of each of them clearly. So the existence of those things would be only a chimaera. G I 241–242/C I 308, my emphasis

A large elephant and an eye of a needle are each internally consistent—we perceive their natures clearly. But they are jointly inconsistent, at least when the conjunction involves the latter passing through the former. When we try to conjoin them, all we get is a chimaera—an unthinkable ens verbale.

The question is whether Laerke’s account can, without positing the formal essence of a non-existent square circle, make sense of the difference between (i) thinking of a square circle and (ii) thinking of a square and a circle. I think the answer is no. In order to distinguish between a unified idea of a square circle and the lump-like idea of a square and of a circle, one must distinguish the objects that they agree with. Each idea, if it exists, is a true idea and true ideas always agree with some object (E1a6). So, there must be some object that the unified idea agrees with that is not simply the essence of a square and/or the essence of a circle. It cannot be a square circle itself, since there are no such things. But nor can it be the formal essence of a square circle, for Laerke does not allow for such entities. Without some suitable proxy for a contradiction which acts as the object of a true idea, the account cannot make sense of a person who thinks of squares and circles as unified. Without this, the account has not provided a framework for inconsistent intellectual content.

Let me sum up the previous two sections. I argued in the previous section that Spinoza’s theory of error precludes the possibility of inconsistent imaginative content. In this section I argued that the impossibility of self-destruction precludes the possibility of inconsistent intellectual content. We can now see that both steps of the argument rely on the more general claim that what we can think about depends on what can follow from God’s nature. We cannot think about the essences of contradictions because essences of contradictions are essences of something which cannot follow from God’s self-affirming nature. But facts about what can follow from God’s nature also play a role in the theory of error, and so also in the impossibility of inconsistent imaginative content. The main reason why the imagination must be consistent is that all imaginative ideas need to be true insofar as they are in God’s mind (E2p32). But in his demonstration of E2p32, Spinoza cites E2p7c:

God’s power of thinking is equal to his actual power of acting. That is, whatever follows formally from God’s infinite nature follows objectively in God from his idea of the same order and with the same connection.³⁷

Since contradictions cannot follow from God’s infinite nature, given the fact that they are self-destructing beings, it follows that there is no imaginative idea of a contradiction either. Spinoza’s error theory is therefore partly grounded in his views about what can follow from God’s nature, including his view that nothing which destroys itself could follow from God’s nature.

V. The Linguistic Nature of Contradictions

I’ve argued that there are Spinozistic motivations, tied to views about what can follow from God’s nature, for denying both intellectual and imaginative inconsistent content. It is impossible, on Spinoza’s view, to desire, intend, think, imagine, or even entertain a contradictory proposition. All mental activity points to the logically possible. But it remains an open question what a contradiction is. After all, it seems to be something. As Suárez points out, the fact that we can talk about contradictions without talking gibberish forces us to account for their nature:

This very thing we are doing, in disputing about beings of reason, does not come about without some thinking about those [beings of reason]. Therefore, unless one does not know what one is saying, one cannot deny that there is something of this kind contrived by thinking alone. DM 54.1.7

In this section I will argue that contradictions are not representations, mental or otherwise, because only minds can represent anything and all representation is therefore consistent. Contradictions are instead linguistic artifacts which merely appear to represent.

Let’s return to Spinoza’s claim that contradictions can be expressed only in language. He never elaborates on what it means to put a contradiction into words, i.e., what makes an ens an ens verbale. We should start by noting that there are two distinct concepts of language present in Spinoza’s system, and so it will be necessary to decipher which concept he has in mind.³⁸ Language in the physical sense consists of shapes of ink on the page, patterns of pixels on the screen, soundwaves in the air, and so on. For example, what appears on this page is physical language. Language in the imaginative sense consists of ideas of shapes on the page, patterns on the screen, and so on. For example, your mental images of the shapes on this page are instances of imaginative language. In normal circumstances, both kinds of language can have content. Spinoza explains:

And from [association] we clearly understand why the mind, from the thought of one thing, immediately passes to the thought of another, which has no likeness to the first: as, for example, from the thought of the word “pomum” a Roman will immediately pass to the thought of the fruit, which has no similarity to that articulate sound and nothing in common with it except that the body of the same man has often been affected by these two, that is, that the man often heard the word “pomum” while he saw the fruit. E2p18s

