New Essays on Human Understanding (Nouveaux essais sur l’entendement humain) – Gottfried Wilhelm Leibniz

A Point-by-Point Rebuttal of Locke’s Empiricism, Section by Section

Preface — The Author’s Program and Method

We are at the opening of the work, where Leibniz lays out his overarching intentions, his disagreements with Locke, and the philosophical stakes of the entire dialogue.

Leibniz begins by stating that the work is a series of “remarks” on Locke’s *Essay Concerning Human Understanding*, following the same order of chapters. He immediately identifies the fundamental point of divergence: innate ideas. Locke had argued that the human mind begins as a *tabula rasa*, a blank slate, with all knowledge arising from experience. Leibniz declares the opposite: “I have always been, and still am, in favour of the innate idea which Descartes upheld, and which M. Locke opposed.” He does not, however, adopt the Cartesian position wholesale. He refines it by introducing the distinction between necessary truths and truths of fact. Necessary truths, such as those of mathematics and logic, cannot be derived from experience because experience only tells us what happens to be the case, not what must be the case. The mind must therefore contain the principles that enable it to grasp necessary truths.

Leibniz then introduces his central metaphor: the mind is not a blank tablet but a block of marble whose veins prefigure the statue to be carved. Experience does not write on nothing; it “brings to light” what is already potentially there. He writes: “I have used the comparison of a block of marble which has veins, rather than a block of marble wholly uniform, or blank tablets (which is what the philosophers call a *tabula rasa*).” The veins are the innate dispositions, tendencies, and principles that determine how the mind will respond to sensory input. This is Leibniz’s theory of dispositions — the mind is not born with fully formed ideas, but with a natural capacity and inclination to form certain ideas under the right conditions.

This preface matters because it establishes the entire framework for the dialogue that follows. Leibniz is not simply denying Locke’s empiricism; he is offering a third way between the blank slate and the full-blown Cartesian innate ideas. The marble-vein analogy becomes the key to understanding every subsequent argument. The reader will see that Leibniz repeatedly insists that what Locke treats as derived from sensation is actually the mind’s own activity, awakened but not created by experience.

Book I: Of Innate Notions — Chapter 1: Whether there are Innate Principles

We are at the first book of Locke’s *Essay*, where Leibniz’s spokesman Theophilus responds to Locke’s spokesman Philalethes, who presents Locke’s arguments against innate principles. The chapter addresses the very possibility of innate knowledge.

Philalethes opens by stating Locke’s position: that there is no innate knowledge because there is no principle universally agreed upon by all humans. Children and “idiots” have no awareness of the principle of identity or non-contradiction. If there were truly innate principles, everyone would know them. Theophilus replies that this argument rests on a misunderstanding of what innateness means. He distinguishes between innate truths and innate knowledge. A truth can be innate without being consciously known from birth. The veins in the marble are present from the beginning, but they require the sculptor’s chisel to become visible. Similarly, innate principles are present in the mind as dispositions or tendencies, not as explicit propositions.

Theophilus then addresses Locke’s claim that innate principles would have to be known to everyone, including children. He retorts: “The proposition does not have to be explicitly known to be innate. It is enough that it can be derived from the mind’s own resources.” The mind contains the seeds of these truths, which emerge gradually through experience and reflection. Experience is necessary, but it is not sufficient — it only “triggers” what is already latent. Theophilus gives the example of the principle of contradiction: no one needs to be taught that a thing cannot both be and not be at the same time. Even a child who has never heard the formula “A = A” will, upon reflection, recognize its necessity. This recognition is not learned from the senses; it comes from the mind’s own nature.

This chapter is crucial because it establishes the ground rules for the entire debate. Leibniz is not claiming that infants are born with explicit knowledge. He is arguing that the human mind has a native structure that determines what can be learned and how it is organized. The blank slate metaphor is rejected, but so is the picture of fully-formed ideas sitting in the mind from birth. The dispositional theory of innateness is Leibniz’s distinctive contribution, and it will be deployed again and again throughout the work.

Book I, Chapter 2: No Innate Principles in the Mind — Continued

We continue in Book I, where Philalethes presses Locke’s further arguments against innate practical principles — moral and religious rules — which Locke says vary too much across cultures to be considered innate.

Philalethes points out that moral principles like “do unto others” are not universally accepted. Some nations practice revenge, others practice theft or cannibalism. If these were innate, they would be known and followed everywhere. Theophilus responds by distinguishing between speculative principles (like mathematics) and practical principles (like morality). Speculative principles are necessary truths; they cannot be violated without contradiction. Practical principles, however, are not known in the same way. They are inclinations or tendencies that require reason and education to be properly developed. The fact that some cultures violate them does not disprove their innateness — it only shows that they have been suppressed or corrupted.

Theophilus then introduces a key distinction: instinctive knowledge versus explicit knowledge. Humans have an innate natural sense of good and evil, a conscience, that precedes all human laws. This is not a set of written rules, but a disposition to approve of certain actions and disapprove of others. He writes: “The principles of morality are not innate in the sense that they are known to everyone. They are innate in that they are derived from the natural constitution of the mind, and can be brought to light by proper reflection.” The mind contains the seeds of justice, just as it contains the seeds of mathematics. The difference is that moral truths are not as easily demonstrated as geometric theorems, because they depend on a harmony with the nature of God and the universe that is not immediately obvious to the senses.

Philalethes objects that if moral principles were innate, there would be no need for laws or punishment. Theophilus counters that the existence of laws does not disprove innateness — it presupposes it. “The laws that are made,” he says, “are but supplements to the innate law of reason, which is obscured by passions and prejudices.” The natural law is written in the heart, but it requires the external law to remind and enforce it. This is the same logic as the marble-vein analogy: the statue is already there in potential, but the chisel must carve away the excess.

This chapter clarifies how Leibniz applies his innateness theory to morality. He is not committed to the absurd position that everyone knows the Ten Commandments from birth. Rather, he holds that the rational nature of humanity includes a teleological orientation toward the good, which can be clouded by circumstance but never entirely erased. The argument from diversity — that different cultures have different moral codes — does not refute innateness, because it mistakes the surface expression for the underlying principle.

Book I, Chapter 3: No Innate Practical Principles

We are at the final chapter of Book I, where Philalethes brings forward Locke’s most specific objections: that even if there were innate principles, they would be useless because they would be known to everyone, and if they were unknown, they cannot be called innate.

Philalethes argues that if a principle is innate, it must be present in the mind from the beginning. But principles like “whatever is, is” are not known by children or the uneducated. Therefore they are not innate. Theophilus replies with the analogy of a hidden figure in a block of marble. The figure does not become visible until the sculptor works, but it was there all along in potential. “Innate truths are like the statues that are in the stone,” he explains. “They are not yet formed, but they are there in the veins of the rock.” The mind’s potentiality is what makes knowledge possible. Without this potential, the senses would be nothing more than noise.

Philalethes then presses a second objection: if innate principles were truly innate, they would be the first things known. Theophilus denies this. The first things known are the particulars of sense, but the principles that give those particulars meaning are known tacitly long before they are consciously formulated. A child uses the principle of non-contradiction every time it refuses to believe that the same apple is both red and green at the same time. The child does not know the principle explicitly, but uses it implicitly. This is the crucial distinction between explicit knowledge and implicit knowledge.

Theophilus sums up his position: “I think that the mind is so constituted that it can discover these truths from its own resources, though it requires the senses to give it the occasion and to direct its attention to certain truths rather than others.” The senses are the occasion for knowledge, not its source. This is the fundamental point of disagreement with Locke. For Locke, the senses provide the material and the mind merely receives it. For Leibniz, the senses provide the occasion, but the mind provides the structure, the principles, and the necessary connections.

This chapter closes Book I with a decisive formulation of the dispositional theory. The debate is not whether we are born knowing things, but whether the mind has a pre-existing structure that determines what it can know. Leibniz insists that it does, and that without this structure, experience would be meaningless flux. The marble-vein analogy is now fully in place, and the reader can proceed to the remaining books with a clear understanding of the philosophical ground Leibniz will stand on.

Book II: Of Ideas — Chapter 1: Wherein is Treated of Ideas in General, and Whether the Soul of Man Always Thinks

We move from the general question of innate principles to the specific investigation of ideas. Locke’s Book II opens with the claim that ideas are the material of thinking, and he defines an idea as “whatsoever is the object of the understanding when a man thinks.” Philalethes reads Locke’s position: that all ideas come from experience, and that the mind begins as a white paper, void of all characters, before any ideas are imprinted upon it. The human understanding, according to Locke, has no innate ideas and must derive all its content from sensation or reflection.

Theophilus immediately contests the claim that the soul sometime thinks not, a position Locke defends on the grounds that sleep without dreaming proves the soul can exist without thinking. Leibniz responds with a characteristic distinction. “I can’t accept the proposition that the soul sometimes thinks not; and still less, that in death it ceases to think altogether.” He argues that perception is always present in the soul, even when we are not consciously aware of it. Unconscious perceptions, or small perceptions (*petites perceptions*), continue to occur during sleep. The soul never ceases to think, but many of its thoughts are too small and too numerous to be individually noticed.

The argument turns on the nature of substance. For Locke, the soul is essentially a thinking thing, but thinking is not necessary to its existence. For Leibniz, the soul is a simple substance whose nature is perception. “A substance cannot be without action; and there is never a body without movement.” The soul always perceives, even if those perceptions are confused and indistinct. The state of being awake and conscious is merely the condition in which perceptions become clear enough to be remembered. The doctrine of unconscious perceptions is thus introduced as a direct challenge to the Lockean model of the mind as a blank slate that only receives ideas when consciously attended to.

Book II, Chapter 2: Of Simple Ideas

Philalethes presents Locke’s classification of ideas into simple and complex. Simple ideas come from sensation or reflection and are “unmixed and uncompounded.” The mind cannot make or destroy simple ideas; it can only combine those it receives from experience. The examples Locke gives are whiteness, coldness, sweetness, and the like—qualities that the senses deliver as basic units.

Theophilus accepts the distinction but immediately complicates it. “These simple ideas, if they are truly simple, are the elements of our thoughts; but I doubt whether any ideas are perfectly simple.” For Leibniz, what appears simple to the senses may be complex in reality. A perception of redness, for instance, may be the result of many minute motions and changes in the body and in the object that the mind does not register. The simplicity is an appearance, not a metaphysical reality.

