Title banner says "The Divine Individual" over a yellow losange with a red Yod in the center.

The Divine Individual

Title banner says "The Divine Individual" over a yellow losange with a red Yod in the center.

Part 4 of the Dualism, Monism & Thelema series

Having established the relationship between Nuit, Hadit, and the Qabalistic Zero, let’s now look at the relationship between Nuit and Hadit, in combination, and the Star.

The Definition of a Star

After introducing Nuit and Hadit as the “elements” of the Thelemic Universe, Crowley then introduces the concept of the Star, defining it as the combination of Nuit and Hadit.

Every event is a uniting of some one monad with one of the experiences possible to it.

“Every man and every woman is a star,” that is, an aggregate of such experiences, constantly changing with each fresh event, which affects him or her either consciously or subconsciously.

Crowley, “Introduction” to the Book of the Law
Animation showing Nuit and Hadit combining to form an experience

On the one hand, we have the monad, which Crowley previously identifies with Hadit or the subjective point of view. It is “that to which all Events occur.” (DC on AL II.2) It unites with Nuit, the “total of possibilities of every kind,” thereby eliciting one of the possible experiences latent within Her.

Animation showing Hadit moving through several instances of Nuit, each one a discrete event.

The change from one experience to another is defined as an event. The Star is defined as the aggregate of such experiences that occur to any one particular monad.

Animation showing how the totality of discrete events constitutes the Star.

As the Star is defined as the occurrence to Hadit of some set of possibilities latent within Nuit, the Star is unintelligible without Nuit and Hadit.

Hadit seems to be the principle of Motion which is everywhere, yet is not extended in any dimension except as it chances to combine with the “Matter” which is Nuit. There can evidently be no manifestation apart from this conjunction. A Khabs or Star is apparently any nucleus where this conjunction has taken place.

New Comment on AL II.2 (emphasis mine)

This aggregate of experiences occurring to Hadit is further defined as the essence of each individual.

Every man and every woman is a star.

AL I.3

This ‘star’ or ‘Inmost Light’ is the original, individual, eternal essence.

New Comment on AL I.8

It is also linked with the figure of Ra-Hoor-Khuit.

We have seen that Ra-Hoor-Khuit is in one sense the Silent Self in a man, a Name of his Khabs, not so impersonal as Hadit, but the first and least untrue formulation of the Ego. 

New Comment on AL III.62

This passage suggests there are other senses in which Ra-Hoor-Khuit does not mean the Silent Self or Khabs of an individual. It is possible Crowley is referring to his prior commentary on AL III.22:

Ra-Hoor-Khuit, like all true Gods, is therefore a Solar-Phallic deity. But we regard Him as He is in truth, eternal […] Ra-Hoor-Khuit is the Crowned and Conquering Child. This is also a reference to the ‘Crowned’ and Conquering ‘Child’ in ourselves, our own personal God

New Comment on AL III.22 (emphasis mine)

In this passage Crowley appears to distinguish between Ra-Hoor-Khuit as a general deity or archetype versus His manifestation as a particular Star. As we will see in a moment, he makes a similar distinction between Nuit and Nuith and Hadit and Hadith.

From this further information we may conclude that Star, Khabs, Silent Self, Ra-Hoor-Khuit (at least “in one sense,” as the personal God of each individual), and the essence of each individual are equivalent, interchangeable terms. They are only rationally distinct from one another. And the condition of intelligibility of any of them is the conjunction of Nuit and Hadit.

The Distinction between the Star and Nuit and Hadit

Diagram showing how Nuit and Hadit separate from the Zero and combine to form the Star. Star is a mode of Nuit and Hadit, and Nuit and Hadit are modes of the Zero.

While the Star is unintelligible in the absence of Nuit and Hadit, the reverse is not true. Nuit and Hadit are each intelligible in the absence of the concept of the Star. This follows from Nuit and Hadit being modally distinct in the type-b sense.

To review, any two things, x and y, which are modally distinct in the type-b sense are intelligible independently of one another (in other words they are prima facie separate substances), but they share a common third condition, z.

