Sources of Spinoza's Metaphysics
Emanation in Neo-Platonism
Kabbalah: Emanation and Divine Names
Ontological Immanence in Nicholas of Cusa
Now, I give the name “Maximum” to that than which there cannot be anything greater. But fullness befits what is one. Thus, oneness—which is also being—coincides with Maximality. But if such oneness is altogether free from all relation and contraction [complicatio], obviously nothing is opposed to it, since it is Absolute Maximality. Thus,
the Maximum is the Absolute One which is all things. And all things are in the Maximum (for it is the Maximum); and since nothing is opposed to it, the Minimum likewise coincides with it, and hence the Maximum is also in all things. And because it is absolute, it is, actually, every possible being...Secondly, just as Absolute Maximality is Absolute Being, through which all things are that which they are, so from Absolute Being there exists a universal oneness of being which is spoken of as “a maximum deriving from the Absolute [Maximum]”—existing from it contractedly and as a universe. This maximum's oneness is contracted in plurality, and it cannot exist without plurality. Indeed, in its universal oneness this maximum encompasses all things, so that all the things which derive from the Absolute [Maximum] are in this maximum and this maximum is in all [these] things. Nevertheless, it does not exist independently of the plurality in which it is present, for it does not exist without contraction, from which it cannot be freed.
Thirdly, a maximum of a third sort will thereafter be exhibited. For since the universe exists-in-plurality only contractedly, we shall seek among the many things the one maximum in which the universe actually exists most greatly and most perfectly as in its goal. (DI, I, 2)
If by careful consideration we extend what was previously manifested to us through learned ignorance: from the sole fact of our knowing that all things are either the Absolute Maximum or from the Absolute Maximum, many points can become clear to us regarding the world, or universe, which I affirm to be only a contracted maximum. Since what is contracted, or concrete, has from the Absolute whatever it is, that which is the [contracted] maximum imitates the maximally Absolute as much as it can. Therefore, [regarding] those things which in Book One were made known to us about the Absolute Maximum: as they befit the maximally Absolute absolutely,43
so I affirm that they befit in a contracted way what is contracted....
But since, as was said, the universe is only the contracted first, and in this respect is a maximum, it is evident that the whole universe sprang into existence by a simple emanation of the contracted maximum from the Absolute Maximum. But all the beings which are parts of the universe (and without which the universe, since it is contracted, could not be one and whole and perfect) sprang into existence together with the universe; [there was] not first an intelligence, then a noble soul, and then nature. as Avicenna53 and other philosophers maintained. Nevertheless, just as in a craftsman's design the whole (e.g., a house) is prior to a part (e.g., a wall), so because all things sprang into existence from God's design, we say that first there appeared the universe and thereafter all things—without which there could not be either a universe or a perfect [universe]... Contraction means contraction to [i.e., restriction by] something, so as to be this or that. Therefore, God, who is one, is in the one universe. But the universe is contractedly in all things. And so, we can understand the following: (1) how it is that God, who is most simple Oneness and exists in the one universe, is in all things as if subsequently and through the mediation of the universe, and (2) [how it is that as it] through the mediation of the one universe the plurality of things is in God. (DI, II, 4)
In the foregoing we found, beyond all understanding, that the world, or universe, is one. Its oneness is contracted by plurality, so that it is oneness in plurality. And because Absolute Oneness is first and the oneness of the universe is derived from it, the oneness of the universe will be a second oneness, consisting of a plurality. And since (as I will show in Conjectures) the second oneness is tenfold and unites the ten categories, the one universe will, by a tenfold contraction, be the unfolding [explicatio] of the first, absolute, and simple Oneness. Now, all things are enfolded [complicatio] in the number ten, since there is not a number above it...