This leads to a deeper point about the nature of ideas. Leibniz insists that ideas are not images or traces in the brain, but dispositions of the soul to produce certain thoughts. “I have said more than once that I believe that ideas are truly in the soul as dispositions, as modifications of the soul’s nature, and that they are imprinted on the soul from its origin.” The Lockean model treats simple ideas as raw data impressed upon a passive mind. Leibniz, by contrast, sees the mind as active even in the reception of simple ideas, because the mind must have the innate capacity to form those perceptions. The simple idea is thus not the beginning of knowledge but the occasion for the mind to exercise its own inherent structure.

Book II, Chapter 3: Of Ideas of One Sense

Locke divides the simple ideas according to the senses that deliver them. Some ideas come through one sense only, such as light and colors through the eyes, sounds through the ears, and solidity through touch. Philalethes reads the passage: “The ideas of colors, sounds, smells, tastes, and the sense of touch, are each derived from a particular sense, and cannot be conveyed to the mind through any other channel.”

Theophilus accepts the classification but notes that the senses themselves are not so neatly separated as Locke assumes. “It is true that each sense has its proper objects; but there are also qualities that are common to several senses, such as figure, magnitude, motion, rest, and number.” These common sensibles, as the Scholastics called them, are perceived by both sight and touch. Leibniz adds that the senses provide only the occasion for perceiving these qualities, not the ideas themselves. The idea of figure, for instance, is not given by the eye alone; the mind must possess the capacity to recognize shape as a property distinct from color.

The deeper issue is whether the senses can give us the necessary truths about these qualities. Locke thinks they do; we learn what a triangle is by seeing triangular objects. Leibniz disagrees. “I believe that the senses give us only instances, that is to say particular truths, and that they are insufficient to establish universal propositions of necessity.” The idea of a triangle, properly speaking, is an innate idea that the mind brings to experience, not one it receives from it. The senses awaken the idea, but they do not produce it.

Book II, Chapter 4: Of Solidity

Locke treats solidity as a simple idea of touch, distinct from hardness. Solidity is “that which keeps two bodies from occupying the same place at the same time.” It is the foundation of the idea of body and of the distinction between body and space. Locke insists that solidity is not the same as hardness, for hardness is a relative property of cohesion, while solidity is the absolute property of impenetrability.

Theophilus praises Locke’s analysis but introduces a metaphysical refinement. “I think that solidity is the property of being impenetrable, which is indeed a consequence of the nature of body; but I do not think that impenetrability is a simple idea of sensation, because it involves a negative, namely that two bodies cannot be in the same place at once.” The idea of impenetrability, for Leibniz, is an intelligible idea that reason adds to the sensory report. We feel resistance, but we understand impenetrability only through a rational judgment about the nature of bodies.

This opens the larger question of the nature of body. For Locke, body is defined by solidity and extension; for Leibniz, body is essentially substance with force as its primary attribute. “I think that there is something more in body than extension and impenetrability; and that is the force or power of acting and resisting, which is the source of its motion and its resistance.” Solidity, in Leibniz’s system, is a phenomenon grounded in the active force of monads. The Lockean analysis, while accurate at the empirical level, misses the deeper metaphysical foundation.

Book II, Chapter 5: Of Simple Ideas of Divers Senses

Locke continues his classification by noting that some simple ideas are received by more than one sense: space, extension, figure, rest, and motion. These are the common sensibles that the mind receives through multiple channels. Philalethes reads: “Thus, for example, I see a sphere with my eyes and feel it with my hands; the idea of the sphere is the same in both cases, though the means of receiving it are different.”

Theophilus finds this unobjectionable but draws attention to a distinction Locke does not make. “These common sensibles are in truth the objects of several senses, but I think that they are also objects of the internal sense or reflection.” The mind is not simply a passive receiver of these ideas from the various senses; it actively synthesizes them into a unified perception. The idea of a sphere is not merely the sum of visual and tactile impressions but a concept that the mind produces by comparing those impressions.

The point is part of Leibniz’s larger argument against empiricist passivity. The Lockean model assumes that ideas enter the mind through the senses and are then stored. Leibniz insists that the mind is always active in forming its ideas, even those that seem most directly given by sensation. The common sensibles are not merely received but constructed by the mind from materials that the senses alone cannot provide. The mind supplies the form; the senses supply only the matter.

Book II, Chapter 6: Of Simple Ideas of Reflection

Locke introduces reflection as the second source of simple ideas, after sensation. Reflection is “the notice which the mind takes of its own operations” — perception, thinking, doubting, believing, reasoning, knowing, and willing. These are simple ideas that arise when the mind turns inward upon its own activities. Philalethes reads: “The understanding cannot have any ideas except those that come from sensation or reflection; and these two are the only sources of all our ideas.”

Theophilus accepts the category but widens it. “Reflection is not limited to the operations of the mind; it also includes the perception of the mind’s substance itself, its duration, and its unity.” For Leibniz, the mind does not merely observe its own acts; it perceives itself as a persisting substance that underlies those acts. The idea of the self is not derived from reflection in the Lockean sense, because the mind does not observe the self as it observes a thought. The self is present in every thought, and the idea of the self is an innate idea that reflection makes explicit.

This leads to a central disagreement. Locke thinks that the mind is a blank slate that acquires all ideas through experience, including the idea of the self. Leibniz thinks that the self is the condition of experience, not its product. “It is the soul itself that has the idea of substance, of unity, of identity, and of duration; and these ideas are not given by the senses but are innate to the soul.” Reflection, for Leibniz, is not a second source of ideas alongside sensation; it is the process by which the soul becomes aware of what it already contains.

Book II, Chapter 7: Of Simple Ideas of Sensation and Reflection

Locke concludes his general discussion of simple ideas by noting that some are derived from both sensation and reflection. Pleasure and pain, for instance, accompany both sensory experiences and mental operations. Existence, unity, power, and succession are also ideas that arise from both sources. Philalethes reads: “Thus, the idea of existence is suggested to the understanding by every object without, and by every idea within; and the idea of succession comes from the observation of the train of our own ideas.”

Theophilus agrees that these ideas are common to both sources but argues that they are not derived from either in the strict sense. “I think that these ideas belong originally to the mind and are innate; they are awakened by occasions from without and from within, but they cannot be produced by those occasions.” The idea of existence, for instance, is not learned from seeing objects; it is the mind’s own concept that it applies to objects when it perceives them. The mind brings the idea of existence to experience; it does not extract it from experience.

The same is true for unity and power. These are not abstractions from particular cases but fundamental categories that the mind uses to organize experience. “The mind has the idea of unity from its own nature; it applies this idea to everything it perceives.” For Leibniz, the Lockean project of deriving all ideas from sensation and reflection is doomed to fail because the most basic concepts—existence, unity, identity, substance, cause—are not given by experience at all. They are the innate furniture of the mind, without which experience itself would be impossible.

Book II, Chapter 8: Some Further Considerations Concerning Our Simple Ideas of Sensation

This chapter contains Locke’s famous distinction between primary qualities and secondary qualities. Primary qualities—solidity, extension, figure, motion, rest, and number—are “utterly inseparable from the body, in what state soever it be.” Secondary qualities—colors, sounds, tastes, smells—are “nothing in the objects themselves but powers to produce various sensations in us.” Philalethes reads the passage: “Thus, the ideas of primary qualities are resemblances of the bodies they are in; but the ideas of secondary qualities are not.”

Theophilus finds this distinction useful but insufficiently grounded. “I think that the distinction between primary and secondary qualities is well taken, but I cannot agree that the ideas of primary qualities are resemblances of the bodies.” For Leibniz, even primary qualities such as extension and figure are not exactly as they appear. The mathematical properties of bodies are real, but the sensory ideas of those properties are not perfect copies. “The senses give us only confused perceptions of primary qualities, which reason must clarify.”

The deeper issue is the nature of body itself. Leibniz agrees with Locke that secondary qualities are subjective, but he argues that primary qualities are also, in a certain sense, appearances. “I believe that the true reality of bodies lies not in extension or figure alone, but in force.” The primary qualities as we perceive them are the phenomenal expression of underlying forces that we cannot sense directly. The Lockean distinction, while correct as a theory of perception, does not reach the metaphysical ground. The monad is the true substance; all qualities, primary and secondary, are its perceptual expressions.

Book II, Chapter 9: Of Perception

Locke defines perception as “the first operation of all our intellectual faculties, and the inlet of all knowledge into our minds.” Perception is the mind’s reception of ideas through the senses, and it is the foundation of all thinking. Philalethes reads: “What perception is, everyone knows better than he can be told by any words.”

Theophilus again introduces the crucial distinction between perception and apperception. “I ought to warn you that I distinguish between perception and apperception. Perception is the internal state of the monad that represents external things; apperception is the conscious awareness of that internal state.” Locke conflates the two, assuming that all perception is conscious. Leibniz insists that most perceptions are unconscious—they are too small and too numerous to be individually noticed. The soul is always perceiving, but it is not always aware of its perceptions.

This distinction is central to Leibniz’s entire system. It allows him to explain how the soul can have innate ideas without being consciously aware of them at birth. The innate ideas are dispositions or virtual perceptions that become actual when the mind attends to them. “Thus, it is not necessary that the soul always thinks with explicit attention; it is enough that it always has perceptions, even when it is not aware of them.” The Lockean model, which requires all ideas to be consciously perceived at the moment they enter the mind, cannot account for the continuity of mental life or for the existence of knowledge that is not presently being thought.

Book II, Chapter 10: Of Retention

We are now in Book II, Chapter 10, where Locke turns from the acquisition of simple ideas through sensation and reflection to the mind’s capacity to retain them over time.

Locke divides retention into two faculties: contemplation, which keeps an idea actually in view for a short period, and memory, which revives ideas that have been absent from the mind. Memory is “the power to revive again in the mind those ideas which, after imprinting, have disappeared, or have been laid aside out of sight.” For Locke, memory is essential to all thinking that extends beyond the present moment; without it, there could be no knowledge, no reflection, and no personal identity. He describes the ideas stored in memory as being “laid up in the repository of the mind,” and notes that some ideas are readily recalled while others require effort or are lost entirely. The forgetfulness of ideas is explained by natural decay, by the crowding out of new impressions, or by simple disuse. Locke further observes that ideas that are “often refreshed” by repetition or that are accompanied by pleasure or pain are retained most firmly.