Since we have already discovered that the common condition of Nuit and Hadit is the Qabalistic Zero, it cannot be the case that the Star (or anything else) could be their common condition. Ergo, Nuit and Hadit are each intelligible absent the Star.

It might be averred that Nuit and Hadit are in some sense compelled by their natures to combine and form Stars, and therefore Stars necessarily follow from Nuit and Hadit existing. As Crowley says

[Nuit and Hadit] can only realize Themselves by creating an infinite variety of forms of Themselves, each one real as it is Their image, illusory as it is a partial and divided aspect of Them.

New Comment on AL I.29 (emphasis mine)

But the question is not how Nuit and Hadit realize themselves. Again, our concept of substance leaves aside questions of existence and only deals with questions of intelligibility. The question is whether we can even conceive of them separately from Stars (and therefore, by definition, separately from one another), and that’s exactly what we did in the previous section when we realized they were distinct modes of the Qabalistic Zero.

Since Stars are only intelligible with reference to Nuit and Hadit but not vice versa, it follows that any Star is modally distinct from Nuit and Hadit.

Monism and the Star

Diagram showing that Nuit and Hadit ground the Star, and the Star depends upon Nuit and Hadit.

Since Stars depend for their intelligibility on Nuit and Hadit (and not vice versa), it follows we are dealing with another case of dependence monism. We cannot speak about Stars entirely separately from Nuit and Hadit, since each Star is dependent upon Nuit and Hadit for its own intelligibility. But we can speak intelligibly about Stars as distinct from Nuit and Hadit, as Crowley does in the following passage.

Each such Star is intelligible to Them [Nuith and Hadith], as a poem is to its author as a part of this soul mirrored by his mind. But it is not intelligible to itself, because it has no relation with any other ideas; it only knows itself as the babe of its mother Nuith, to whom it yearns, being stirred by its father Hadith to express that instinctive attachment by inarticulate cries.

Ibid.

The names Nuith and Hadith do not appear in the Book of the Law, but Crowley tends to use them in the commentaries when speaking of Nuit and Hadit from the most abstract point of view. I will follow his usage.

This passage demonstrates that Crowley speaks of Nuit(h) and Hadit(h) in terms that indicate both their separation and connection to Stars in a way which we are defining as modal or a relationship of dependence monism. Yet this passage further determines the type of monism holding between Nuith, Hadith, and Stars.

Stars are intelligible to Nuith and Hadith. This is exactly what we would expect from a relationship of dependence monism where Nuith and Hadith are ground, and the Star is their consequent. The relationship of author (Nuith/Hadith) to poem (Star) implies that the nature of each Star is transparent to Nuith and Hadith. Crowley further determines this relationship of intelligibility by comparing Nuith and Hadith to the idea of a triangle and the Star to an actual triangle.

For no triangle can express the idea of a triangle. Any triangle must be either equilateral, isosceles or scalene, either acute, right-angled, or obtuse; and no one triangle can be all these at once; while the idea of a triangle includes all these, and infinite other, possibilities.

Ibid.

The way Crowley describes the relationship between the idea of a triangle and (actual) triangles is what we have been calling a modal distinction. As everything that can be proved about any particular triangle has its ground in the idea of a triangle, so do all things that follow from a particular Star have their ground in Nuith and Hadith. From this we may gather that Nuith and Hadith serve as a kind of paradigm or Platonic Idea of Stars in general.

In the language we have developed up to this point, we would call this an instance of derivation monism. Not only do all Stars depend upon Nuith and Hadith for their intelligibility. The meaning of each Star ultimately reduces to some meaning latent within Nuith and Hadith themselves. In other words, a complete understanding of Nuith and Hadith would, by analysis, reveal each and every Star, its particular position in space, its relations to all other Stars, and the experiences each and every Star would ever go through.

Diagram showing the Star and its position in space reducing to Nuith and Hadith.

From the level of Nuith and Hadith, the entire Thelemic Universe is, at least in principle, computable. Theoretically there exists an algorithm which exhaustively explains each and every Star, its relationships to all other Stars, and all of its experiences.

However, in the very same passage where Crowley tells us that each Star is intelligible to Nuith and Hadith, we also find out that it is not the case that each Star is similarly transparent to itself.

