Neoplatonic Virtue: The Two Souls, Mathematics, and Fate | Reading Proclus’ On Providence – Transcript

The Separability of the Soul from the Body: An Aristotelian Investigation

Chapter 1: Transition from Providence to the Nature of the Soul

Instructor: Okay, let’s go 15. Okay. So 15. But enough about this topic. So we finished talking about providence and fate. Let us now proceed if you agree to our second investigation, namely that concerning the two kinds of soul. Yeah, one that is separable from bodies and another that is inseparable.

Chapter 2: The Aristotelian Principle – Activity and Substance (Proposition 15)

Instructor: Take them this principle also from the philosophy of Aristotle. He says that every soul with an activity that does not need body is also endowed with a substance of this kind—be free from body and separable. Yeah, this is what Aristotle keeps on saying about—

Student: If the intellect, if thinking doesn’t need a body then—

Instructor: Yeah, exactly, exactly. Is it’s a challenge in—now it’s totally taking this as a principle.

Student: Yes, yeah, yeah.

Instructor: So this is necessarily the case. If we bring the substance of the soul down to the level of the body whereas its activity occurs without a body, then—right, then they can be—then the activity explains it this way. Then the activity will be superior to the substance since it will be nothing of the inferior to be in its natural state, whereas the substance will be rooted in it.

In other words, and because we have this rule that activity is posterior to substance and they explain something like the natural state being the activity of the substance, and then it would—if something would have an—in a non-bodily activity—sorry—and if we have a body that whose activity is non-substance and it sort of doesn’t need it substance for its activity, which doesn’t exactly doesn’t make sense.

Student: It doesn’t make sense because the activity is just, you know, it’s a power of the substance that’s an act, right?

Instructor: So, but this is impossible. Therefore the soul that can act separately from the body must also have an existence separable from the body. And then on theology, this is the arguments of especially Proposition 17, but 15, 16 as well, right there. And there he appeals to the idea that what’s self-changing turns towards itself.

Student: Yeah, it’s basically the same thing.

Instructor: So he starts off with, you know, he appeals to Aristotle a lot because he’s saying, like, even Aristotle, who is famous for, you know, denying a separate soul, he admits this principle that if there were something that has a separate activity, it would have a separate substance. And so he’s established that, now he has to turn to the question, well, do we have such an activity?

Chapter 3: Examining Which Soul Faculties Require Bodies (Proposition 16)

Section 1: Sense Perception – Eliminated as Separable

Instructor: Right. Okay, now 16. Examine then, my friend, which of the souls in us which will admit does not need body to exercise its natural activities. Could it be sense perception? Clearly not, as every sensitive faculty uses bodies as organs and is active with them regarding its proper sense objects, undergoing change and being affected together with the eyes and ears and all the other sense organs.

Okay, so it’s both uses the body—whatever sense the faculties—and is changed along with it, like your there’s a change in your ear when you hear something, and therefore whatever is the form of that or the soul corresponding to sensing, it’s also being affected or moved or changed.

Student: Yeah.

Section 2: Anger and Desire – Eliminated as Separable

Instructor: But then could it be anger and desire? Okay, but you see that would be like the two lower soul parts of the Republic.

Student: Right, the soul parts.

Instructor: Yeah, okay. But you see that these two often work together. Like in Aristotle also there’s something corresponding to that, like the, I don’t know, like desiring soul or something like that.

Student: Oh right, yeah, like faculty of—

Instructor: Yes, but you see, and these two often work together with such bodily parts as the heart and the liver. That’s what it says in the Timaeus [Plato’s Timaeus], and that they are not free from bodies. Right, also outside of Timaeus, Aristotle gives us a cultural definition of anger as the boiling of blood or of the heart.

Student: Right, right.

Instructor: How and how could faculties that are active together with sense perception not need a body, since perception is always moved through a body? And—okay, so so one is that these, these, like what we would call emotions I guess, are—do need bodies for, for like as their matter or something. They work through bodies and also—

Student: So, they are going along with sense perception.

Instructor: Yeah, they’re provoked by things that we perceive.

Student: Right.

Instructor: That the appetite effectively operates with perception we all, I believe, know for. How could one get angry about what is not perceived? Just like out of mind.

Student: Right.

Instructor: And how could one not desire? I see.

Section 3: Digression – Can Purely Intellectual Content Provoke Anger?

Student: I guess like nobody gets angry about thoughts besides like some weird philosophers or will say something like he got angry because someone didn’t take his question seriously or something. It’s not the—

Instructor: Well you, I mean you have to hear the thought, right? But and—and that it seems like if you had a purely—if you had a purely intellectual relationship with the thought, if it’s just something that you understood, it wouldn’t make you upset or something. Maybe the way that you formulated, the way you see it written in the book—

Student: Right, but then you’re already entering the domain of the imagination.

Instructor: Imagination. But does the, does just some kind of intellectual content have enough to make you angry? I guess that would mean like in some sense, I mean maybe, but sounds like a you problem, right? It sounds like it’s some, like, why would knowledge threaten your, like, make you think that you’re being disrespected? Well, that just as a rational subject, that should not make you feel disrespected knowledge.

But maybe you’re—but maybe you, I don’t know, you imagine yourself in a false way, right? I mean Christians have this, you know, these stories about the devil and he feels indignant when he learns that God plans to become incarnate in a human being. And so there is something purely intellectual that the devil is getting upset about and he’s feeling that he’s not being respected because he should be the highest creation and that this lower thing is going to be better than him.

But this self-image that seems to already require some kind of imagination. It’s not just knowledge. He sees himself as having a certain status.

Student: Right.

Section 4: Digression – Intellectual Desire vs. Appetitive Desire

Student: And I guess things like desiring of higher things or something, we would like to ascribe to a different faculty really, like we do talk about the intellect having desire in it or according to some, or you would talk about loving God and so on.