Imaginative words have two levels of content. The first level of content is the physical word, e.g., the shapes on this page. The imaginative words have this content for the same reason that all imaginative ideas have content: there is a change in the body that is caused by an external body. In this case that external body is the shapes on this page.³⁹ But once those shapes have been experienced in the presence of other objects, an associative link is formed and that link grounds a second level of content. For example, the idea of the shapes ‘apple’ is associated with the ideas of apples and so the second level of content includes apples. Physical words have only one level of content—the second level of content—and they get it by piggy-backing on the content of the imaginative words. For example, the shapes ‘apple’ have apples as content by virtue of the fact that one’s idea of the shapes ‘apple’ becomes associated with the idea of apples. When Spinoza says that contradictions exist only in language, he cannot have imaginative language in mind. After all, he explicitly says that contradictions cannot be expressed in the imagination and imaginative language is part of the imagination. And it is not as if this is a slip of the pen—as I’ve argued, Spinoza has good reasons to think that the imagination must be consistent. So, when he says that contradictions exist only in language, he must mean that they exist only in physical language, in the scribbles on a page.

But, again, it is not exactly clear what this means. At first glance it might seem like Spinoza is saying that physical language can sometimes have content independently of imaginative language and that this independent representation occurs when the content is inconsistent. For example, the words ‘square circle’ have contradictory content even though no mind can think the content of the words.⁴⁰ But I do not think this is Spinoza’s view. An entity has content when it is about something and he thinks that only mental reality is ever fundamentally about anything. In the Ethics, for instance, he lists intentionality as an essential feature of all individual thoughts: ‘there are no modes of thinking, such as love, desire, or whatever is designated by the word “affects of the mind,” unless there is in the same individual the idea of the thing loved, desired, and the like’ (E2a3).⁴¹ Individual thoughts are modes of the attribute Thought and an attribute is always conceptually independent of all the other attributes: ‘each attribute of a substance must be conceived through itself’ (E1p10). It follows that nothing outside of Thought and its modes essentially involves any intentionality. When physical words have content, it is only by piggy-backing on ideas via association. As Spinoza says in the Principles of Cartesian Philosophy, ‘I cannot express anything in words, without its being certain from this that there is in me an idea that is signified by those words’ (G I 149/C I 238).⁴² There is no opportunity for piggy-backing on ideas when contradictions are involved because no idea has inconsistent content. So, it can’t be Spinoza’s view that contradictions exist only in physical words in virtue of only being represented by physical words. Nothing can be represented only in words.

So, in what sense does language express contradictions? It is not in virtue of being contradictory, because nothing is contradictory. But neither is it in virtue of representing contradictions, since physical stuff lacks the power to represent independently of being associated with ideas and no idea has inconsistent content. All representation is therefore consistent. Fortunately, there is a third option: some physical words have a unique structure and a linguistic expression is a contradiction when it has that structure.⁴³ To support this third option, it is important to note that the structure of physical words often makes a difference to which ideas occur in the mind. Consider common jokes about sentences not using the Oxford comma, such as when one reads the sentence ‘I had eggs, toast and orange juice’ as someone addressing to orange juice and toast that they had eaten some eggs (rather than as a report of having had a breakfast with three items). A contradiction is a physical linguistic expression whose constituents or matter can be taken up in thought—that is, whose constituents are linked to ideas in the mind—but whose structure or form cannot be taken up in thought. Recall Spinoza’s earlier comment about the phenomenon of failing to unify content: ‘[I]f by chance we should say that men are changed into beasts, that is said very generally, so that there is in the mind no concept, i.e., idea, or connection of subject and predicate’ (G II 24/C I 28). What occurs in the mind when it reads ‘men are changed into beasts’ is not a structured idea but an unstructured mental lump—there is correspondence between the matter of the idea and the matter of the utterance, but not between their forms. That is, the linguistic expression has three constituents—men, change, beasts—and a specific predicate structure, but the mental lump has only constituents and no structure. It amounts to a mental list rather than an act of predication. Perhaps we feel like we are mentally predicating beasthood of men because we vacillate back and forth between ideas of men and ideas of beasts. Spinoza is no stranger to using vacillation to explain conceptual errors. For example, in E2p44s, he uses vacillation to explain why we think that the future is open or full of possibilities. In the same way, the physical words ‘square circle’ express an unstructured mental lump of ideas of squares and circles and perhaps it only feels like a structured thought, a unified concept of the impossible, because we vacillate between the ideas very quickly.⁴⁴