But it is not intelligible to itself, because it has no relation with any other ideas; it only knows itself as the babe of its mother Nuith, to whom it yearns, being stirred by its father Hadith to express that instinctive attachment by inarticulate cries.

Ibid. (emphasis mine)

By definition the Star is a combination of one particular monad (one instance of Hadit) with one set of possibilities latent within Nuit. It can be affected by Nuit, but it is by definition limited to its own point of view and can in principle have no knowledge of Nuit from other points of view.

It knows that it is in a relationship of dependence with Nuith and Hadith (considered now as abstract principles). It knows Nuith to be its “mother” and Hadith to be its “father”. However, it is not transparent to itself. It is not able to carry out the same reductive analysis of itself that Nuith and Hadith would theoretically be able to carry out on it.

So the relationship between Nuith, Hadith, and the Star is a monistic relationship, but it’s a different kind of monistic relationship depending on the perspective.

From the perspective of Nuith and Hadith, it is a relationship of derivation monism. But from the perspective of the Star itself, it cannot carry out the derivation, even if it knows that the derivation is at least theoretically possible from a more universal perspective. Let’s call this a relationship of derivability monism to indicate the in-principle possibility of a derivation without it being practically possible by the Star itself.

Diagram showing the impossibility of the Star reducing itself to Nuith and Hadith

Derivability monism implies that the Star is aware that its “true nature [is a form] of the Infinite” (Ibid). As any particular triangle possesses all the principle attributes of a triangle, so does any Star possess all the principle attributes of its divine parents. This is just what it means that each Star is a mode of Nuith and Hadith, which themselves are modes of the Qabalistic Zero. We’re still dealing here with one divinity, just under three different forms: Zero, Nuith and Hadith, and the Star.

However, when we get to the level of the Star, there’s a fundamental difference. While the Star is technically part of a larger context (Nuith and Hadith) of which it is a mode, and while this fact is available to the Star, from the Star’s perspective, its own individuality as a Star is irreducible to that larger context.

We will return to this point and examine it in depth when we consider why it is the Star must incarnate.

Crowley’s Critique of Gnosticism

Animation depicting separation of souls from the pleroma

We are confronting an important point of difference between Thelema and any spiritual system according to which the “soul” is a “broken off” aspect of a higher, impersonal divine reality to which it “returns” either at death or spiritual attainment. Crowley targets Gnosticism in particular with committing this error when, commenting on AL I.8, he says:

Why are we told that the Khabs is in the Khu, not the Khu in the Khabs? Did we then suppose the converse? I think that we are warned against the idea of a Pleroma, a flame of which we are Sparks, and to which we return when we ‘attain’. That would indeed be to make the whole curse of separate existence ridiculous, a senseless and inexcusable folly. 

New Comment on AL I.8

Pleroma is a Greek word (πλήρωμα) which literally means fullness. It is a technical term in the texts of Gnostic Christianity where it refers to the totality of divine powers. Crowley tended to think of it as an “impersonal unity” analogous to Brahma or Ain Soph. (See Crowley’s essay “Berashith,” passim.)

According to Gnostic cosmogony, the world we find ourselves in is outside of the pleroma. However, each individual carries a bit of the pleroma within themselves. If you find this pleroma within yourself, you can save yourself from a state of “deficiency” characteristic of the material world and restore yourself to an otherwise inaccessible sense of divine “fullness”.

Thus fullness [pleroma], which has no deficiency but fills up deficiency, is provided to fill a person’s need, so that the person may receive grace. While deficient, the person had no grace, and because of this a diminishing took place where there was no grace. When the diminished part was restored, the person in need was revealed as fullness.

The Gospel of Truth

Different Gnostic sects had different accounts of pleroma, different cosmogonies, and therefore different accounts of salvation, and it’s difficult to tell precisely which account Crowley had in mind when he made the pleroma remark. However, the contours of the general theory he’s critiquing are evident from the context.

He’s rejecting the idea that there is some original, undifferentiated, divine whole—”a flame”—of which each individual soul is a broken off part or “spark,” and he is rejecting the notion that salvation consists in abandoning one’s sense of separateness and reuniting with this whole.