Instructor: Exactly, yeah. That’s not a, not an act of the, how do you call it, the desire or the—

Student: Yeah, well if you want to use the word you can say the desiderative faculty, but—

Instructor: Yeah, but but but it’s even different, it’s the different words the Greek, right? So does it like an appetite would be, you know, whereas the when you say about the like desiring you would say that you know it turns towards or it has an orexis [ὄρεξις: Greek term for desire or striving]. And there we are, and there of course we need something more like that the goods—it’s like the sense of desire, it’s just that they function as norms for its knowledge. There are standards according to which it knows all things. It’s a different sense then.

The Nature of Desire, Love, and Intellect: Bodily Affections and the Incorporeal Soul

The Distinction Between Bodily Appetite and Intellectual Desire

Student: Is there a sense, I’m just wondering now, is there a sense of like a human being loving, like talk about *eros* [Greek: erotic love/desire] right or is there a loving of intellect or of divine things or separate things with the like would the heart whatever whatever hormones or whatever they would call it aren’t used when when you love a bodily thing would they also be working when you love a non bodily thing or when when you do the ascent right you start loving well beautiful itself or whatever?

Instructor: Well I think loving, you know, loving beautiful things is part of loving the beautiful itself like it’s it’s part of the ladder [referring to Plato’s ladder of love in the *Symposium*] and that part certainly involves the the same hormones. And I think it it depends but I I guess so as long as we’re in this body and even like when we’re outside this body like before if we just have like a pneumatic body [Greek *pneuma*: spiritual body composed of spirit/breath] we just love the self-image of ourselves so it’s no longer hormones but we do have like memories and affections those those are this those continue and have imaginations.

I just like I wonder if when we’re up there following our star we don’t have a pneumatic body we just have an astral one which is which doesn’t change I think up there we it seems like that there is no nothing like the emotions we experience here.

The Inseparability of Willing and Knowing the Good

Student: Would we want to say maybe that there’s some kind of—I mean this might be also a prejudice of ours. We might be separating what causes us to will and what causes us to think too much. Like Damascene [John of Damascus, 8th century Christian theologian] might push this point, right? Saying like intellect is also just willing the good, right? And it’s not just knowing the good, it’s also willing the good. Maybe there’s also an affective component to our higher knowledge as well.

Instructor: Yeah I think I believe that so the question is like why it’s yeah I mean well if we think about the emotions you know there’s one sense in which we can think about them as sure they depend on perception they depend and there are changes in our body that were or changed in us that sort of that that refers to that and like okay I got angry because someone stepped on my toe.

Emotions as Qualia: The Feeling Beyond Perception

But there’s also the sense of emotions where we can think of them as like qualia [philosophical term: the subjective, qualitative properties of experiences] right so like there’s the feeling of being angry there’s a feeling of being sad sad independent of any action of being happy or sad right and and there are some emotions that present primarily as this right they don’t primarily present as responses to a certain perceived situation so for instance boredom right. Boredom doesn’t seem to be provoked by anything it’s rather there’s a lack of stimulus or something like that and but there isn’t also like positive things they’re like their feelings of bliss right it’s unclear why these more universal will be well couldn’t be present also in without the body.

The Rambam Debate: Knowledge vs. Love in the Afterlife

Student: I guess my question is something like this debate, if it would be only the knowing God, which would be eternal, like working with this Aristotelian framing, we got into this this big debate like someone like Rambam [Maimonides, Rabbi Moses ben Maimon, 1138-1204] would say the only thing that remains is your knowledge and therefore it’s only knowing knowing of divine things that that you know that survives the body and so on.

And then other people would come and say well no what about loving what about loving them and like that shouldn’t loving God also be something internal and we say well do you love God with your body like with your heart with your like fleshy heart well and that dies or once you’re saying well no it’s like intellectual love or something then that becomes just another name for like this this intellectual effect kind of like the norm or something a lot more abstract than like loving.

Instructor: Yeah I think so, I don’t think it’s just another name, and actually, since the highest, in some sense, the highest thing to be known is the good, or is value, then it would seem that at the, if anything, at the highest level, knowing is just a name for the feeling, right?

And so, of course, there is some element to our relationship to incorporeal things now, which is through the imagination. And that would, of course, end. Right.

Can You Love What You Cannot Perceive?

Student: I guess you could ask the opposite question. If we assume that part of the definition of these appetites is that they’re affected by sight or some kind of perception, nobody loves a person that they haven’t… I guess that’s not really true. I don’t know. I guess perception or imagination and like there’s this like question what does it mean to say love God if you cannot see him and you could say well you can have an imagination and then there’s this whole question if the imagination is God or it’s like an infinity or something.

Instructor: But the thing is like yeah you can love God without without knowing him and that’s actually part of like one of the reasons for thinking that we also have as it were yeah we have non-bodily emotions right so because that’s like very very important for for progress and you know that’s right that you this our love for unity our love for for the gods is prior to you know knowledge because we even share it with plants and rocks and right.

Student: But that wouldn’t like that’s like not the emotion of love it’s something like the the orientation of everything towards the god which maybe is experienced as a motion of love sometimes also I don’t know.

Instructor: Yeah but I mean for what no I you know like what what does it mean I think why isn’t in the case of the rock is this general orientation but things like if it’s in us it’s inside a life and so it has to be somehow you know within within life within we want to say consciousness maybe.

Student: Yeah maybe we want to say consciousness and so it has to have some correspondent there.

Student: Okay. Okay, anyways, that’s all.

Return to the Text: Affections Require Perception and Body

Instructor: So, anyways, but regular affections would be only to do with perception, and therefore the appetite of body and angry *thumos* [Greek: spirited part of the soul, seat of anger and honor] wouldn’t be non-bodily. And what could one desire?

As Aristotelian [likely referring to Proclus or another Neoplatonist commenting on Aristotle] rightly says, affections are either perceptions or not without perception so those are the two things that he just said. Hence if both the irascible and the appetitive part are accompanied by perception the irascible has the perception of what is painful the appetitive part of what is pleasurable right that’s what we have just like two parts and if what acts what acts with perception acts with body for perception goes together with body, then every irascible and appetitive faculty must act together with body.