Leibniz seizes on this chapter to press his objection against the tabular rasa model. If ideas are merely imprinted on the mind from outside, and if memory is simply the revival of those imprints, then what accounts for the active capacity to recall them? He argues that memory is not a passive storage bin but an expression of the soul’s own dispositions. “I believe that memory is not a mere vestige, like an impression that remains after the image has passed; it is rather that the soul itself, in its perfections, expresses all that has happened to it.” For Leibniz, the “repository” metaphor is misleading because it suggests that ideas are independently existing entities housed in the mind. Instead, every perception leaves a trace in the soul’s own nature — a tendency or disposition to produce that perception again under the right circumstances. This is why, he argues, we can recall things we were never consciously aware of at the time of their occurrence, such as when we remember something that was only peripherally noticed. The soul does not receive ideas from without; it unfolds its own perceptions in response to the world, and memory is the continuity of this unfolding.

This distinction matters because it reframes the entire question of innateness. If memory is a dispositional property of the soul, then the difference between an innate idea and an acquired memory is one of degree, not kind. Both are expressions of the soul’s own nature. The Lockean model, by contrast, must treat memory as a purely mechanical storehouse of impressions from the outside. Leibniz observes that if we take Locke at his word, it becomes impossible to explain how the mind can actively search its own memory — how it knows what it is looking for before it finds it. “For the mind must already have some notion of what it seeks, in order to recognize it when it appears.” This, for Leibniz, points directly to the innate structure of the understanding: the mind does not merely receive and retain; it actively produces its own contents from its own ground.

Book II, Chapter 11: Of Discerning, and Other Operations of the Mind

This chapter moves from retention to the active operations of the mind, where Locke discusses discernment, comparison, composition, and abstraction — the faculties that transform simple ideas into complex ones.

Locke begins with discernment, which he defines as the mind’s ability to perceive the difference between its ideas. Without this, all ideas would be indistinguishable and thought itself would be impossible. He then presents comparison as the faculty of relating ideas to one another, composition as the joining of simple ideas into complex ones, and enlarging and abstraction as the means by which general ideas are formed. Abstraction, for Locke, is the highest operation of the understanding: it is the process by which the mind takes particular ideas, separates them from their accompanying circumstances (time, place, individual details), and forms general ideas that can stand for many particular things. “Thus the same colour being observed to-day in chalk or snow, which the mind yesterday received from milk, it considers that appearance alone, makes it a representative of all of that kind; and having given it the name whiteness, it by that sound signifies the same quality wheresoever to be imagined or met with.” This power of abstraction, Locke argues, is what distinguishes humans from brutes, who may have ideas but cannot form general ones.

Leibniz challenges Locke’s account of abstraction at a fundamental level. For Locke, abstraction is a process that the mind performs on ideas it has already received from sensation and reflection. For Leibniz, this cannot be the whole story, because abstraction presupposes the very general concepts it is supposed to produce. “I think that the mind is capable of abstraction not because it strips away particular circumstances from a particular idea, but because it has within itself the general concepts that allow it to recognize what is common to many individuals.” Leibniz insists that general ideas like substance, unity, identity, and cause cannot be derived from particular sensations by stripping away details; they must be innate to the understanding itself. Even the concept of whiteness, which Locke uses as his example, requires a prior notion of likeness — the ability to recognize that two different objects share a quality. That recognition, for Leibniz, is not itself derived from sensation; it is an operation of the intellect upon sensation.

This section is crucial because it marks the deepest division between Leibniz and Locke on the nature of the mind. Locke’s model is empiricist through and through: all content comes from experience, and the mind’s operations are simply ways of rearranging that content. Leibniz’s model is rationalist: the mind contributes its own formal structures — categories of thought, principles of reasoning, notions of being and unity — without which experience itself would be incoherent. The Lockean mind is a blank page on which experience writes; the Leibnizian mind is a living fire that brings its own light to what it encounters. The disagreement is not about whether abstraction occurs, but about what makes it possible.

Book II, Chapter 12: Of Complex Ideas

Locke here formally introduces the category of complex ideas, which the mind forms by combining, comparing, and abstracting from simple ideas. This chapter is taxonomic: Locke divides complex ideas into three kinds: modes, substances, and relations.

Modes are complex ideas that do not contain the notion of subsisting by themselves; they are dependent on substances, such as triangle, gratitude, or murder. Substances are ideas of things that subsist by themselves — such as man, horse, or gold — and are taken to represent real, independent beings. Relations are ideas that arise from comparing one idea with another, such as father, larger, or cause. Locke explains that simple ideas are the materials of all knowledge, and that complex ideas are the products of the mind’s own activity upon those materials. He gives the example of the idea of beauty: it is a mode composed of the simple ideas of colour, order, and figure, arranged in a pleasing combination. “Thus the ideas which are the objects of our understanding, when we think of a man, of a centaur, of a crime, of a feast, are all complex ideas.”

Leibniz’s response to this chapter is not one of outright rejection but of critical refinement. He accepts Locke’s distinction between simple and complex ideas but denies that simple ideas are genuinely simple in the way Locke imagines. For Leibniz, every idea — even the simplest sensory quality — contains an infinity of perceptions that are not consciously noticed. “What appears simple to the senses is not for all that simple for the understanding; the idea of blue, for instance, is simple only in appearance, because we do not perceive the subtle motions and configurations that produce it.” Furthermore, Leibniz argues that the category of substance cannot be derived from experience alone. When the mind forms the idea of a substance — say, a horse — it is not merely combining the simple ideas of shape, colour, movement, and sound. It is positing a subject in which those qualities inhere, and that subject is not itself an object of sensation. “The idea of substance is one of those innate ideas that the mind must already possess in order to unite the simple ideas under a common subject.”

This analysis reveals a fundamental asymmetry. Locke treats complex ideas as combinations of simple ones, built up from sensory atoms. Leibniz treats them as expressions of deeper realities, in which the unified subject — the substance — is the real thing, and the sensible qualities are its manifestations. For Leibniz, the mind does not build up the idea of substance by adding together qualities; rather, it already possesses the notion of substance as a category and applies it to the perceived qualities to make sense of them. The Lockean approach, he argues, puts the cart before the horse: one cannot construct the idea of a substance from qualities that have no substance to inhere in.

Book II, Chapter 13: Of Simple Modes of Space — and Chapters 14–15: Duration and Expansion

Locke now turns to the simple modes of space (Chapter 13), duration (Chapter 14), and their comparison in expansion and duration (Chapter 15). These chapters form the core of Locke’s account of the fundamental frameworks of experience — where and when things are.

Locke derives the idea of space from the senses of sight and touch. By perceiving bodies at a distance, and by moving one’s own body through intervals, the mind acquires the simple idea of space — which, when considered as extended in three dimensions, gives expansion. Duration, by contrast, comes from reflection on the train of ideas passing through the mind; by noticing that one idea follows another, we acquire the idea of succession, which yields duration. Locke emphasizes that space and duration are distinct: space is about coexistence and order of positions, while duration is about succession and order of events. He introduces the concept of simple modes of space — such as inch, foot, mile — which are repeated units of the same simple idea. Similarly, the simple modes of duration — minute, hour, day, year — are repetitions of the idea of a fixed interval of time. For Locke, both space and time are relative notions: they depend on the perception of bodies and the succession of ideas.

Leibniz’s engagement with these chapters is among the most philosophically significant passages in the entire work, because it is here that he develops his own theory of space and time in opposition to Locke (and, implicitly, to Newton). He argues that space and time are not real entities in themselves, nor are they derived from sensation in the simple way Locke suggests. Rather, they are ideal — orders of relations among phenomena. “I hold space to be something merely relative, as time is; space being an order of coexistences, time an order of successions.” For Leibniz, space is not a container in which bodies exist; it is the set of relations of distance, position, and arrangement between coexisting bodies. Time is not a flowing river; it is the order of events considered as successive. This is the origin of the famous relational theory of space and time that Leibniz would later develop in his correspondence with Samuel Clarke.

Leibniz also challenges Locke’s derivation of duration from the train of ideas. If duration were merely the succession of perceptions, then a mind that fell asleep and had no perceptions would experience no duration — but the world itself would continue. “It must be admitted that even when we are not aware of any succession, there is still a real duration of things.” Leibniz posits that the soul always perceives, even in dreamless sleep (as argued in Book II, Chapter 1), and that this continuous perception grounds the continuity of time itself. For Leibniz, time is not dependent on the human mind’s noticing succession; it is a feature of the order of all things, and our perception of it is the expression of that order at the level of consciousness. This leads to a profound conclusion: space and time are not absolute realities but phenomena bene fundata (well-founded phenomena) — they express the relations of monads, the true substances of the universe.

Book II, Chapter 16: Of Number

We are now in Book II, where Leibniz follows Locke’s taxonomy of ideas, turning from the simple modes of space and duration to the simple mode of number, which Locke treats as the simplest and most universal of all ideas.

Locke presents number as the most precise and universal simple mode, accessible through sensation and reflection. He argues that the idea of number is acquired through the senses (by seeing or touching discrete objects) and that its simplest idea is that of unity or one. From this simple idea, the mind can repeat the idea of unity without ever arriving at a limit, thereby generating the infinite series of numbers. Locke states that number is “the most simple and most universal idea we have,” for it applies to everything, whether material or immaterial. He emphasizes that the certainty of mathematical knowledge derives from the clarity and distinctness of the ideas of numbers, and that the mind can compare these ideas with complete precision.

Leibniz agrees with much of Locke’s account but presses further on the nature of unity and the foundation of arithmetic. He notes that the idea of number is not merely derived from the senses but is a pure intellectual idea rooted in the mind’s own capacity for reflection. “Number is, as it were, an immaterial figure, and it is the most universal instrument of the understanding.” Leibniz argues that the idea of unity is not a simple idea derived from sensation alone; it is an idea we already possess in the understanding, which we apply to things we perceive. He points out that although we can count sensible objects, the number itself—the abstract relation—is an object of the intellect, not of the senses. The mind, by reflecting on its own operations of combining and repeating, discovers the formal properties of number. Leibniz also stresses that unity is the simplest and most fundamental concept, for every being is one being, and the concept of number presupposes this primitive idea. He adds that arithmetic, like geometry, is an eternal truth grounded in the divine understanding, not merely a product of human mental operations.