Animation depicting the fulfilled soul's return to the pleroma

A full understanding of this critique will have to wait until we have analyzed the distinction between the Khabs and the Khu and thereby have a fuller understanding of incarnation, but even at this juncture it is possible to identify deep, fundamental differences between Gnosticism (and any analogous spirituality) and Thelema on the basis of Thelema’s metaphysics of the individual soul.

Gnosticism and Thelema share the idea that there is a modal distinction between the individual soul and the ultimate divine reality. Gnosticism describes the inner pleroma as a piece of the larger pleroma, and the Star within each individual is “a partial and divided aspect of” Nuith and Hadith. (New Comment on AL I.29)

The difference is that the Star which is the essence of each individual is irreducible. To discover divinity within oneself does not mean the reduction of one’s individuality into an impersonal divine “flame,” because the very nature of the Star in principle prevents that reduction. Again, its derivation from a higher reality is only in principle possible but is never in fact possible for the Star.

It’s important to point out that this irreducibility of the Star to a more fundamental context has nothing whatsoever to do with our mode of sensibility (Nephesh) or the limitations of the discursive intellect (Ruach). If that were the case, then all of these distinctions would simply be rational distinctions. Rather, it follows from the primary attributes of the Star itself as reflected in Jechidah-Chiah-Neschamah.

We can see a similar point of contrast with what Crowley has called “mystic monism” or what we are calling identity monism. If Thelema were a form of identity monism, there would only hold a rational distinction between the Star and Nuith and Hadith. It would technically be an illusory distinction. Hence some explanation is required of the following passage in which Crowley himself describes this distinction as “illusory.”

[Nuith and Hadith] can only realize Themselves by creating an infinite variety of forms of Themselves, each one real as it is Their image, illusory as it is a partial and divided aspect of Them.

New Comment on AL I.29 (emphasis mine)

We have to be careful with our terms here. From the perspective of Nuith and Hadith, it makes sense to say that the separation between them and any Star is “illusory,” but only in the sense that the Star does not constitute a separate substance from them. As we have seen, each Star is a mode of Nuith and Hadith.

Furthermore, from the perspective of Nuith and Hadith, there is no “mystery” in how the Star relates to them or other Stars. They could theoretically supply a reductive explanation of why each Star finds itself in the part of space it does, related to other Stars the way it is, etc.

From the Star’s perspective, the Star is also a mode of Nuith and Hadith; however, there is a mystery of exactly how it relates to the universe. But in neither case is Crowley merely making a rational distinction between Nuith, Hadith, and Stars.

The irreducibility of the Star is not an illusion it can unravel, nor is it an illusion it desires to unravel. It is already a “real image” of its parents and has all the primary divine attributes within itself. Even if the Star could somehow “dissolve” itself back into an undifferentiated, impersonal state, it would not gain anything from it.

The result is that, in Thelema, the individual as individual is the ultimate divine reality.

Deus est Homo

Animation in which the Star turns into a pair of Vs concealing a Yod and turns back into a Star again.

This is a fundamental characteristic of Thelema which differentiates it from other forms of spirituality.

Spiritual attainment entails the breakdown of illusory division and ends the sense of being cut off from divine reality, but the divine reality you’re being reunited with is none other than yourself. It’s your true will.

We don’t have the vantage point at this moment to fully articulate all the implications of this. Again, that will require an analysis of the distinction between the Khabs and the Khu. But we can already see that the derivability monism of the Star means that, from the perspective of the Star, the only reality that can ever mean anything for it is Itself.

The Star constitutes the pre-eminent reality of Thelemic spirituality. One’s individuality is as inescapable as it is irreducible. In principle, there can never be any higher reality for an individual than the individual him-or-herself. This is not a limitation on the Star but rather a condition of the expression of its divinity.

Title banner that says "the cosmic egg"

The Cosmic Egg: Nuit, Hadit, and the Zero

Title banner that says "the cosmic egg"

Part 3 of the Dualism, Monism & Thelema Series

Nuit and Hadit as Foundations

The Book of the Law presents Nuit and Hadit as the two exclusive deities of the Thelemic universe.