And so, we find three universal onenesses descending by degrees to what is particular, in which they are contracted, so that they are actually the particular. The first and absolute Oneness enfolds all things absolutely; the first contracted [oneness enfolds] all things contractedly. But order requires [the following]: that Absolute Oneness be seen to enfold, as it were, the first contracted [oneness], so that by means of it [it enfolds] all other things; that the first contracted [oneness] be seen to enfold the second contracted [oneness] and, by means of it, the third contracted [oneness]; and that the second contracted [oneness be seen to enfold] the third contracted oneness, which is the last universal oneness, fourth from the first, so that by means of the third contracted oneness the second oneness arrives at what is particular. And so, we see that the universe is contracted in each particular through three grades. Therefore, the universe is, as it were, all of the ten categories [generalissima], then the genera, and then the species. And so, these are universal according to their respective degrees; they exist with degrees and prior, by a certain order of nature, to the thing which actually contracts them. And since the universe is contracted, it is not found except as unfolded in genera; and genera are found only in species.71 But individuals exist actually; in them all things exist contractedly. Through these considerations we see that universals exist actually only in a contracted manner. (DI, II, 8)
Seeing the differences of things, we marvel that the one most simple Essence of all things is also the different essence of each thing. Yet, we know that this must be the case; [we know it] from learned ignorance, which shows that in God difference is identity. For in seeing that the difference of the essences of all things exists most truly, we apprehend—since it is most true [that this difference exists most truly]—the one most true Essence-of-all-things, which is Maximum Truth. Therefore, when it is said that God created man by means of one essence and created stone by means of another, this is true with respect to things but not true with respect to the Creator... (DI, II, 9)
Nicholas of Cusa called this paradoxical unity-in-diversity a “coincidence of opposites” which overcomes limits of discursive reasoning, and goes beyond both positive and negative theology:
In God we must not conceive of distinction and indistinction, for example, as two contradictories, but we must conceive of them as antecedently existing in their own most simple beginning, where distinction is not other than indistinction (Cusa, 1997).
Cusa recognized that the coincidence of opposites is an expression of the principle of Incarnation, wherein God’s identification with creation in Jesus coincides with God’s transcendence above all creation. In God the opposites of identity and difference coincide. Thus Cusa presents a conception in which the ineffability of the Infinite coincides with its expressibility in the finite, in which creator coincides with creation, transcendent coincides with immanent, and One coincides with Many. Cusa says in De Docta Ignorantia that the best way to evoke these mystical insights is through mathematical symbols:
Since there is no other approach to a knowledge of things divine than that of symbols, we cannot do better than use mathematical signs on account of their indestructible certitude (Cusa, 1997).
For example, Cusa compared the relationship between the finite, discursive intellect and the infinite Truth to the relationship between a polygon and a circle:
For the intellect is to truth as an inscribed polygon is the inscribing circle (Cusa, 1985).
As the number of sides to the polygon increases, it more closely approximates the circle. But no polygon actually coincides with the circle. The polygon and the circle only coincide when the number of sides of the polygon is actually infinite. Such a polygon, however, is inconceivable to the rational mind. Yet, this mathematical symbol evokes a sense of connection between the conceivable and the inconceivable, a way to approach the divine through its representations in finite forms. As the number of sides to the polygon becomes infinite, the rational mind fails, opening awareness up to something beyond, where the infinite sides of the polygon (the Many) coincide with the perfect continuity of the circle (the One).
- Thomas J. McFarlane
Let us describe a circle, bc, which is being rotated about a point a as would the upper circle of a top; and let there be another fixed circle, de: Is it not true that the faster the movable circle is rotated, the less it seems to be moved? Suppose, then, that the possibility-to-be-moved is actual in it; i.e., suppose that the top is actually being moved as fast as possible. In that case, would it not be completely motionless? Since the motion would be infinite velocity, points b and c would be temporally present together at point d of the fixed circle—without its being the case that point b was temporally prior to point c. (For if b were temporally prior to c, the motion would not be maximal and infinite.) And yet, there would not be motion but would be rest, since at no time would points b and c move away from the fixed point d. Hence the maximal motion would at the same time also be minimal motion and no motion. In that case, just as the opposite points b and c would be always at point d, would they not always also be at the opposite point from d, namely, at e? Would this not likewise hold true for all the intermediate points of the circle bc? Therefore, the whole of the circle would at every instant be simultaneously present at point d. And the whole of the circle would be not only at d and e but also at every other point of the circle de. Let it suffice, then, that by means of this image and symbolically we are somehow able to see that (if the circle bc were illustrative of eternity and circle de were illustrative of time) the following propositions are not self-contradictory; that eternity as a whole is at once present at every point of time and that God as the beginning and the End is at once and as a whole present in all things. (CI, pp. 83-84)
Let the line AB be a similitude of the truth and stand between the first truth and nothing. Let B be the end of the similitude in respect to the nothing. B should be folded over C in an enfolding motion toward A, and thus represent the motion, with which God summons from non-existence into existence. The line AB is fixed, so long as it egresses from the origin as AC does, and movable, so long as it is moved enfoldingly over C toward the origin. In this motion, CB with CA causes various angles, and CB unfolds by means of this motion different similitudes. First it causes in a less formal similitude an obtuse angle, which is its being; then in a more formal similitude an angle, which is its life; and then in the most formal and most acute angle it causes its understanding. The acute angle participates more in the activity of the angle and in its simplicity and is more similar to the first Origin.