Leibniz’s refinement matters because it reinforces his distinction between truths of fact (derived from experience) and truths of reason (derived from the understanding). By placing number in the realm of intellectual ideas, he secures the necessity and universality of arithmetic against a purely empirical account. For Leibniz, the certainty of mathematics is not a human construction but a reflection of the divine order of all possible worlds.

Book II, Chapter 17: Of Infinity

The chapter on infinity is a major philosophical battleground. Locke argues that the idea of infinity is a negative idea—a product of the mind’s ability to endlessly add units—while Leibniz defends the reality of the infinite as a positive concept accessible to the understanding.

Locke’s account of infinity is deeply empiricist. He claims that we have no positive idea of infinity; instead, we derive the idea from the endless repetition of finite ideas, particularly number and duration. The mind, observing its own capacity to add one unit to another without limit, forms the idea of “infinite”—which is merely the negation of an end. “Infinity, in its true meaning, is a negative idea: it is the negation of an end.” Locke argues that we cannot comprehend the infinite because our finite minds cannot grasp an endless series as a whole. He distinguishes between the idea of “endless addition” (which we can conceive) and the idea of “an infinite whole” (which we cannot). For Locke, any attempt to think of infinite space or infinite duration as a positive idea leads to confusion, for we have no experience of such a thing.

Leibniz responds forcefully, arguing that the infinite is not merely negative and that the understanding can indeed grasp it, albeit imperfectly. He asserts that “we have a positive idea of the infinite, though not a comprehensive one.” The infinite is not simply the denial of a limit; it is a property of the absolute, of God, and of the ideal order of things. Leibniz points out that in mathematics, we can reason about infinite series and infinite quantities with perfect precision—this would be impossible if the idea were merely negative. “We conceive the infinite in arithmetic and geometry, and we demonstrate truths concerning it, which shows that we have an idea of it.” He distinguishes between the syncategorematic infinite (the endless series we can always continue) and the categorematic infinite (the actually infinite whole), and argues that while we cannot have a complete sensory representation of the infinite, the intellect has a clear notion of it. Leibniz also criticizes Locke’s claim that we can only conceive the infinite through addition; he notes that we can also conceive it through division, as matter is actually divided into infinitely many parts.

Leibniz’s intervention highlights a deep difference in their epistemologies. For Locke, all ideas are ultimately derived from sensation and reflection, and the infinite is merely a shadow cast by our finite operations. For Leibniz, the infinite is a positive feature of reality, and the human mind—as a mirror of the divine intellect—has the capacity to grasp it intellectually, even if not exhaustively. The infinite is not a failure of the mind but a sign of its participation in a higher order of truth.

Book II, Chapter 18: Of Other Simple Modes

Locke turns to other simple modes beyond space, duration, and number, including modes of thinking, motion, power, and qualities like trust and distrust. This chapter is shorter but continues the pattern of cataloging how the mind combines simple ideas into more complex structures.

Locke lists several categories of simple modes derived from reflection: the modes of thinking (such as attention, reverie, study, and reasoning); the modes of motion (such as sliding, rolling, walking, and running); and the modes of power (which he will treat extensively in the following chapter). He also includes modes of trust and distrust, and modes of doubt and assent. Locke emphasizes that these modes are all built from simple ideas that the mind can vary and combine without limit. For example, the idea of “attention” is a mode of thinking where the mind fixes on a particular object, while “reverie” is a mode where ideas float without direction. None of these modes introduce new simple ideas; they are only different configurations of the mind’s own operations.

Leibniz offers brief comments, mostly in agreement but with characteristic precision. He notes that the modes of thinking are not simply combinations of simple ideas but are grounded in the nature of the apperception—the mind’s awareness of its own perceptions. He points out that many of these modes, such as “doubt” and “assent,” involve degrees of judgment and not mere association of ideas. Leibniz also remarks that the modes of motion are not merely empirical classifications but can be understood geometrically, as variations of direction and speed. He adds that the modes of power (which Locke will treat in the next chapter) are central to understanding substance and causality, and that he will have much more to say on this subject.

This chapter, while brief, sets the stage for the most important discussion in Book II: the idea of power, which for Locke is the foundation of our ideas of causality, substance, and will.

Book II, Chapter 21: Of Power (Part 1 — The Nature of Power and Liberty)

This is the longest and most important chapter in Locke’s *Essay*, and Leibniz’s responses are correspondingly extended and detailed. The chapter covers the idea of power, the nature of the will, and the concept of liberty or freedom.

Locke begins by establishing that the idea of power is derived from sensation and reflection. We observe changes in external objects (one ball moving another) and in ourselves (our ability to move our bodies or direct our thoughts). From these experiences, we form the idea of power—the capacity to produce or receive change. Locke distinguishes between active power (the ability to produce change) and passive power (the capacity to receive change). He argues that we get the clearest idea of active power from our own minds, particularly in the power of the will to command our thoughts and bodily motions. The will is the power of the mind to direct its own operations, and volition is the actual act of willing. Liberty is the power to do or not do something according to one’s will; it is not the will itself but a property of the agent. Locke famously argues that the will is determined by uneasiness—a state of discomfort caused by the absence of some good. The mind seeks to remove this uneasiness, which drives volition and action. “The motive to change is always some uneasiness: the greatest present uneasiness is the spur that determines the will.”

Leibniz launches a sustained critique of Locke’s account of the will and liberty. He begins by distinguishing the will from mere appetition. For Leibniz, the will is not simply a response to uneasiness; it is the inclination to act in accordance with reason. He writes: “The will is the endeavor to act in accordance with the representation of the good.” Leibniz argues that Locke’s “uneasiness” is too passive and sensory a concept; true volition involves the perception of reasons, not merely the pressure of discomfort. He also rejects Locke’s claim that liberty is the power to do otherwise given the same circumstances. Leibniz holds that the will is always determined by the strongest reason—the perceived good that appears most advantageous to the understanding. “The will is never indifferent; it always follows the last judgment of the understanding.” However, Leibniz insists that this determination is not coercion; it is a form of spontaneity, because the agent acts according to its own nature and its own understanding of the good. Liberty, for Leibniz, consists in acting according to reason, not in an impossible capacity to choose without motives.

Leibniz and Locke thus disagree on the mechanism of volition. Locke sees the will as pushed by uneasiness; Leibniz sees it as pulled by the representation of the good. This difference reflects deeper metaphysical commitments: Locke’s empiricism leads him to emphasize sensory discomfort, while Leibniz’s rationalism leads him to emphasize intellectual judgment. Leibniz also introduces a crucial distinction between contingent and necessary determination. The will is determined by reasons, but these reasons do not necessitate with absolute necessity; they incline without compelling. This allows Leibniz to defend freedom of the will while acknowledging that every choice is made for a reason.

Book II, Chapter 21: Of Power (Part 2 — Liberty, Necessity, and the Divine Will)

Leibniz continues his engagement with Locke’s account of power, moving from human freedom to the nature of the divine will and the problem of necessity.

Locke applies his analysis of liberty to the divine will, arguing that God, being supremely perfect, necessarily does what is best. However, Locke maintains that this necessity is not incompatible with freedom, because God acts according to His own nature—He is not compelled by any external force. “It is the highest perfection of a rational agent to be determined by the best.” Locke also discusses the freedom of the mind in relation to judgments of understanding: we are not free to believe or disbelieve at will, because belief is determined by the perceived evidence. He distinguishes between voluntary actions (which depend on the will) and involuntary judgments (which depend on the understanding). The mind, for Locke, has no direct power to command belief; it can only direct its attention to evidence, and then the judgment follows necessarily.

Leibniz agrees with much of Locke’s account of divine freedom but adds important refinements. He argues that God’s will is perfectly free because it is determined by the best, and the perception of the best is the highest expression of reason. “The more perfect the being, the more determined it is to the best.” Leibniz also rejects any notion of indifference in God’s will; God does not choose arbitrarily but according to His infinite wisdom. For Leibniz, this is the foundation of theodicy: the world is the best of all possible worlds because God’s will is determined by the perfection of the universe He creates. Regarding human freedom, Leibniz argues that our judgments are not forced upon us by evidence in the same way Locke suggests. The understanding can be influenced by the will itself—by directing attention, by weighing reasons, by considering consequences. This interplay between will and understanding is crucial for Leibniz’s account of moral responsibility: we are responsible for our choices because we could have deliberated differently.

The debate over power, will, and liberty is the philosophical heart of the *New Essays*. For Locke, freedom is essentially the absence of external constraint; for Leibniz, it is the positive capacity to act according to reason. Leibniz’s account preserves the necessity of divine providence while maintaining human responsibility—a delicate balance that he defends throughout the rest of the work.

Book II, Chapters 22–24: Of Mixed Modes, of the Relations of Modes, and of Collective Ideas of Substances

These chapters continue Locke’s classification of complex ideas, examining mixed modes (combinations of simple ideas from different sources) and collective ideas (like an army or a flock). Locke also begins to discuss relations, particularly causality and identity.

Locke defines mixed modes as complex ideas composed of simple ideas from both sensation and reflection. For example, the idea of “gratitude” combines the idea of a benefit received with the idea of an intention to repay it. These modes are often conventional and vary across languages and cultures. Locke argues that mixed modes are voluntary combinations—the mind chooses which simple ideas to put together and gives the combination a name. He then turns to relations, which arise when the mind compares one idea with another. The most important relation is causality, which links cause and effect. Locke argues that the idea of cause is derived from observing that one thing regularly produces a change in another. The relation of identity is also crucial: the identity of a substance consists in the same continuation of existence (for a living being, the same life).

Leibniz makes several significant contributions to these chapters. He agrees that mixed modes are often arbitrary but insists that some combinations are natural, grounded in the real relations of ideas. “There are natural combinations that are more perfect than others, and these are the ones that correspond to true definitions.” On causality, Leibniz argues that the relation between cause and effect is not merely observed but is grounded in the nature of substance and the principle of sufficient reason. Every effect must have a reason, and that reason must be found in the nature of the cause. He also refines Locke’s account of identity: the identity of a substance is not merely the continuation of existence but the continuity of a single indivisible substance—a monad—which remains the same throughout all changes. Leibniz draws a sharp distinction between the identity of a living organism (which has a soul) and the identity of a machine (which is only a collection of parts). For Leibniz, personal identity is rooted in the self-consciousness of the rational soul, not merely in memory or bodily continuity.