One might wonder whether something physical like words on a page can properly be called contradictory. After all, they don’t instantiate contradictory properties and, on Spinoza’s account, they don’t represent any contradictory properties at all either. So in what sense is a contradiction an ens verbale? Two things can be said in response to this worry. First, this charge should could just as easily be leveled at any purely formal logical system. There are no contradictory properties instantiated in such systems, nor any representations either (as it is a purely formal system). Within such a system, a contradiction is simply a well-formed formula of a certain structure which licenses inferences of a certain kind (in a classical system, inferences of any kind). But second, and more importantly, I think this worry reflects a failure to take seriously Spinoza’s claim that there really is nothing contradictory—no things and no representations. As he says, a chimaera is ‘nothing but a word, and impossibility cannot be numbered among the affections of being’ (G I 241/C I 307). We will never get a satisfactory answer from Spinoza if we ask how a physical thing can really be contradictory. The most one can hope for is an explanation for why we ever thought that contradictions were anything more than just a feature of physical language in the first place. And Spinoza has just such an explanation insofar as he repeatedly warns against the deceptive nature of language. For example, in the TdIE, he says that ‘it is not to be doubted that words, as much as the imagination, can be the cause of many and great errors, unless we are very wary of them’ (G II 33/C 38).⁴⁵ One of the ways language causes errors is by enjoying an independence of expression: ‘we affirm and deny many things because the nature of words—not the nature of things—allows us to affirm them’ (G II 33/C I 38).⁴⁶ Language is independent in the sense that what is well-formed in language does not necessarily correspond to a well-formed thought, let alone to reality itself.⁴⁷ In fact, Spinoza blames at least two philosophical errors on the independence of language from thought. First, many people delude themselves into thinking that they can doubt God’s existence merely because they can say things like ‘God might not exist’: ‘although many people say that they doubt whether God exists, nevertheless they have nothing but the name, or they feign something which they call God’ (G II 20/C I 24, my emphasis). Second, the independence of language is the cause for why philosophers reify contradictions as mental entities. Consider the argument by Suárez quoted at the beginning of this section:

This very thing we are doing, in disputing about beings of reason, does not come about without some thinking about those [beings of reason]. Therefore, unless one does not know what one is saying, one cannot deny that there is something of this kind contrived by thinking alone. DM 54.1.7

Suárez reifies contradictions as beings of reason because he thinks they’re not gibberish. But the fact that they’re not gibberish just means that, unlike gibberish, they are well-formed linguistic expressions. To infer that they are therefore mental things is to make a fallacious inference. As Spinoza says, ‘philosophers preoccupied with words or grammar, should fall into such error [because] they judge the things from the words, not the words from the things’ (G I 235/C I 301). Once we realize that more can be expressed in language than can be expressed in thought, the inference at the heart of Suárez’s argument disappears.

So, what is a contradiction? It is a bit of physical language whose structure is well-formed but whose structure cannot be thought. We only ever mistook it for something else because we were under the mistaken impression that language must correspond to thought. And the fact that we were under this impression is not hard to explain in the case of contradictions. First, when we consider a ‘P and not-P’ linguistic expression, we do think the constituent contents, viz. the ideas corresponding to ‘P’ and to ‘not-P’. Something is occurring upstairs, so to speak, when I focus on a contradiction. Second, in normal circumstances, we’re used to the physical structure of linguistic expressions making a difference to the structure of ideas. So, we anticipate that the same holds true with contradictions, i.e., that the syntactic structure corresponds to a mental structure. The phenomenon of vacillation likely deludes us into thinking that there is this correspondence. But there is no such correspondence. A contradiction is just an ens verbale

VI. Conclusion

I’ve argued that Spinoza departs from Scholastic tradition by explicitly endorsing the logical consistency of all mental content. I’ve also argued that he is committed to this view by some of his most Spinozistic views, perhaps most fundamentally his view that thought is limited by what can follow from God’s nature. I have also argued that this view on mental content pushes him to a linguistic view of contradictions—contradictions are literally just words with a certain structure that, due to the deceptive nature of language, we mistake for representations with a certain structure. The view is not only novel, it also raises an important question for Spinoza’s geometrical method. Many of Spinoza’s arguments in the Ethics aim to derive contradictions from competing philosophical views, i.e., to show that they contain latent contradictions. But if a contradiction is just a physical thing—and as such neither instantiates nor represents any contradictions—then it is not obvious what it would mean for a competing philosophical view to contain a latent physical thing. So, if Spinoza is truly committed to the linguistic view I’ve defended, then we are forced to consider new ways of understanding the demonstrations of the Ethics.⁴⁸

Competing Interests

The author has no competing interests to declare.