Accordingly, these forms of life, which are all irrational, have their natural activity together with body. Okay. 17. Interesting definition of the…

The Rational Soul’s Corrective Functions and the Nature of Reason

The Irascible Soul and Its Relation to Pain and Pleasure

Instructor: It seems like the desire also perceives pain. So it’s a curious thing. I mean, maybe you can say something like, since it’s not that one doesn’t perceive pain or the other doesn’t perceive pleasure, it’s that one is better. We know the irascible, right? The things that the irascible is best known for is getting angry, and getting angry is a response to some kind of pain. And desire—we know desire best and what it is from cases of pleasure and seeking pleasure, and therefore we say that it desires pleasure, right? Something like that. So it’s just what they’re most—what they’re best known for, how they’re best known, but not any kind of the…

Student: Yeah, we could do it in a more general way.

Instructor: I was reading in Aristotle or some commentary about—it works with a lot more restricted definitions of courage and, what do you call it, temperance. And you could define courage and temperance as the two main virtues because courage is about what destroys life and temperance is about what gives life, or something like that. Like what preserves the person—all the things that preserve you have like temperance having to do with the appetite and correct behavior relative to that, and everything that—like that wouldn’t work for all kinds of honor, I guess.

Student: Those still—still—still. Well, I mean, maybe it was like problems more than with like pleasures. Like that’s like a very general sense.

Instructor: Yeah. And I mean in the sense that if you have a bad enough reputation someone will kill you, so preserving your reputation is always preserving you from that fate. Something like honor has to do with—like political honor has to do with something like—like what is—like what kind of—what happens to someone that bothers you, or how you react to like difficult situations, or like war.

Student: What it’s about in the beginning, right?

Instructor: Yeah, yeah. Or so you can say that just, you know, honor—me and you know, having honor means that people won’t attack you and you can attack other people, right? Something like that. And so it’s a—it’s about just, yeah, your susceptibility to pain or something like that.

The Rational Soul: The Third but Also the First

Instructor: But you know, and [section] seventy—and now look up at the rational soul itself and consider its life, the third but also the first, riding upon the inferior lives. Lives it either the first—like depending from where you start counting, I guess—or the first like in importance or something. And either corrects what is deficient in their knowledge, as when it refutes from above perception—from above perception, that is deceived in regards to its own objects.

Refuting Deceived Perception

Instructor: Oh, for example, for instance, when perception declares that the sun is only a foot in diameter. So like, pers—yeah, some—that’s what’s called refuting perception, or really, like the sun seems small, but that’s like—it’s not that the perception is wrong, it’s that it’s very far, so you have to take into account that.

Student: Yeah. So there’s an appearance that your foot can cover the sun, right?

Instructor: And the—this is “perception is deceived in regard to its own objects.” So it’s this appearance, you know, has to be interpreted or something like that. And that’s what the rational soul does, right? That’s what corrects what is deficient in their knowledge.

Student: Mm-hmm.

Instructor: Or expresses a similar illusion coming from the sensible objects with the usual deceit.

Student: Not show any like another other examples?

Instructor: I don’t know. I don’t know that spoons, yeah, like [bent spoons in water].

Castigating the Irascible Part

Instructor: Or it castigates the immoderate character of emotions when it strikes the irascible part, shouting the Homeric words, “endure my heart,” and drawing it back from its impulses, as if it were a raging dog. So, yeah, the restraining of anger.

Containing Desire

Instructor: Again, when it attempts to contain the desire that springs up on the occasion of the pleasures that burst forth from bodies, warding off their spell with temperance, right? So, and restraining desires for pleasurable things.

Platonic Context: “Endure My Heart”

Instructor: The “endure my heart” has a Platonic history because of the *Phaedo* [Plato’s dialogue on the immortality of the soul]. It’s used as an example of showing that the soul is not a harmony, it’s independent of the body, because it can tell the body to stop doing things. And so there’s that.

The warding off their spell—so this general idea that the sensible world is like a witch, or that, you know, is trying—is bamboozling us with its spells, you know, right?

Student: This is also like the *Republic’s* [Plato’s *Republic*] argument for multiple souls, like because they’re coming in conflict.

Instructor: Yeah. And also it’s an allegory of Circe [the enchantress from Homer’s *Odyssey*] and the meeting with Circe, and how Hermes [Greek god, messenger of the gods], right—so thinking is what gives the potion to Ulysses [Odysseus] that makes him be able to resist her charms and not become a beast.

Student: Okay.

Instructor: On the raging dog. Okay.

The Rational Soul’s Proper Activities

Instructor: And all such activities and the rational soul’s shows that it disdains all irrational emotions, both cognitive and appetitive, and liberates itself from them as though they were alien.

Methodological Principle: Nature vs. Perverted Use

Instructor: Now when searching for the nature of something, one should start not from those activities that make a perverted use of it, but from those that act according to nature.

When, then, reason in us functions as reason, it rebukes the illusory painting of the pleasures of desire, it chastises the impetuous movement of the irascible sort, disdains perception as full of illusion, saying that we neither hear nor see anything accurate, and it clears this looking at its internal reasons [*logoi*: rational principles], none of which could be seen through the body or bodily cognitions.

Identifying the Perverted Use of Reason

Student: What would be the—the non—the perverted use of our reason?

Instructor: So I guess I lost my—okay, the perverted use of reason, I take it—I guess the perverted use of reason would be what that’s in the service of irrational emotions. The one that just, you know, just thinks about how to achieve irrational ends. Maybe that would be the idea of the perverted use of it.

I mean, just from the contrast here, I can check, one moment. I think I have opened—no, I need to open here. I had the notes in a separate file. So, let’s see, I’ll say translate.

Mathematics as Purification: The Soul’s Self-Reflective Activity and the Ascent to Certainty

The Natural Activity of Reason Versus Its Perverted Use

Instructor: So, let’s see, translators have an idea here, 73, not really, they just, yeah, they’re just observing. Are there a bunch of references to the Phaedo here? Yeah, so I guess just by contrast, the best idea is that the perverted use is when it’s in service of irrational goals, goals that it hasn’t set itself, for which there are no good reasons.