Leibniz’s refinements deepen the metaphysical foundations of Locke’s empirical categories. The world is not a collection of arbitrary constructions; it is a unified system of substances whose relations are determined by their natures.

Book II, Chapter 25: Of Relation

Locke now systematically treats the nature of relation itself, defining it as the comparison of one idea with another. Relation, for Locke, is not a property of things but a mental act of comparison. However, he acknowledges that some relations are founded on real qualities in things.

Locke defines relation as “the comparing of one idea with another.” He distinguishes between natural relations (such as father-son, which are grounded in real facts) and instituted relations (such as citizen, which are established by human convention). Locke notes that all relations ultimately depend on simple ideas: the relation of “causality” depends on the ideas of cause and effect; the relation of “identity” depends on the idea of the same substance existing over time. He argues that the mind is active in forming relations, and that the same thing can stand in many different relations simultaneously. Relation is not a real being but a comparison—the mind adds it to the things compared. “Relation is not contained in the real existence of things, but is something external and superadded.”

Leibniz offers a subtle critique. He agrees that relation involves a mental act of comparison, but he insists that relations are not merely subjective constructions. “Relations are real, though they are not substances. They are founded in the modifications of things.” For Leibniz, every relation has a foundation in the properties of the things related. The relation between father and son, for example, is grounded in the real act of generation. Leibniz distinguishes between internal relations (which hold between the properties of a single substance) and external relations (which hold between distinct substances). He argues that in a universe of monads, every relation is ultimately internal—each monad expresses the whole universe from its own point of view, so all relations are implied in the nature of each substance. This is Leibniz’s principle of expression: every substance expresses all others, so relations are not added from outside but are discovered in the nature of things.

Leibniz’s account of relation is a natural extension of his monadology. If all substances are self-contained but express the entire universe, then relations are not arbitrary additions but discoveries of the rational order inherent in creation.

Book II, Chapters 26–28: Of Cause and Effect, of Identity and Diversity, and of Other Relations

Locke continues to develop his account of relations, focusing on the three most fundamental: cause and effect, identity and diversity, and moral relations (including law and obligation).

Locke defines cause and effect in empirical terms: “That which produces any simple or complex idea, we denote by the general name cause; and that which is produced, effect.” He emphasizes that we observe constant conjunction, not necessary connection. For Locke, the idea of power is the foundation of causality, but we have no insight into the necessary connection between cause and effect. On identity, Locke distinguishes the identity of a substance (which depends on its continued existence), the identity of a living being (which depends on the same life), and the identity of a person (which depends on consciousness). Personal identity, for Locke, is a forensic concept—it is the foundation of moral responsibility. A person is the same as long as consciousness can reach back to past actions. When consciousness is interrupted (as in sleep or amnesia), the person is not strictly identical. Diversity is simply the absence of identity—two things are diverse when they occupy different times and places.

Leibniz responds with a comprehensive critique of Locke’s theory of personal identity. He agrees that personal identity is based on consciousness, but he insists that it also requires a substantial foundation. “If personal identity consisted merely in memory, then if a man lost all memory, he would not be the same person.” Leibniz argues that the soul is a simple substance (a monad) that remains the same throughout all changes, and this substantial identity grounds personal identity. Memory and consciousness are signs of identity, but they do not constitute it. A person who loses all memory is still the same person because the same soul is present. Leibniz also criticizes Locke’s account of causality: “The idea of power is not derived solely from our observation of constant conjunction; we also have an intellectual idea of efficient causality as the production of one thing by another.” This intellectual idea is innate, not derived from experience. On moral relations, Leibniz argues that law and obligation are grounded in the eternal truths of reason, not merely in human convention or divine command. The moral law is written into the nature of rational souls as a reflection of divine wisdom.

Leibniz’s account of personal identity is more metaphysical than Locke’s, but it avoids the paradoxes that arise from Locke’s purely psychological criterion. For Leibniz, the continuity of the soul guarantees the continuity of the person—a view that aligns with his commitment to the immortality of the soul and the rationality of moral order.

Book II, Chapter 29: Of Clear and Obscure, Distinct and Confused Ideas

Locke turns to the quality of ideas themselves, distinguishing between clear and obscure, distinct and confused ideas. This is an epistemological chapter that lays the groundwork for Book IV’s discussion of knowledge.

Locke defines a clear idea as one that the mind perceives with vividness and immediate awareness, while an obscure idea is faint and indistinct. A distinct idea is one in which the mind can perceive the differences that separate it from all other ideas; a confused idea is one that cannot be separated from others with certainty. Locke takes as an example the idea of a color: we can have a clear idea of red, but it may be confused with orange if we cannot distinguish the precise boundary between them. The causes of obscure and confused ideas include lack of attention, poor sensory organs, or the use of vague language. Locke stresses that the clearness and distinctness of ideas is essential for knowledge: if our ideas are vague, our knowledge will be uncertain. He also observes that many of our ideas of substances are relatively obscure and confused because we do not know the real essences of things.

Leibniz refines Locke’s distinction, drawing on the Cartesian tradition. He agrees that clear and distinct ideas are essential for knowledge but argues that most of our ideas of sensible qualities are confused in the sense that they contain a multitude of minute perceptions that we cannot discriminate. “Our idea of color, for instance, is clear but not distinct. We can recognize it when we see it, but we cannot analyze it into its components.” Leibniz introduces the concept of symbolic knowledge—knowledge we have through signs and words, even when we do not have a clear intuitive grasp of the thing itself. For example, we have a distinct idea of a chiliagon (a thousand-sided figure) through mathematical definition, even though we cannot form a clear sensory image of it. Leibniz also stresses that confused ideas are not necessarily defective; they are the way the mind perceives complex realities that it cannot fully analyze. The perception of a single color is a confused perception of many minute vibrations, but it is still a clear perception for the purposes of daily life. “Nature has given us confused ideas for practical purposes, and distinct ideas for the purposes of reason.”

Leibniz thus offers a more nuanced account: clearness and distinctness belong to the intellectual order, not merely the sensory one. Our ideas can be clear in sensation but confused in understanding; they can be distinct in definition but obscure in intuition. The goal of philosophy is to transform our confused perceptions into distinct intellectual knowledge, but this is an infinite task.

Book II, Chapter 30: Of Real and Fantastical Ideas, Chapter 31: Of Adequate and Inadequate Ideas, Chapter 32: Of True and False Ideas

These three chapters complete Locke’s taxonomy of ideas, examining the correspondence between ideas and reality, the completeness of ideas, and the truth of ideas.

Locke distinguishes real ideas (which have a foundation in nature) from fantastical ideas (which are products of the mind’s own invention without any basis in reality). The idea of a golden mountain, for example, is fantastical because no such thing exists. Adequate ideas are those that perfectly represent the archetype they are taken from; inadequate ideas are partial or incomplete representations. Locke argues that our ideas of modes (like numbers) can be adequate because the mind itself creates their archetypes, but our ideas of substances are always inadequate because we do not know their real essences. True ideas are those that are conformable to their archetypes; false ideas are those that the mind wrongly takes to represent something they do not. For instance, the idea of a centaur is not false in itself (it is a real combination of ideas), but it is false if taken to represent an actual animal.

Leibniz engages with each distinction carefully. He agrees that ideas of substances are inadequate but argues that God has adequate ideas of everything. “The human understanding is finite; only God has a perfect knowledge of all things.” For Leibniz, an adequate idea is one in which all the constituent notions are themselves understood clearly and distinctly—a state we can approach in mathematics but rarely achieve in physics. On truth and falsity of ideas, Leibniz argues that an idea is true if it is possible—if it does not involve a contradiction. The idea of a centaur is true in this sense because a centaur is a possible being, even if it does not actually exist. The idea of a round square, however, is false because it is impossible. Leibniz thus introduces the crucial distinction between actual existence and logical possibility: an idea can be real even if it has no actual object, as long as it is logically consistent.

Leibniz’s refinement grounds his metaphysics of possibility. The realm of possible worlds is the realm of all consistent ideas in the divine understanding. Our finite minds can grasp some of these possibilities, and this capacity is the foundation of our knowledge of necessary truths.

Book III: Of Words — Chapter 1: Of Words or Language in General

Book III marks a shift from ideas to language. Locke argues that words are the signs of ideas, and that language is the primary tool for communicating thoughts. This is a crucial transition, for Locke believes that many philosophical confusions arise from the misuse of language.

Locke begins by observing that man is naturally capable of articulating sounds, but language requires the ability to use sounds as signs of internal ideas. These signs are arbitrary: there is no natural connection between the word and the idea it signifies—only a voluntary imposition. Words are sensible marks that the mind uses to communicate its thoughts to others and to record its own ideas for later use. Locke emphasizes that words are immediately the signs of the speaker’s ideas, not of things in the world. When I say “horse,” I refer to the idea in my own mind, not directly to the animal. Communication is possible because people generally have similar ideas associated with the same words, but the connection between word and idea is conventional and can be learned.

Leibniz agrees with the arbitrary nature of words but adds that language is not entirely arbitrary. “There is a natural relation between sounds and the ideas they signify, though this relation is often obscure.” He points to onomatopoeia and the symbolic power of certain sounds as evidence of a non-arbitrary element. Leibniz also argues that language is not merely a tool for communication but an instrument of thought itself. The structure of language reflects the structure of the mind; learning a language is, in part, learning to think in certain patterns. He introduces the concept of a characteristic language—an ideal philosophical language in which every symbol would correspond to a simple idea, making reasoning as certain as calculation. This is a vision that Leibniz developed throughout his life and that connects to his work on the calculus and symbolic logic.

Locke’s account of language is practical and conventional; Leibniz’s is systematic and ideal. The debate anticipates later work in the philosophy of language, including the relationship between language, thought, and reality.

Book III, Chapters 2–3: Of the Signification of Words, and Of General Terms

Locke continues his analysis of language, focusing on general terms—words that signify general ideas (universals). He argues that most words in language are general, not proper names, and that the formation of general ideas is essential for knowledge and communication.