I am Heaven, and there is no other God than me, and my lord Hadit.

AL I.21

Furthermore Crowley took Nuit and Hadit to constitute the elements of the universe.

The elements are Nuit—Space—that is, the total of possibilities of every kind—and Hadit, any point which has experience of these possibilities. (This idea is for literary convenience symbolized by the Egyptian Goddess Nuit, a woman bending over like the Arch of the Night Sky. Hadit is symbolized as a Winged Globe at the heart of Nuit.)

“Introduction” to the Book of the Law

If Nuit and Hadit are both exclusive and elementary, then in our established terminology, they appear to be really distinct substances.

Forming a clear, distinct idea of space as distinct from the subjective point of view presents no difficulty. In fact they seem close in meaning to Descartes’s bodily substance and mental substance respectively.

This would appear to commit Crowley to mind-body dualism and make the Thelemic cosmology dualistic.

The Qabalistic Zero as Common Condition

Nuit and Hadit separating from the Cosmic Egg

However, in Crowley’s early essay, “Berashith,” he lays a framework for deriving Nuit and Hadit from an ontologically prior “nothingness”.

I assert the absoluteness of the Qabalistic Zero […] Our Cosmic Egg, then, from which the present universe arose, was Nothingness, extended in no categories

Crowley, “Berashith”

He then goes on to describe the creation of the universe in terms that anticipate the Thelemic cosmology of Magick in Theory and Practice chapter 0, where the infinitely great (Nuit) and the infinitely small (Hadit) combine to create Ra-Hoor-Khuit. (Magick, p. xxvii and p. 137. All references to Magick will be to the Weiser Second Edition, ed. by Hymenaeus Beta.)

So while there appears to be a real distinction between Nuit and Hadit, they share a common necessary condition in the Qabalistic Zero, which makes them modally distinct.

This implies that, while Thelemic cosmology initially appears dualistic, it is in fact monistic. All things are One (or “None,” as Crowley says) in the Qabalistic Zero.

But we need to make a distinction between two kinds of monism.

Identity Monism versus Dependence Monism

Identity monism entails a rational distinction

If two things are rationally distinct, then the difference is only in the concept we are applying to them. They are in fact one and the same thing. Let’s call this identity monism.

Crowley is not saying that the distinction between Hadit and Nuit is merely a rational distinction. Therefore we are not dealing here with a case of identity monism.

Dependence monism entails a type-b modal distinction

Instead, Crowley is implying that Hadit and Nuit are modally distinct: one is intelligible without the other, but they share a common third condition—the Qabalistic Zero—upon which they are mutually dependent.

So instead of calling this identity monism, I will follow Paul Franks and call this an instance of dependence monism. (Paul Frank, All or Nothing: Systematicity, Transcendental Arguments, and Skepticism in German Idealism, Harvard University Press, 2005.)

The implication is that, while Hadit and Nuit share a common condition in the Qabalistic Zero and hence are not really distinct substances, they are distinct modes of a single substance, and therefore the interaction between them is not illusory.

This is relevant to Crowley’s critique of “mystic monism” and its denial of the “interplay” of parts.

This is something the same as mystic monism, but the objection to that theory is that God has to create things which are all parts of himself, so that their interplay is false.

New Comment on AL I.3

In the context of this quote, Crowley is referring specifically to the interplay of Stars, but the point applies equally to the interplay of Nuit and Hadit.

Further, we can clarify his meaning of “mystic monism” in this passage. He is referring to what we are defining as identity monism, not necessarily all kinds of monism.

This is important, because it is only by committing himself to certain types of monism that other aspects of Thelema remain intelligible. This is especially true of its soteriology, which we saw previously requires the individual to transcend duality.

Is the Qabalistic Zero a Substance?

One might object to my line of reasoning thus far in the following way:

  1. A modal distinction between x and y assumes x and y are modes of a substance, z.
  2. A substance is a being.
  3. The Qabalistic Zero is defined as “Nothingness, extended in no categories,” i.e., the opposite of a being.
  4. Therefore, Nuit and Hadit cannot be considered modes of the Qabalistic Zero.