Okay. So, right. Because his point is just that he wants to show how the rational acts against the other two parts. Right. And I guess the thing is, what’s the context? He wants to show that there’s a separate activity.

Addressing the Objection: Does Reason Always Depend on Perception?

And so one thing that someone could say is that, well look, you’re always depending on perception and imagination when you’re reasoning, right? Because either what you want is ultimately given by a desire which depends on a perception, or you can’t think unless you have a picture in your head, something like that. And so he wants to say no, we should look at—and here maybe natural here is like also when it shows itself as distinct from the others, right, and having its own nature as opposed to the other. So he says you have to focus on those things. And of course, you can talk a lot about reason, only talk about things that are mixed up with the other faculties. But if we want to know what it is, we have to take a look at these moments when it distinguishes itself.

Reason’s Self-Distinguishing Activity: Disassociation from Sense and Passion

Hence, it is clear that the soul acting in that way manifestly disassociates itself from sense perceptions, which condemns—it condemns, meaning it fixes, I guess, because it’s not really like saying that they’re entirely false—and from pleasure and pain which it eliminates. Right, which it eliminates. So this is now more closely what we saw describing purificatory virtue, right, where you know, from the rational calculus, pleasure and pain just don’t mean—are just not relevant. Like whether something’s good or bad has, you know, well that it causes pain to you or to others, that’s like one factor in it, but that doesn’t immediately tell you whether it is something good or bad.

Right. And again, so I guess I was thinking since there are all of the—there are these other references to the Phaedo—he’s thinking of those arguments there. So also like that you can’t really know as long as you’re in the body, think like that.

A Higher Activity: The Soul Reflecting Upon Itself (Section 18)

Instructor: All right, 18. Let’s consider after this another and better activity of the rational soul, where the inferior active faculties are already at rest and make no noise such as that is usually found among the masses. It is the movement by which the soul reflects upon itself and sees its own essence, the powers in itself, the harmonic proportions of which it consists, and the many lives of which it is the plenitude, and discovers that it is itself a rational world, the image of the being before it of which it left out, and the paradigm of things after it which it presides over.

The Soul’s A Priori Knowledge and Existential Plenitude

Right. So, as I’ll explain in a bit, this is to do with mathematics and in general, knowing things that are a priori, right, from its own innate concepts. So that it has the harmonic proportions of which it consists—this is of course a reference to the Timaeus [Plato’s Timaeus, where the World Soul is constructed from mathematical proportions], right, the soul’s made out of these proportions. Proportions in Greek is *logoi*, right, so same word for concepts or forms. And so it has all these concepts that you need.

And it’s interesting, right, that it’s not just—he has this theoretical pre-knowledge, the harmonic proportions of which consists, but also the many lives of which it is the plenitude. So you know, it’s not just that it can develop an a priori science of all these things, it can also be these things. That goes back to what I was saying about telestic madness being maybe like this madness of theater where we really believe that we are what we are playing in the ritual. And that has to do with the fact that we have all these possible lives within us as souls, right.

The Soul as a Rational World: Placement on the Scale of Virtues

And so it discovers that it is itself a rational world. So this is the passage from—if we’re thinking about the scale of virtues, right, from the purificatory life which we just described—rather this is still the purificatory life, but it’s like the more positive side of it, where the soul is turning towards itself and knowing itself as a rational immortal soul.

Mathematics as the Instrument of Purification

Instructor: All right. Everything is here, here arithmetic my friend and geometry, the mother discipline—so he’s an engineer—so which was a daughter of geometry, are both said to contribute much to this activity of the soul. They detach it from sense perceptions, purify the intellect from confused irrational forms of life, lead it on to grasp the incorporeal forms.

The Mystery-Rite Analogy: Mathematics as Lustral Water

As before the most sacred rituals, lustral water is offered to those who are to be initiated. Right, remember Damascus made this correspondence as well. He said that the political virtues are like the purifications that the most of—the greater amount of people—do in the mystery rites. But then those that are actually going to be initiated and see the great sight, right, the mysterious sight, the *epopteia* [Greek: the highest stage of the Eleusinian Mysteries, the revelatory vision], they have these additional purifications. And this is what he’s saying, like as before those sacred rituals, lustral water’s offered to those for it to be initiated, right. So this is the activity of arithmetic and geometry, right.

The Argument: How Mathematics Purifies the Soul

Consider indeed how these sciences which are established prior to intellectual, purely intellectual activities, have come to possess the purifying power we mentioned. For when they receive the soul filled with images which does not know anything clearly and without the confusion, they display arguments that have the irrefutable necessity of demonstrations and forms filled with all precision and immateriality, which in no way draw over them the vagueness found in sensible objects.

How then will they not purify our intellectual life from the things that fill us with stupidity and at the same time lead it to the vantage point of divine beings?

Unpacking the Purifying Mechanism

So he’s giving an argument for why to think that mathematics is something that purifies the soul. And he’s saying that the character of necessity that we find in mathematical demonstrations and geometrical demonstrations—they present a standard of precision, right, that you don’t find anywhere in sense objects, right. And this then—so what is purification? So it would separate us from our perceptions and it would attach us to higher things.

So I guess the idea is that when it presents this new standard of certainty or of necessity of precision, it separates the soul from taking as its standard just “oh, this seems likely, I’ve always experienced this and so it should continue.” But showing, you know, you can have something more than just “oh, I have good arguments for this side or that side,” right. You know, you can do more than rhetoric. And so this is the—and so they introduced this new—

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Mathematics as Purification: Distance, Precision, and the Recognition of Vagueness

The Contrast Between Mathematical Necessity and Ethical Vagueness

Instructor: And so it’s interesting in all this. So of course, you see that the focus is on mathematics and on unfolding our innate concepts. And so he [Proclus] actually here doesn’t make use of the fact that it’s also a plenitude of lives, types, and different kinds of life. But here it’s just focused on arithmetic and geometry and working out the harmonic proportions of which it [the cosmos] consists.