Locke argues that general terms are indispensable because the mind cannot have a distinct idea of every individual thing. To manage the multiplicity of experience, the mind forms abstract general ideas by leaving out the particular circumstances of individual things. For example, the general idea of “man” is formed by abstracting from particular men their common features (shape, reason, etc.) while ignoring their individual differences (height, weight, name). These general ideas are then signified by general terms. Locke stresses that universals are not real entities existing in the world; they are creatures of the understanding—mental constructs that we impose on the world for convenience. “Universality belongs not to things themselves, but to signs.” The nominal essence of a species is the abstract idea signified by the general term; the real essence is the unknown internal constitution of things on which their properties depend.

Leibniz agrees with much of Locke’s account of abstraction but challenges the claim that universals are purely mental constructs. “Universals are not mere names; they have a foundation in the nature of things.” He argues that the mind does not arbitrarily create general ideas; it discovers real similarities between things—resemblances that exist in the things themselves, not merely in the mind. These similarities are grounded in the essences of substances, which are possibilities in the divine understanding. Leibniz introduces the distinction between nominal definitions (which describe the properties by which we recognize a thing) and real definitions (which reveal the inner nature or essence). In mathematics, we often have real definitions; in natural philosophy (physics), we usually have only nominal definitions. The task of science is to move from nominal to real definitions by discovering the inner natures of substances.

Leibniz’s realism about universals reflects his commitment to a universe of natural kinds—types of substances that have genuine essences, even if we do not know them fully. For Locke, the species boundaries are human constructions; for Leibniz, they are discovered.

Book III, Chapters 4–5: Of the Names of Simple Ideas and of Mixed Modes

Locke now applies his general theory of language to specific kinds of ideas: simple ideas (like sweet, white, pain) and mixed modes (like gratitude, theft, murder). He argues that the names of simple ideas are the least ambiguous, while the names of mixed modes are the most variable.

Locke notes that names of simple ideas are the most difficult to define because they refer to immediate sensations that cannot be analyzed into simpler components. You cannot define “sweet” to someone who has never tasted sugar; you must point to an instance. These names are indefinable and are learned by direct experience. The names of mixed modes, by contrast, can be precisely defined, because the mind itself creates the combination of ideas that the word signifies. For example, the idea of “theft” is a combination of taking something, without consent, with the intention of depriving the owner of it. This definition can be learned without experience. However, the names of mixed modes are volatile—they vary across languages and cultures because different societies make different combinations. Locke emphasizes that the meaning of a mixed mode is instituted by the mind, not given by nature.

Leibniz largely agrees but adds a rationalist note: the best definitions of mixed modes (especially moral concepts) are not arbitrary but are grounded in eternal truths of reason. The definition of “justice” is not a cultural convention; it is a relation of ideas that can be discovered by reason. Leibniz also argues that the names of simple ideas are not entirely indefinable. A color like red can be defined in terms of the vibration of light, though this is a scientific definition that goes beyond ordinary language. For Leibniz, every idea, even a simple one, has a real definition in terms of its causes or constituents, even if we do not know it. The progress of science is the gradual discovery of these real definitions.

This chapter thus connects language to the deeper issue of definition—a theme that runs throughout the *New Essays*. For Locke, definitions are nominal and conventional; for Leibniz, they are discoveries of real structures.

Book III, Chapters 6–7: Of the Names of Substances and Of Particles

Locke turns to the names of substances (gold, horse, man) and the function of particles (and, but, not, if) in language. The names of substances are the most difficult to define because they must capture both the nominal essence and (ideally) the real essence.

Locke argues that the names of substances are tied to nominal essences—the collections of observable qualities that we combine into a general idea. The word “gold” signifies the idea of a yellow, malleable, fusible, heavy body. This is all we can know of gold through our senses. The real essence of gold—the internal constitution of its parts that produces those qualities—is unknown to us. As a result, definitions of substances are always incomplete and subject to revision. If we discover a new quality (such as ductility) that belongs to gold, we may add it to the nominal essence, but we can never be certain that we have captured the real essence. Locke also discusses particles, which are words that connect ideas and indicate relations between them. They are, in his view, the most abstract and difficult part of language.

Leibniz offers a profound critique of Locke’s nominalism about substances. He agrees that we do not know the real essences of bodies through the senses, but he argues that real essences are not unknowable in principle. “The real essence of a substance is its complete individual concept, which contains everything that will ever happen to it.” For Leibniz, every individual substance has a concept so complete that from it, a perfect intellect could deduce all its properties. Our finite minds cannot grasp these concepts fully, but we can approach them through reason. Leibniz also argues that the names of substances are not merely classifications based on observed qualities; they refer to the substantial forms that unite those qualities in a single subject. The word “gold” refers not merely to a collection of qualities but to the substance whose nature produces those qualities. Leibniz applies the same principle to organic bodies: a horse is not merely a shape plus a set of observable behaviors; it is a substance with a soul that organizes its body.

Leibniz’s deep point is that language about substances is not just about our ideas; it is about real beings with real natures. The task of philosophy is to move from nominal definitions to real ones, from appearances to essences.

Book III, Chapters 8–11: Of Abstract and Concrete Terms, Of the Imperfection of Words, and Of the Abuse of Words

Locke concludes Book III by diagnosing the sources of linguistic confusion. He argues that words are imperfect because they often fail to communicate clear ideas, and they are abused when used without clear meaning, for rhetorical effect, or to obscure ignorance.

Locke distinguishes abstract terms (whiteness, humanity) from concrete terms (white, human). Abstract terms are signs of abstract ideas—they are useful for reasoning but can become a source of confusion when they are reified (treated as real things). The imperfection of words arises from several causes: the ambiguity of words (many words have multiple meanings), the obscurity of ideas (the speaker’s own idea may be unclear), and the wrong connection between words and ideas (people often assume that where there is a word, there is a distinct idea). Locke lists the chief abuses of words: using words without clear ideas, using them inconsistently, using them as if they were the names of real essences, and using them for rhetorical deception. He recommends remedies: define your terms, use words consistently, and avoid obscure jargon.

Leibniz agrees with the practical advice but offers a deeper diagnosis: the abuse of words is ultimately a failure of reason. He argues that philosophical confusion arises not merely from sloppy language but from a failure to analyze ideas into their simple components. “If we could reduce all ideas to their simplest elements, and represent them by a characteristic language, all disputes would end.” Leibniz admits that this is an ideal that may never be fully realized, but it is a regulative principle for philosophical inquiry. He also criticizes Locke’s claim that abstract terms are particularly dangerous; on the contrary, abstract ideas are essential for necessary truths—truths that hold for all possible instances, not just observed ones. The remedy for linguistic confusion is not to avoid abstraction but to ensure that our abstractions are grounded in clear and distinct ideas.

Book III ends with a sense that language is both a tool and a trap. For Locke, the solution is practical discipline; for Leibniz, it is the construction of an ideal language. Both agree, however, that the critique of language is essential for the progress of knowledge—a theme that will be explored fully in Book IV.

Book IV: Of Knowledge and Opinion — Chapter 1: Of Knowledge in General

Book IV is the culmination of the *Essay*. Locke finally defines knowledge and distinguishes it from judgment and probability. This chapter sets the foundation for everything that follows.

Locke defines knowledge as “the perception of the agreement or disagreement of our ideas.” Knowledge is not the perception of things-in-themselves; it is the perception of relations between our ideas. Locke distinguishes four kinds of agreement or disagreement: identity or diversity (that red is not blue), relation (the comparison of two or more ideas, as in mathematics), coexistence (that gold is malleable), and real existence (that something actually exists). Knowledge is thus a relational affair: it connects ideas within the mind, not the mind directly to the world. Locke also distinguishes actual knowledge (the immediate perception of agreement) from habitual knowledge (stored in memory, ready to be recalled). He admits that our knowledge is limited: we know the agreement of our own ideas with certainty, but we cannot be certain that our ideas correspond to external things except in the case of intuitive and demonstrative knowledge.

Leibniz carefully examines Locke’s definition of knowledge. He agrees that knowledge is of the agreement or disagreement of ideas, but he insists that this agreement is grounded in real relations between things, not merely in mental comparison. “The agreement of ideas is not arbitrary; it reflects the order of the universe.” Leibniz also argues that Locke’s four categories of agreement are not exhaustive. There is also the agreement of necessary connection—the relation between a cause and its effect, or between a premise and its conclusion—which is not captured by simple identity or relation. Leibniz introduces the concept of virtual knowledge: knowledge that is implicit in our perceptions but not consciously recognized. For example, when we perceive a color, we implicitly perceive a multitude of minute vibrations, though we do not know them consciously. True knowledge is the explication of these implicit perceptions. Leibniz concludes that knowledge is not a static state but an activity—the progressive unfolding of the mind’s innate ideas.

This chapter is the hinge of the *New Essays*. Locke’s definition of knowledge as the perception of relations between ideas sets the stage for his treatment of the degrees of knowledge (intuition, demonstration, and sensation) and the limits of human understanding. Leibniz’s response deepens the concept of knowledge, making it a dynamic and rational process.

Book IV, Chapter 2: Of the Degrees of Our Knowledge

Locke now distinguishes three degrees of knowledge: intuitive, demonstrative, and sensitive. These degrees differ in the certainty and immediacy with which the mind perceives the agreement or disagreement of ideas.

Intuitive knowledge is the highest degree. It occurs when the mind perceives the agreement or disagreement of two ideas directly, without any intervening ideas. For example, we see immediately that white is not black, or that a circle is not a triangle. Intuitive knowledge is irresistible, certain, and immediate. Demonstrative knowledge occurs when the mind must use intervening ideas (proofs) to perceive the agreement or disagreement. This is the knowledge of mathematics and logic: we follow a chain of reasoning step by step until we reach the conclusion. Each step in the demonstration must be intuitive, or the whole chain collapses. Demonstrative knowledge is as certain as intuitive knowledge, but it is harder to achieve and more prone to error. Sensitive knowledge is the lowest degree. It is the knowledge of the existence of particular external objects through sensation. Locke admits that sensitive knowledge is less certain than intuition or demonstration, but he insists that it deserves the name “knowledge” because it carries a strong degree of probability—enough to guide action. “The certainty of things beyond our senses is not so great as that of intuitive and demonstrative knowledge, yet it is sufficient for us in our present state.”