But for the purposes of our argument, we are defining substance as intelligible on its own terms. It’s defined without reference to existence.

The Qabalistic Zero is intelligible. This is evidenced in “Berashith” and later in Chapter 5 of Magick Without Tears, where Crowley provides a mathematical proof of the common origin of Nuit and Hadit in the Qabalistic Zero.

Not only that. He infers certain of their characteristics (like that Nuit is infinitely great and Hadit infinitely small). It’s impossible to make inferences from something if it’s unintelligible.

The particulars of the argument—which constitute the 0=2 theorem—need not preoccupy us. All we need understand is that Crowley treated the Qabalistic Zero as the intelligible, common ground of Nuit and Hadit.

Derivation Monism versus Dependence Monism

Since by Crowley’s lights the respective existences and qualities of Nuit and Hadit can be derived using logic and mathematics from their common condition, in addition to describing this as a form of dependence monism, I will again follow Franks and describe this as an example of derivation monism.

Not all examples of dependence monism are also examples of derivation monism. We might know that x is the necessary condition of y, and hence there exists a modal distinction between x and y, but it does not necessarily follow that we can know the particular qualities of y through examining x (or vice versa).

In other words we might identify x as the condition of the intelligibility of y without being able to explain or reduce all of the qualities of y to x.

For example, a triangle is a modification of shape, but it does not follow that we can deduce the sum of the interior angles of a triangle solely by means of an examination of the meaning of shape.

This distinction will be essential to make sense of Crowley’s thoughts about the Star.

To summarize:

  1. Hadit and Nuit are the dual foundations of Thelemic cosmology.
  2. Hadit and Nuit share a common condition in the Qabalistic Zero.
  3. So the distinction between Hadit and Nuit is modal, not rational. They are intelligible independently of one another but mutually depend upon the Qabalistic Zero. This is an example of dependence monism, not identity monism.
  4. Certain qualities of Nuit and Hadit can be derived from the Qabalistic Zero. This is an example of derivation monism.
  5. Not all instances of dependence monism are also instances of derivation monism.

Next we’ll look at how Nuit and Hadit are distinct from the Star.

Part 4

Logical Framework

Part 2 of the Dualism, Monism & Thelema Series

For there to exist a dualism between two terms, there must be a distinction to be made between them. Likewise, to speak of the same two things from a monistic perspective means in some sense to deny the distinction between them.

The philosophical tradition has acknowledged at least three kinds of distinctions since the time of Descartes in the 17th century: real distinctions, modal distinctions, and rational distinctions.

In order to understand the three kinds of distinctions, it’s necessary to understand the terminology Descartes used to talk about substances and properties.

Substances and their Properties

Substances

A substance is anything that does not depend on anything else for its existence.

Strictly speaking, from Descartes’s perspective, God is the only substance, since all things come from God and depend upon His continual support. More loosely speaking, though, anything that depends only on God for its existence could be thought of as a substance.

Under this looser criteria, Descartes recognizes the existence of three substances: God, body, and mind.

Principle Attributes of Substances

Substances can have many properties, but any property which makes the substance the kind of substance it is is called a principle attribute.

We have no idea what the principle attribute of God is, but the principle attribute of body is extension, and the principle attribute of mind is thought.

Principle attribute is just another way of saying essence.

Modes of Substances

A mode is a way of being of a principle attribute of a substance.

For example, shape is a principle attribute of a bodily substance, but being square is a mode.

Thought is a principle attribute of a mental substance, but being preoccupied is a mode.

Having established substances, principle attributes, and modes, let’s see what sorts of distinctions hold between them.

Distinctions between Substances, Principle Attributes, and Modes

Descartes tended to talk about distinctions in terms of the conditions of the existence of substances. I’m going to follow Leibniz instead and talk about the intelligibility of substances.

The Leibnizian school preferred talking about substances in terms of their respective intelligibilities rather than their existences, because otherwise it led to the conclusions of Spinozism, according to which there are no finite, dependent substances.