Student: Yeah. I wanted to ask you about this. So we saw this a few times already—math and math-like purifying science, or the thing that corresponds to these waters. How would this speak to nowadays? It seems like people have a problem with the standards of proof that math gives you. The interesting thing here is that they’re saying, well, the mathematical necessity is only—it’s better than physical kinds of arguments or necessity, but is not really intellect yet, not really the contemplative itself.

And I guess many people trying to talk about either ethics or metaphysics—which would be very different really here—because some of ethics, or at least political virtue, is less than mathematic, precisely because it’s about these very fuzzy things. How do you call them? Vague? The things that suffer from inherent vagueness?

And then people have this—there’s this whole logical positivism thing, which is like anything that isn’t math therefore isn’t a correct statement. And they have this difficulty—you can’t say metaphysical truths in a—they don’t have the kind of proofs. Or, well, I guess it’s not clear that math has those kind of proofs either ultimately, with meta-math and all of that. But we associate mathematics with this very—there seems to be a sort of debate between the mathematics people and the more interesting people, because of math having this reputation of being dry and formal?

Aristotle’s Principle: Domain-Appropriate Standards of Precision

Instructor: Right. So this, of course, goes back to Aristotle, where Aristotle says you can’t expect ethics to have the same standards of precision as math. That’s actually being a bad scientist. The scientist asks, you know, what kind of knowledge can we have in each domain? It’s just not that kind of thing. And I don’t think that Proclus would deny that.

And as you mentioned, so this is, first of all, distinct from political [virtue]. And we saw in Proclus’s biography that Marinus kind of tells us his [Proclus’s] studies in the order of the scale of virtues, and part of political virtue is the studies in rhetoric, right? So the mathematics—it’s not that mathematics will, oh, it purifies you and so now you treat all situations mathematically, you use mathematics to understand all the situations.

How Mathematics Enables Recognition of the Fuzzy as Fuzzy

But, you know, even just—so consider a fuzzy situation where you have, you know, it’s an ethical dilemma where there are arguments on both sides. You know, I guess just having the standard of mathematical proof will let you, as it were, relativize the situation and separate yourself from it. Like, well, in any case, this is a situation where there isn’t actually the kind of necessity we find in mathematics. There isn’t true knowledge.

So for instance, one consequence of this already is that it purifies you in the sense of—you know, the people are shouting on both sides as if they’re certain about their position. But since we do math, we know that no, no, this is not the kind of thing you can be certain about. Right?

So even understanding that the fuzzy is fuzzy, that requires the contrast of mathematics, right? And so, and that’s kind of the point here about it purifying. It detaches you from taking the fuzzy as certain, right?

Mathematics Reveals Reconciliation Beyond Bodily Opposition

And also, if we think about—yeah, so in the political world, because it’s involved with the passions, there are these oppositions and bodies, right? So someone is going to get the prize, someone is not going to get the prize. If you choose to not have children, then okay, you have more time for study and that kind of thing. But you know, having children is part of contributing to society and things like that, like pensions.

But so there are these kind of tragic dilemmas. And in the domain of the bodies, these are always going to oppose each other. But of course, when we think abstractly, we can think of—you know, Neoplatonists love this kind of thing—it’s because the cause is separate from everything that it is such a superabundant cause. And so in the level of mathematics, we can see that what appears to be opposed in the level of bodies is actually reconcilable.

So for instance, also in astrology—you’ll see, oh, here we have, you know, it’s just astronomical motions—but then you see, oh, here you have the principle of division, of war, Mars, together with Venus, right? So up there it works, but here, of course, that involves the tension and difficulty.

So mathematics also purifies us in the sense of also showing a domain of objects where what seems to be incompatible here is compatible there.

Mathematics as Stimulus for Theological Inquiry

This is actually something that Thomas [Aquinas] says in the *Parmenides* commentary about how mathematics stirs us to do theology and helps us do theology, because it presents things that seem impossible or contradictory to sense perception. So for instance, he gives the example of the infinite divisibility of a straight line. Like, how can this finite thing be also infinite? Right? That leads you to do metaphysics.

And that’s the—and that’s the way that mathematics—this is a different point—that it leads us to the vantage point of the divine beings.

Summary: Mathematics Provides the Distance Necessary for Recognition

So I guess, yeah, to return to your question, it seems that mathematics—that we recognize fuzzy, vague things as such only when we have distance from them, and that’s what mathematics gives us. And then…

Mathematics, Metaphysics, and the Ascent of the Soul: Proclus on Purification and Intellection

The Precision of Dialectic and Its Unhypothetical First Principle

Instructor: Yeah, it’s supposed to be even more precise. Yeah. It’s supposed to be even more precise because, well, ultimately it has an unhypothetical first principle. But we can read the next section where we’ll start talking about metaphysics.

Whether Mathematicians Are Better Prepared for Metaphysics

Student: Okay. And I guess I’m trying to think like the thought would be something like mathematicians would have an easier time or are easier to speak to for metaphysics at these kind of things.

Instructor: Yeah, I don’t know. I guess in some sense, I could see the lower thing. Yes, like Bertrand Russell has this autobiographical description where he learned some math as a kid, and he said, “Wow, so now I know what it means to prove things.” And then his rest of his life was realizing that you can’t prove anything.

Student: Who has the story?

Instructor: Bertrand Russell. Right. Yeah, this thing about realizing the proof things. This happens again and again in history where people read Aristotle’s *Organon* [Aristotle’s logical treatises] like when Arabs get it and then Latins get it and like, “Wow, we can do a demonstration. We don’t need to just keep arguing.” And so throughout the history of philosophy we have people doing this. And that’s kind of also the excitement that people had around German idealism, right? These deductions of what people thought, you know, were just metaphysical givens. And then there’s like, “What? You can actually prove these things?”

And yeah, so the idea is that it would be easier for a metaphysician to talk to a mathematician. Yeah, I think that’s partially true. I wonder if I’m doing justice to your initial point though about how—I guess the initial point is like, but mathematics seems an improper way to describe these realities.

The Problem: Mathematics Doesn’t Seem to Improve Moral Life

Instructor: And it’s like you would say, well, it doesn’t seem like mathematicians today are better at moral decisions than other people, people who are from literature departments—not that people from literature departments seem very good at moral decisions either. And so, but I mean, of course there’s the easy answer, which is, well, they just do mathematics as a curiosity or as a hobby, but they leave the department, they go get drunk or whatever.