Leibniz accepts Locke’s three degrees but offers important refinements. He argues that intuitive knowledge is not simply the perception of simple identity (like white not being black); it also includes the immediate perception of necessary connections—for example, that a whole is greater than its part. For Leibniz, intuition includes the perception of eternal truths that are self-evident to the rational mind. On demonstrative knowledge, Leibniz stresses that the certainty of a demonstration depends not only on the certainty of each step but on the validity of the inference from one step to the next. This inference itself must be justified by a principle—the principle of non-contradiction or the principle of sufficient reason. On sensitive knowledge, Leibniz is more generous than Locke: he argues that sensation provides certitude of existence because it is a well-founded phenomenon—it is the expression of the real order of monads. “We cannot doubt that there are bodies, because our perceptions are coherent and regulated.” However, Leibniz insists that sensitive knowledge is not knowledge in the strictest sense; it is probability or moral certainty, not metaphysical certainty.

Leibniz’s account of the degrees of knowledge is more integrated than Locke’s: intuition, demonstration, and sensation are not separate faculties but different modes of the same rational soul’s relation to reality.

Book IV, Chapter 3: Of the Extent of Human Knowledge

Locke now asks a crucial question: how far can our knowledge reach? His answer is sobering: our knowledge is very limited, confined to the agreement of our own ideas. We have intuitive and demonstrative knowledge of abstract relations (mathematics, morality) but very little knowledge of coexistence in substances (physics) and no knowledge of the real essences of things.

Locke argues that we have no knowledge of the real essences of substances, and therefore we cannot know which properties necessarily follow from them. We cannot deduce that gold is malleable from its real essence, because we do not know that essence. The coexistence of properties in substances (such as the fact that gold is both yellow and fusible) is learned only from experience, not from rational deduction. As a result, natural philosophy (physics) can never become a demonstrative science; it will always be a collection of empirical observations. By contrast, mathematics and morality can be demonstrative sciences, because they deal with relations between our own ideas, which we can define clearly. Morality, for Locke, is as capable of demonstration as mathematics: “The idea of a supreme being, infinite in power, goodness, and wisdom, … and the idea of ourselves as understanding rational beings; these ideas, I say, being clear and distinct, I think we may be capable of knowing certain moral rules with as great certainty as mathematical ones.”

Leibniz challenges Locke’s pessimistic conclusion about physics. He argues that the real essences of substances are not unknowable in principle; they are known to God and can be approximated by human reason. “The real essences of things are the complete individual concepts that contain all their properties; and we can discover some of these properties by reasoning from the nature of the substance.” For example, from the nature of a circle we can deduce all its properties; similarly, from the nature of force we can deduce the laws of motion. Leibniz argues that physics can become a rational science if we ground it in metaphysical principles—especially the principle of sufficient reason and the principle of the identity of indiscernibles. He also disputes Locke’s claim that morality is as certain as mathematics, arguing that moral concepts are often more complex and less clear than mathematical ones. However, he agrees that morality is based on eternal truths of reason and is therefore capable of a degree of demonstration.

The debate over the extent of knowledge reveals the divergence between Locke’s epistemic modesty and Leibniz’s rationalist optimism. For Locke, our knowledge is bounded by the limits of our ideas; for Leibniz, those limits are not fixed but can be expanded by reason and reflection.

Book IV, Chapter 4: Of the Reality of Our Knowledge

Locke confronts an apparent paradox: if knowledge is only the perception of the agreement of our ideas, how can we claim that our knowledge is real—that it corresponds to things in the world? His answer depends on the distinction between real ideas (which have a foundation in nature) and fantastical ideas (which do not).

Locke argues that knowledge is real when our ideas are conformable to their archetypes. For simple ideas, the archetypes are things themselves, and we can be certain that our simple ideas (like whiteness or sweetness) correspond to real powers in objects, because they are produced by those objects. For mixed modes (like justice or murder), the archetypes are the ideas themselves, so knowledge of them is always real: “The reality of mathematical knowledge consists in its being about the ideas themselves, which are the archetypes.” For substances, the situation is more difficult: our ideas of substances are complex combinations of simple ideas that we take to represent real things. The reality of our knowledge of substances depends on the coexistence of those ideas in actual things. We can have real knowledge that gold is yellow and heavy because we observe these qualities together in actual gold. But we cannot know whether a given combination will always coexist in nature. Locke concludes that our knowledge of substances is real but limited—we know that certain qualities coexist, but we do not know why.

Leibniz refines Locke’s account by introducing the concept of phenomenal reality: our knowledge of the external world is real because the phenomena we perceive are well-founded—they are the expressions of the underlying monadic reality. “We have real knowledge of bodies because the phenomena of bodies are the appearances of substantial beings.” Leibniz also argues that the reality of our mathematical and moral knowledge is grounded in the divine understanding. The truths of mathematics are not merely arbitrary constructions of the human mind; they are the eternal truths of the divine intellect, which we discover through reason. This gives them an objective reality that does not depend on actual existence. For Leibniz, even a mathematical truth about an imaginary figure (like the properties of a perfect circle) is real, because it reflects a possibility in the divine understanding.

Leibniz thus secures the reality of knowledge by rooting it in God and in the objective order of essences. This is a stronger foundation than Locke’s empirical one, though it depends on metaphysical commitments that Locke does not share.

Book IV, Chapters 5–7: Of Truth in General, Of Universal Propositions, and Of Maxims or Axioms

These chapters examine the nature of truth, the conditions of universal propositions, and the role of maxims (self-evident principles) in knowledge. Truth, for Locke, is the joining or separating of signs (words or ideas) in accordance with the agreement or disagreement of the things they signify.

Locke defines truth as “the joining or separating of signs, according to the agreement or disagreement of the things they stand for.” He distinguishes verbal truth (the correct use of words) from real truth (the correct correspondence between ideas and things). A proposition is true when the words are combined in a way that reflects a real agreement or disagreement of ideas. For example, “a circle is a round figure” is verbally true if our definition of “circle” includes roundness; it is really true if there exist circles that are round. Locke then discusses universal propositions, which are statements that apply to all members of a class (such as “all gold is malleable”). He argues that such propositions are only as certain as our knowledge of the real essences of things. Since we do not know the real essences of substances, universal propositions about substances are never certain; they are only probable. By contrast, universal propositions about modes (like “all triangles have three angles”) are certain because we define the modes.

Leibniz engages with the status of maxims or axioms—self-evident principles like the law of non-contradiction. Locke argues that these maxims are not the foundation of all knowledge; they are useful but not necessary. Children and uneducated people know many truths (like “two and two are four”) without knowing the principle of non-contradiction. Maxims serve as checks on reasoning but are not the source of knowledge. Leibniz strongly disagrees: “Maxims are the foundation of all demonstrative knowledge.” He argues that the principle of non-contradiction and the principle of sufficient reason are innate and are implicitly used in every act of reasoning, even when not explicitly stated. Without these principles, no deduction is possible. Leibniz also defends the role of axioms in mathematics: they are not arbitrary but are self-evident truths that express the necessary relations of ideas. He admits that children may not explicitly know the axioms, but they use them implicitly when they reason. “The axioms are the natural light of the mind, which is present from the beginning.”

The debate over maxims reflects a fundamental difference in epistemology. Locke sees knowledge as built up from particular experiences; Leibniz sees it as grounded in innate principles that structure all experience.

Book IV, Chapters 8–9: Of Trifling Propositions and Of Our Knowledge of the Existence of Other Things

Locke now criticizes trifling propositions—statements that are true but convey no new information (like “a man is a man”)—and turns to the crucial question of how we know that things exist besides ourselves and our ideas.

Locke dismisses trifling propositions as useless for expanding knowledge. These include identical propositions (A is A) and predications that are part of the definition (a triangle has three sides). He argues that such propositions are certain but trivial; they add nothing to our understanding. The real work of knowledge is done by instructive propositions (like “the external angle of a triangle is equal to the sum of the two opposite interior angles”), which reveal relations we did not previously see. Locke then addresses our knowledge of the existence of things. He distinguishes three kinds: knowledge of our own existence (intuitive), knowledge of God’s existence (demonstrative), and knowledge of the existence of other things (sensitive). The existence of other things is known through sensation, which provides testimony that is not as certain as intuition or demonstration but is sufficient for practical life. Locke admits that we cannot prove the existence of an external world by reason alone; we must rely on the reliability of our senses, which is a gift of God.

Leibniz affirms Locke’s distinction between trifling and instructive propositions but argues that even identical truths have a role in reasoning: they are the basis of the principle of non-contradiction, which is the foundation of all deduction. He also refines Locke’s account of our knowledge of the existence of other things. For Leibniz, sensation does not give us direct knowledge of bodies; it gives us phenomena that must be interpreted by reason. The existence of the external world is not a brute fact of sensation but a rational inference from the coherence and regularity of our perceptions. “The existence of bodies is a well-founded phenomenon, and we can have moral certainty of it, though not metaphysical certainty.” Leibniz also notes that our knowledge of our own existence is the most certain: the cogito (“I think, therefore I am”) is an intuitive truth.

Leibniz’s rationalism is evident: even the existence of the external world is, in the strictest sense, a truth of reason grounded in the systematicity of phenomena—not merely a truth of fact delivered by the senses.

Book IV, Chapter 10: Of Our Knowledge of the Existence of a God

Locke now offers an argument for the existence of God, based on the principle of causality and the impossibility of an infinite regress. This is one of the most important theological sections of the *Essay*.

Locke begins with the knowledge of his own existence: I exist, and I know this with intuitive certainty. But I am a finite being—I know that I have not always existed, and that my existence is not self-caused. Therefore, something must have caused me to exist. Either something else has always existed, or there is an infinite chain of causes. But an infinite chain of finite causes still requires a first cause outside the series. And since the cause of my existence must have not only intelligence (to produce my own intelligence) but also power, there must exist an eternal, most powerful, and most knowing being—which is what we call God. Locke insists that this argument is a demonstration, as certain as any mathematical proof, provided we accept the principle of causality. He also argues that we cannot conceive of nothing producing something, so there must be an eternal being.