As it turns out, Crowley is much more of a Leibnizian than a Cartesian or Spinozist. As we’ll see, in order to conceive of multiple Stars, each being “God of Very God,” we will need the concept of a finite, dependent substance.

Real Distinctions

Two things are really distinct if and only if each is intelligible independently of the other. They must be either distinct substances or modes of distinct substances.

For example, I can conceive of (i.e., understand) the properties of a triangle without understanding anything about joy. I don’t ever have to have experienced joy or even heard of it in order to be able to deduce that the interior angles of a triangle add up to 180°. On the other hand, I don’t have to know the first thing about the geometry of triangles in order to know joy.

This is because triangularity and emotion are modes of independent substances (bodily substances and mental substances, respectively).

If we’re not being too strict, we could also say I don’t need to understand how to play chess in order to know how to drive (and vice versa). They are really distinct disciplines.

One of the implications of two things being really distinct is that negating one has no impact on the other.

Another implication is that, if x and y are really distinct, and if the ground of x is x’ and the ground of y is y’, then negating x’ has no impact on y, and negating y’ has no impact on x.

For example, the knowledge of trigometry (x) is based in the knowledge of geometry (x’). The knowledge of joy (y) is based in the knowledge of happiness (y’). Having never known happiness has no necessary impact on my understanding of trigometry, and having never known geometry has no necessary impact on my knowledge of joy.

Modal Distinctions

Two things are modally distinct if and only if (a) one is intelligible independently of the other but not vice versa, or, (b) either can exist without the other, but they have a necessary condition of their intelligibility in common.

Modal distinctions hold between (a) the essential property of a substance and a mode of the same substance, or, (b) between modes of the same substance.

An example of a modal distinction of the (a)-type is the distinction between being square (y) and having a shape (x). Shape is the essential property of a bodily substance. Being square is a mode or modification of shape. I can conceive of shape without knowing anything about squares in particular, but the reverse does not hold.

This is called a relationship of ground (x) and consequent (y). The negation of x necessarily entails the negation of y, but not vice versa.

The (b)-type modal distinction is between modes of the same substance.

For example, I was surprised when I got to college and realized I could do calculus without having to do algebra. (The teacher didn’t care if we reduced our answers.)

It’s not that algebra and calculus are really distinct, though. They’re modally distinct. Both are modifications of our understanding of number.

Another example of the (b)-type modal distinction is any distinction made between two very different emotions, e.g., love and hate. If I had never experienced the emotion of hate, it would have no impact on my ability to understand love and vice versa.

On the other hand, if I had no understanding at all what an emotion was, I would not be able to understand either.

If we want to speak more loosely, another example is that I don’t need to understand how to play jazz guitar in order to drum (or vice versa), but I need to understand how to keep time to do either.

One of the implications of the (b)-type modal distinction is that if x and y are modally distinct in this sense, then neither is the ground nor consequent of the other. Rather, they are both consequents of the same ground, z. The negation of x will not necessarily entail the negation of y (or vice versa), but the negation of z entails the negation of both x and y.

Another implication of the (b)-type modal distinction is that two things can appear to be really distinct when they are in fact modally distinct in the (b)-type sense.

Rational Distinctions

Two things are rationally distinct if and only if the distinction is being made between the object and itself, considered under two concepts.

In other words, we’re attempting to make a distinction between the substance and its principle attribute.

An example of a rational distinction would be between any bodily substance and its extension, since without extension, a bodily substance is inconceivable.

Modern philosophers talk about the difference between connotation and denotation. The same object (x) can be denoted (basically, referred to) under two connotations (basically, meanings).

The classical example of this is the distinction between Morning Star and Evening Star. These are two different connotations for the same object, the planet Venus.

The kinds of rational distinctions we’re going to look at will look very much like distinctions between different connotations of the same thing.

One of the implications of two things being rationally distinct is that the affirmation or negation of one will necessarily entail the affirmation or negation of the other. This is because they are both referring to (denote) the same thing.

Now that we have some tools, let’s use them to look at exactly what sorts of distinctions hold between:

  1. Nuit and Hadit.
  2. Nuit and Hadit and the Star.
  3. The Star and its Khu.
  4. One Star and any other Star.

Part 3