And also, I had an Argentine professor who I think I’ve already mentioned this a couple of times—he found it absolutely unconvincing when people talk about chess as some kind of enlightened form of entertainment. It’s like, no, in Argentina people are addicted to chess and it’s just as violent as soccer and people just want to win and things like that.

So of course you can have all these passions and these things even if you are involved in a highly abstract sphere. And so one thing is saying that, yeah, there’s a disconnect in their life. They don’t understand that mathematics has revealed that they can have a higher standard of certainty about what sense perception gives them.

Mathematics as a Way of Life: Not Mathematizing Everything

Instructor: So, yeah, I wonder if there’s an also—yeah, so I mean, it would be mathematics as a way of life. Mathematics is a way of life, but also it doesn’t involve applying mathematics to everything, right? So I guess that’s also maybe the other thing. Some people complain, I guess maybe the purificatory potential of mathematics is thwarted also when then you try to mathematize everything, right? Because the point is that, no, it reveals that there’s a separate domain, and that then in virtue of that domain, everything here you can weigh things correctly. But when you try to say, “No, it’s all mathematics,” that kind of ruins it.

You can say that maybe that’s the tendency we have today because, you know, our physics and even lots of our social science tries to show, “No, everything is mathematical.” And so that kind of ruins the possibility that mathematics has for showing that there’s a different world, you know?

Student: Okay. Or yeah, like everything in a very advanced stage of it, it’s come not like if you say, well, physics and social or even ethics, we can do these utilitarian calculations kind of things. And so it turns out that math—the material, the material sensible world is also numbers. And then it’s only if you get to this very weird, deeper questions and say, so is modern physics really idealist physics? Because doesn’t it really believe in any matter? Everything is just math. And so it’s even worse than Plato because there isn’t any underlying thing. And then that’s a problem for itself.

And then I guess very advanced mathematicians might tend to not be materialist, but the general popular way of teaching seems to stay at the level of matter.

Proclus’s View vs. Modern Self-Reflection on Mathematics

Instructor: Right, but yeah, but then also, of course, Proclus is kind of—I mean, people would say he’s naive about the math matter, right? So we have this much more self-reflective way of thinking, “Well, you know, maybe it’s just there are many theories.” But he had this idea, of course, that, you know, mathematics is axiomatic intuitions that are known by *nous* [Greek: intellect/intuitive reason], right, that are just immediately grasped. Whereas we, you know, there are a bunch of different theories nowadays about how math really works.

And right now I’m thinking, I did read studies—most mathematicians are really what we now call mathematical Platonists. I believe that mathematical objects exist. It’s kind of hard to do math without that being the background, although if you’re pressed on the metaphysics you get stuck, so you start denying it.

Educational Strategy: Using Mathematics as Propaedeutic

Instructor: Yeah, that’s—yeah, I wonder, I don’t know, what would be a good educational strategy? People like Proclus and others, they seem to say things like this: “Yeah, if you don’t get metaphysics, maybe you need to do some math first, right?” And questions if we could do that. Could I make a school that does that, or is—yeah, in a very specific way?

Well, I mean, we do this a bit in philosophy, in some philosophy courses where there’s the obligatory formal logic. And it is the case that I think one—it certainly is true that contact with logic, with math, you know, opens people’s eyes to, you know, how to properly argue and what, you know, how certain an argument is.

But that’s the—yeah, it’s the case. And also, you know, this is something that I kind of pointed out here, that Proclus doesn’t seem also to develop his intuitions completely. He’s—so this part about us having all these lives and us—he doesn’t use it all, just the fact that we have these *logoi* [Greek: rational principles/reasons] in us.

Transition to Section 19: The Supreme Intellection

Instructor: Okay. Okay, 19. So yeah, 19: “After both these activities as stated of this rational soul”—both meaning both the way when it restrains or blocks the irrational soul and when it reflects on these abstract things like math—”let us ascend to its supreme intellection by which it views its sister souls in the world, have been allotted the heavens and the entire world of becoming according to the will of the Father.”

Student: Sister souls meaning?

Instructor: I think so. Famously, Plotinus [3rd century CE Neoplatonist philosopher] says that the world soul is our sister. And here I think he means probably the souls of the heavenly bodies and—

The Soul’s Ascent: From Physics Through Dialectic to Divine Inspiration

The Monads of the Gods Above Intellect

Instructor: Right, so these are probably the monads of the gods themselves above the intellect. So these then are things like the first forms, the so-called intelligible forms, and the principles of the series of beings. These would be the monads of the gods, for above all unified things must be established in unifying causes, just as above beings made alive the causes of life, and above beings made intellectual the causes of—sorry, the causes of life, and above being intellectually cause of intellect, and in general above all participating the unparticipating beings, the unparticipated hypostasis.

Okay. So this must be the principle of the intellectual things.

The Soul’s Breakthrough to Mystical Union

Following all these anagogic insights, I make it clear, I think, for all those who are not completely blind, that the soul, having abandoned sense perception below, as well as the bodies, breaks forth from the vantage point of an intellectual part into a bacchic frenzy at the calm and truly mystical intuitions of the hypercosmic gods.

From where, from what sort of activities, have the offspring of the gods revealed to us the invisible orders of the gods? How are souls said to be possessed by the gods and in contact with them, having taken on madness? I mean, for example, the Sibyl who, as it is told, began to say wondrous things soon after her birth and those present could hear from her who she was and from what order she came into this place on earth, or some other soul if there has been one that partakes in such so much divine nature.

The Reference to Divine Inspiration and the Sibyl

Right, so here he’s clearly moved on to talk about the activity of the soul, right, when he talks about the bacchic frenzy and the Sibyl and being possessed by the gods, being mad. The offspring of the gods—that’s a reference to the *Timaeus*, right? So after the creation of planets, there’s this thing: “Oh, we should also pay attention to the offspring of the gods,” who tell us about this genealogy, and they should know because they should know their own parents. And Proclus takes this quite seriously, and so he thinks he’s talking about a special kind of soul, which is like the soul of Plotinus, and because it’s chosen the right life, it’s in tune with its own god, and so it has actually access to intellectual full insight and can tell us about the gods themselves.