Leibniz fully endorses the cosmological argument but adds his own metaphysical refinements. He argues that the existence of God can also be demonstrated from the eternal truths themselves: “The eternal truths are not merely possible; they are actual in the divine understanding.” For Leibniz, the possibility of the world—the fact that there is a consistent set of essences—requires a being in whom those essences are realized. This is a version of the ontological argument, which Leibniz finds compelling when properly understood. He also criticizes Locke’s account of the causal principle: “The principle of causality is not a truth derived from experience but an innate truth of reason, without which we could not reason about the world at all.” Leibniz argues that the existence of God is the most fundamental truth of reason, and that every effect ultimately depends on God as the first cause.

Leibniz thus reinforces Locke’s theism while providing a more rationalist foundation. For both philosophers, the existence of God is a certainty of reason—not a matter of faith or probability.

Book IV, Chapters 11–13: Of Our Knowledge of Other Things, Of the Improvement of Our Knowledge, and Some Further Considerations Concerning Knowledge

Locke concludes his discussion of knowledge by considering how we know other finite beings, how knowledge can be improved, and the limits of human understanding.

Locke argues that our knowledge of other finite beings (other people, animals, objects) is sensitive—it depends on the testimony of our senses, which is reliable but not infallible. He notes that the existence of other beings can never be demonstrated with certainty; it is always subject to skeptical doubt. However, practical life requires us to act on this probability, and God’s goodness assures us that our senses are not systematically deceptive. For the improvement of knowledge, Locke advocates a method of careful observation and reasoning. We should collect experience, form clear ideas, use words precisely, and test our hypotheses. Locke is optimistic that we can improve our knowledge of nature by following this empirical method, but he reiterates that we will never achieve demonstrative certainty in physics. He also discusses intuitive and demonstrative knowledge as the highest forms of knowledge, but admits that most of our daily knowledge is only probable.

Leibniz agrees with Locke’s practical advice but argues that the improvement of knowledge depends fundamentally on the discovery of real definitions. “As long as we only know the nominal essence of things, we will never go beyond probability. To advance to certainty, we must discover the real essences—the complete concepts from which all properties can be deduced.” Leibniz points to the example of geometry, where real definitions (like the definition of a circle as the set of points equidistant from a center) allow us to deduce an unlimited number of properties. He argues that the same could be done for physics once we discover the real natures of physical substances—specifically, the nature of force. Leibniz also criticizes Locke’s skeptical conclusion about other minds: “We cannot doubt that there are other rational beings, because we infer their existence from the coherence of our perceptions and their analogy to our own experience.” This inference is a form of rational demonstration, not merely probable.

Leibniz’s vision of the improvement of knowledge is grander than Locke’s: the goal is not merely to accumulate observations but to deduce the laws of nature from the essence of substance itself.

Book IV, Chapters 14–16: Of the Nature of Judgment, Of Probability, and Of the Degrees of Assent

Locke now turns from knowledge (certainty) to judgment (probability). Most of our beliefs about the world are not certain but probable, and they require us to exercise assent according to the degree of evidence.

Locke defines judgment as the mind’s ability to perceive the agreement or disagreement of ideas without certainty—that is, with probability. Probability is the appearance of truth based on evidence that is not sufficient for demonstration. The grounds of probability are of two kinds: conformity with our own experience and testimony of others. When these agree, we have the highest degree of probability; when they conflict, we must weigh the evidence. Locke then discusses the degrees of assent: from absolute certainty (when the evidence is overwhelming) through various degrees of confidence and doubt to unbelief. He argues that we should proportion our assent to the strength of the evidence: “The degree of our assent ought to be proportional to the grounds of probability.” This is the epistemological foundation of rational belief. Locke also warns against enthusiasm—belief that is based on feeling or inspiration rather than evidence.

Leibniz largely agrees with Locke’s account of judgment and probability, but he introduces an important distinction: moral certainty (the highest degree of probability) can be as compelling as demonstrative certainty in practice, though not in principle. “We have moral certainty of the existence of bodies, and of the testimony of history, and these are sufficient for all the purposes of life.” Leibniz also argues that the weighing of evidence is itself an act of judgment that can be refined by reason. He introduces the concept of probability as a rational estimate: the mind does not simply feel degrees of assent; it calculates them by considering the number and strength of independent testimonies. Leibniz is optimistic that this process can be formalized—a precursor to his work on probability and the art of combination.

For Leibniz, even the realm of probability is subject to rational analysis. Judgment is not a mere feeling but a form of reasoning with incomplete evidence—a discipline that can be perfected.

Book IV, Chapters 17–18: Of Reason, and Of Faith and Reason

The final substantive chapters of the *Essay* examine reason as the faculty of discursive thought and the relationship between reason and faith. Locke distinguishes the proper spheres of each and warns against the encroachment of faith upon reason’s domain.

Locke defines reason as the faculty of discovering the certainty or probability of propositions by drawing inferences from known truths. He divides the process into sagacity (the ability to discover intermediate ideas) and illation (the ability to draw the correct conclusion). Locke argues that reason is the sole judge of truth in all matters that are accessible to human understanding. Faith, by contrast, is the acceptance of a proposition on the basis of divine revelation. Locke insists that faith cannot override reason: if a proposition contradicts clear and certain knowledge (such as a mathematical truth), it cannot be accepted as revelation. “No proposition can be received for divine revelation, if it be contrary to the clear and self-evident dictates of reason.” Faith is only legitimate for propositions that are above reason (not contrary to it)—mysteries that reason cannot discover on its own but that do not contradict it. Locke also distinguishes between original revelation (direct communication from God to an individual) and traditional revelation (handed down through scripture or testimony), and he argues that the latter must be judged by reason to determine its authenticity.

Leibniz largely agrees with Locke’s division but offers a more integrated view: reason and faith are not opposites but are grounded in the same divine source. “Revelation is itself a truth, and truth cannot contradict truth.” For Leibniz, faith is not mere belief in authority; it is a form of knowledge based on the testimony of God, who is the source of all truth. Reason can investigate the credentials of revelation (miracles, prophecies, etc.) and can understand the content of revelation, even if it cannot fully comprehend mysteries like the Trinity or the Incarnation. Leibniz argues that these mysteries are above reason but not contrary to reason: they do not contradict any demonstrated truth. He also warns against enthusiasm—the claim to private revelation that is not supported by public evidence. Reason must judge all claims to revelation by the criteria of coherence, consistency, and moral worth.

Leibniz’s account of faith is more rationalist than Locke’s: faith itself is a form of rational assent based on evidence, not a leap into the irrational. Both philosophers agree, however, that reason is the ultimate arbiter in matters of belief.

Book IV, Chapter 19: Of Enthusiasm

Locke added this chapter in the fourth edition of the *Essay* (1700) to combat the dangers of enthusiasm—the claim to direct divine inspiration without rational evidence. This is a vigorous attack on irrationalism in religion.

Locke defines enthusiasm as the belief that one has received immediate revelation from God, without any external evidence to support it. The enthusiast takes the strongness of his own persuasion as evidence of its truth: “It is a revelation because they firmly believe it, and they believe it because it is a revelation.” Locke identifies this as a logical circle and a dangerous source of error. The enthusiast mistakes the feeling of certainty for actual certainty, and in doing so, they abandon reason as the guide of judgment. Locke argues that the only way to test a purported revelation is by reason: we must examine whether the revelation conforms to the known attributes of God (goodness, wisdom, truth), whether it is supported by external signs (miracles, prophecies), and whether it leads to moral action. “Reason must be our last judge and guide in everything.”

Leibniz fully supports Locke’s critique of enthusiasm. He adds that the criterion of truth is not subjective feeling but objective reason, which is grounded in the divine understanding. Leibniz argues that true inspiration does not bypass reason but elevates it: “The Spirit of God does not extinguish but perfects the natural light.” Enthusiasm, for Leibniz, is a form of confused perception—the enthusiast cannot distinguish the true light of reason from the heat of passion. The remedy is clear and distinct ideas: we must discipline our minds to seek evidence, test arguments, and resist the temptation to mistake intensity for certainty. Leibniz also notes that enthusiasm often arises from a misunderstanding of grace—the belief that God’s action in the soul suspends the ordinary operation of reason. In fact, grace works through reason, not against it.

This chapter is a powerful conclusion to Locke’s epistemology: the sovereignty of reason is absolute, and no claim—not even a claim to divine revelation—can stand against the test of rational scrutiny.

Book IV, Chapter 20: Of Wrong Assent, or Error

The *Essay* concludes with a diagnosis of the sources of error—the causes of wrong assent or false belief. Locke identifies four main causes: lack of proofs, lack of ability to use them, lack of will to use them, and wrong measures of probability.

Locke lists the wrong measures of probability that lead to error: 1. Propositions that are not certain but taken as certain — accepting doubtful claims as demonstrated truths. 2. Received hypotheses — clinging to popular opinions or traditional doctrines without examining them. 3. Predominant passions — allowing emotions to override reason, especially hope, fear, and desire. 4. Authority — relying on the opinions of others (especially those we admire or fear) without critical evaluation.

Locke argues that the most dangerous source of error is submission to authority, because it abandons the use of reason altogether. He urges his readers to think for themselves, to examine evidence, and to proportion assent to the strength of the grounds. “Our knowledge being so narrow, yet we are certain of nothing so much as of the existence of a God.” Error arises not from the limits of our understanding but from the misuse of our faculties. Locke ends with a call to humility and industry: we should acknowledge our ignorance, strive to improve our knowledge, and always be ready to correct our mistakes.

Leibniz adds to Locke’s list a further cause of error: the confusion of ideas. He argues that many errors arise from the failure to analyze ideas into their simple components—a failure that can be remedied by the development of a characteristic language. Leibniz also stresses the role of prejudice—the uncritical acceptance of opinions from childhood—which shapes our mental habits before reason can develop. He notes that even the most rational thinkers can be subject to errors of inattention and haste, and recommends a method of slow and careful analysis. For Leibniz, the ultimate remedy for error is wisdom—the clear and distinct perception of the order of the universe and the love of God as the source of all truth.

The *New Essays* ends with these reflections on error, but the work is incomplete—cut short by the death of the author. The final words of Philalethes (the Leibniz-figure) gesture toward a unified vision of knowledge, reason, and faith, grounded in the eternal truths of the divine mind.