And it is in the other angles, namely, in that of life and of being. Likewise the angle of life is in that of being. And what intermediate differences there are between being and life and understanding and what can be unfolded, you will see likewise in the enigma. (TNCF, pp. 311-12)
Duns Scotus: Univocity, Singular Essences, and Intensive Infinity
Take a thing (A) and its essence (B). Now B is a being and [by hypothesis] it isn’t A; thus it is something else, and therefore it has an essence. The essence of B is either the same as B or it is something else. If it is the same, then there should be a stopping point in the first case [of A and B]. If it is something else, let it be C, and I raise the same question about C, and so on to infinity. (Questions on the Metaphysics. 7.7.23)
[It follows that A is the same as its essence, and since A is an individual thing, then so is its essence.]
On this view it’s clear that the singular is one essence. . . And if the singular is one essence, it is intelligible per se
, even the singular differentia. (7.15.154)[The definition expresses] a universal essence, not an individual essence; not every formula indicating the essence of a thing is a definition. Therefore, the formula taken from the specific nature with the individual differentia added on to it is not a definition. (7.13.91)
We do not grasp Adam as a unique individual, for we have no cognitive purchase on the ‘Adamizer’ (his individual differentia); we instead construct an admittedly inadequate general concept ‘individual human’ to apply to him, perhaps associating it with other features that serve to pick Adam out. What it is to be Adam—his singular essence—is not open to us, as Scotus concludes: “The singular is intelligible for its part, since it is an essence, but it is not intelligible to us at the present time by a simple positive understanding” (7.13.172).
Our current cognitive infirmities do not prevent the singular essence from being knowable, of course, and furthermore in principle allows for the possibility of demonstrative knowledge of Socrates (7.13.160 and 7.15.39). If there is such knowledge, God has it—or the appropriate correlate to demonstrative knowledge, since God knows everything by direct non-discursive intuition. Essences, even singular essences, are the ground of knowledge. (Peter King, Scotus on Singular Essences)
Scotus thinks we can have a positive conception of infinity, according to which infinity is not a negative, relational property, but instead a positive, intrinsic property. It is an "intrinsic degree of perfection."
How do we acquire that conception of positive, intrinsic infinity? The story goes like this. We begin with "the potentially infinite in quantity." According to Aristotle, you can never have an actual quantitative infinity, since no matter how great a quantity you have, you can always have more. What you can have (and in fact do have, Aristotle thinks) is a quantitative infinity by successive parts. The next step is to imagine that all the parts of that quantitative infinity remained in existence simultaneously. That is, we imagine an actual quantitative infinity. Scotus then asks us to shift from thinking about an actual quantitative infinity to thinking about an actual qualitative infinity. Think of some quality (say, goodness) as existing infinitely: so that there is, as it were, no more goodness that you could add to that goodness to make it any greater. That's infinite goodness. But notice that you can't think of infinite goodness as in some way composed of little goodness-bits (just an infinite number of them). If I say that an angel is better than a human being, I can't mean that a human being has a certain number of goodness-bits while the angel has that many plus some extras. Rather, the specific degree of goodness of a thing is just an intrinsic, non-quantitative feature of that thing. Infinite being is just like that. Scotus describes it as "a measure of intrinsic excellence that is not finite." This is why the concept of "infinite being" is the simplest concept available to us for understanding God. Infinity is not some sort of accidental addition to being, but an intrinsic mode of being. Of course, if this is right, then the concepts of ‘infinite goodness’, ‘infinite power’, and so forth, are every bit as simple as the concept of ‘infinite being’. So why does Scotus make such a big deal about ‘infinite being’? Because ‘infinite being’ "virtually contains" all the other infinite perfections of God. That is, we can deduce the other infinite perfections from infinite being. So besides being the next best thing to a simple concept, it's the most theoretically fruitful concept we can have of God in this life. (Thomas Williams, John Duns Scotus)
Descartes: Extension and Thought
Mathematics
Physics
Optical Theory
Mind and Body
Descartes' Books
Spinoza's Treatise on Descartes