Reconstructing the Structure: Three Layers of Soul Activity

So here in this whole paragraph, he’s condensed two different things, right? He’s condensed, on the one hand, dialectic, which moves from the mathematical hypotheses on to the ultimate first principles. So that goes from—that’s the first part of the paragraph—after both of these activities to the unparticipated hypostasis. So there is describing some kind of intellectual assent by which the soul moves to first the souls and then to what the souls see, the intellect, and then the monads of the gods.

Layer One: Physics

I see that there’s actually something—maybe the first part describes physics. So he says, “After both these activities, the state of this rational soul, it is centered supreme inflection by which it views its sister souls in the world have been allotted to the heavens and the entire world according to the will of the Father.” And so that sounds like this idea that what is physics? Physics is knowing all of the perceptible world as it is dependent on first causes, as it is dependent. And so that includes ultimately, you know, primarily the Demiurge, but also things prior to the Demiurge like the Living Being Itself. And so that seems to describe what’s done in the *Timaeus*, right?

Layer Two: Dialectic

And then, and then it sees above all this, the souls, all the orders of the intellectual beings. For above every soul a god-like intellect is superposed which grants an intellectual disposition. So part of physics we will also talk about intellects, for instance time and so on, and the Demiurge and also things prior to the Demiurge.

But then it says, “Next it sees prior to them the monads, the gods themselves about the intellect, from which the intellectual multitudes receive the unification, for above all unified things there must be established unified causes,” et cetera, et cetera, “to unparticipated hypostases.” So that might be dialectic in the sense of the *Parmenides*, where you see that everything is dependent on the One, and you’re not just explaining the world of change, right, the entire world of becoming, but rather you’re just explaining all everything that is, all unified things, right?

Layer Three: Divine Inspiration

And then as then the further step point you have this union with the gods themselves through bacchic frenzy, et cetera, et cetera, the calm and truly mystical intuitions of the hypercosmic gods.

So why—I mean the hypercosmic of course can be very specifically the gods in Proclus that are responsible for soul itself. I’m not sure if he’s saying it in that sense. He might just be saying like the gods themselves as distinct from their activity of the world.

Summary: The Progressive Argument for the Soul’s Independence from Body

So that’s how I take this whole passage. So besides the corrective activity and the mathematical activity, there’s also this dialectical activity and also this inspired activity of the soul, right? And this is making even stronger the case that ever since, I guess, mathematical activity, he’s going to want to say that the soul is engaged in things that don’t depend on body.

Maybe you say that mathematics still depends on body because, you know, it does cross diagrams [as discussed in the *Republic*]. But then certainly with the dialectical activity, you’re not supposed to, because, you know, it ultimately depends on our innate knowledge of unity, right, which is certain and undeniable. And then from that and from intuitions like that, one of the properties that being is and not being is not—and so it starts off from these absolutely certain things instead of just making these hypotheses.

And then there’s something even more than that, which is the divine inspiration as well. So that’s even less dependent on body.

So it’s a very dense paragraph, but I mean, you—questions, comments?

Student: Yeah, no, there’s too many things.

The Soul’s Separability from Fate and the Law of Middle Terms

The Soul’s Separable Substance and Independence from Fate

Instructor: Okay, let’s continue then to summarize. Paragraph 20: “Whenever the rational and intellectual soul moves somehow according to its nature, it gets outside of bodies and beyond sense perceptions.” Right, the previous paragraph was like how far away from body you can get, which turns out to be very far. Hence—but there wasn’t really his point, I guess. You just have to say all these things because hence it must also have a substance that is separable from both. Right, after this has become clear till now by evident of itself, that the soul acts according to its nature, it is superior to the condition of being led by fate.

But when it is brought down to sense perception and made irrational and corporeal, it goes along with the things below, lives together with them as with some drunken neighbors, and it is dominated by the cause that reigns over them.

Right, so here he is making the point that the soul, since it has a separate substance, it can act independent of bodies. And since he’s already shown that bodies are what is controlled by fate, it can be not under fate. And this is also where it’s important that he’s shown that providence is a superior principle that dominates even things that are not controlled by fate, so that this being free of fate is not like entering some chaotic, totally free state, right? It’s still under a higher ordering principle.

The Metaphor of Drunken Neighbors: Moral Pressure from Sense Perception

Instructor: This thing about being brought down to the sense perception and as it were—so it’s falling along with perceived things as if they were drunken neighbors. Remember that like for Plotinus in *On Virtue*, he has this idea that—how do you put this—that we become better as like when we’re rational and we’re living an ordered, measured life. We live as if reason is in us and it’s as it were a very wise neighbor that we’re ashamed to act badly in front of, right? And then eventually, of course, we adopt the perspective of reason on ourselves and we identify with that rather than the purely emotional part, right?

Here’s the opposite. So here we actually—the appetites are as it were drunken neighbors in ourselves, right? And since we have these drunken neighbors, we care less about how we act. We don’t care about embarrassing ourselves in front of them, or rather we maybe we care about embarrassing ourselves in front of them by doing something uncool, by doing something that’s not really drunken. And it’s this kind of moral pressure that if you pay attention to perceptible things, there’s this moral pressure to act in a way according to the perceptible world. And of course, as long as we are guided by things that we perceive and we just react to the bodies around us, we’re gonna be caught in the stories that articulate those bodies, that organize those bodies, which is fate.

Student: Very good.

The Law of Middle Terms: Intermediate Beings Between Fate and Eternity

Instructor: Now, and it goes along and is dominated by the cause that reigns over them. Okay. “For there must also exist such a class of beings that are in their substance above fate, but are sometimes placed under fate through relation. For if there are some beings that are for all eternity established above the laws of fate, and others that are for all their lives subordinated to the periods of fate, then there must indeed be a nature intermediary between them, a nature that is sometimes outside the action of fate and sometimes subject to it, because of the law of middles somehow.”

So like in the same way that souls are like this thing that have an eternal substance but temporal activity and so on, which just translates now into the same language of fate.

“For the processions of being leave no void, even less so than do the positions of bodies.”

So this is like the non-void principle tied to causality, I guess, or it’s like chains of being.

Student: Precisely.

Instructor: And that’s also the point about the law of middle terms—you can only apply it when there is a causal relation between the two. So it’s because the things under fate are dependent on the things, the eternal things, that you can then say that there has to be things that are sometimes under fate, sometimes not under it.

And of course, I guess this depends on the prior explanation that the things under fate are divided things, things that need to be connected, and therefore they need to receive their unity from things that are prior to them that don’t need an external source of connection. And of course, these would be things that, for instance, don’t have past parts and future parts that need to be connected into a single narrative. So those would be the eternal things, and therefore you also need the fact that there’s a middle term.

The Principle of Superabundance and Causal Chains

Instructor: The idea, of course, is that things only create—you know, production has to do with superabundance. So things create by simply being themselves, and then effects separate themselves from their causes. They remain with their causes and separate themselves from them, but like a part of them is always with their cause. So that means that things can technically only be the causes of things that are most like them, you know, that are only different from them in a minimal extent. So that means that you can only have one thing causing a very different thing if you have the chain of middle terms.

So we need to have some things—”On the contrary, everywhere there are intermediate natures between the extremes; they provide their connection with one another.”

This is interesting, of course, that he’s bringing connection here in another context. So there’s connection in time and space—sympathy and narrative. But then there’s also the connection between levels of reality, right? And it’s also sympathy that goes up and down levels of reality, and that’s the sympathy that theology draws on, right? There’s no problem calling it sympathy, but then it’s a connection that’s through being itself, through reality itself, and not time and space.

Student: Okay.

Connection Through Being and the Analogy Between Providence and Fate

Instructor: And that, I guess, also explains—maybe, I think that this connection, of course, is what unites all of reality and distributes the good to all reality. So maybe that’s the way in which providence can be seen to be analogous to fate as well.

Student: That would make sense.

Instructor: Meaning that—so like if we go back to paragraph 14, I believe—so he draws this number of analogies between providence and fate. “You should therefore consider that there are two realms, the intelligible and the sensible, each with its own kingdom: that of providence above, ruling over the intelligible and the sensible, and that of fate below, ruling over the sensible. Providence is to be distinguished from fate as God’s—”

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The Chaldean Oracles on Fate: Elitism, Contemplation, and the Reinterpretation of Fated Narratives

The Oracles’ Elitism and the Distinction Between Divine Men and Fated Herds

Instructor: And the Oracles, they have this thing about—there’s this elitism, right? That’s what he makes actually here, right? Those divine men who are deemed worthy to be heroes of those mystical words are distinguished from the fated herds. So, most people behave following the life of fate and the narratives that have been pre-written for them. And this is—of course, there isn’t an idea in Proclus and the Oracles that you should try to liberate everyone from it, that it’s part of the structure of the world, that most people are these fated herds.

This idea that people follow, as it were, a herd mentality is also expressed when Proclus talks about, for instance, the idea that there are shepherds, right? There are these patron deities, these patron daimones of clans or of cities, which play such an important role in explaining tragedy, right? And they’re like shepherds of these groups. And so they—and that’s as people are parts of fated herds, right?

The Oracle’s Command: “Do Not Gaze at Nature”

Then if you follow the Oracle—like what is it? What does it say? “Do not gaze at nature.” That means somehow to not live that life, and then you’re not under fate.

Student: Yeah.

Instructor: So you—so look, you should not—we go back to the idea that the *Theaetetus* teaches that you become like what you contemplate, you pay attention to. So if you just pay attention to nature—and of course he’s talking with you to an engineer and someone who’s only paying attention to nature—and I guess that’s like part of what he said back there, like, “Oh, you think the world’s a mechanism because that’s what you deal with.”

And so you shouldn’t—I guess there’s maybe a criticism here too of like Stoic astrologers, right? Who just pay attention to the mechanisms of the world, and then they just think, “Oh, we’re just fated to do this.” And so you shouldn’t dedicate your life just to doing physics, or even if you do physics, have your physics like the *Timaeus*, which is leading the perceptible world up to its intelligible causes, to the principles. And that would be then the—

The Logical Implication: The Existence of a Separate Soul

And so, this is—I guess, since the issue is the existence of a separate soul, the idea is that if you can do it, you must be able to do it. If you must be able to do it, you have a separate existence, right? So, the Oracles, by saying, “Be free from fate,” imply that we have some kind of existence outside of fate.

Student: Okay.

Instructor: But relative to the question of fate, what those would mean is something like the philosophers, the contemplative virtue people are beyond fate somehow, or only their souls are, but they don’t care about their body.

How Contemplative Persons Transcend Fate: Reinterpreting Fated Narratives

We’ll get to the sense in which they’re beyond fate. The fact that they are—that fate isn’t one body pushing another, it’s not a mechanical thing, but it’s this formal thing that involves the possibility that we can maybe reinterpret these narratives, right?

And so, for instance, it might be fated for me to have a huge fire in my house, and that can actually be a material fire, but it can also be—oh, I don’t know—I give away my books, right? And things like that. So the person who’s contemplative, they can maybe follow their narrative in a different way. They’re not fated to just follow the most literal expression of that narrative.

Student: All right. So like the whole escaping the world from the—the *homoiōsis* [ὁμοίωσις: likeness/assimilation to God] with like—is escaping fate in that way?

Instructor: Yeah, yeah.

Student: Okay.

Closing

Instructor: It’s 10 o’clock. Yeah. So this was good. We’re going to stay with this time, I think. So I hope I’ll be able to make it, but yeah.

Student: Okay, right. So until you got—okay, until the 14th then?

Instructor: Okay, yeah. We’ll see you next week, I guess.

Student: Okay. Yeah. Yeah.

Instructor: Okay. All right. Thank you so much. Bye-bye.