Ancius Manlius Severinus Boethius
(475?-524)
Reading: Second Commentary on Porphyry's Isagoge
Beothius represents the final glory of Rome. The Roman Empire had been in serious trouble for over a hundred years by now. The first (nominally) Christian Emperor, Constantine, had ruled from 306-337 (just after the death of Porphyry). [His Christianity was quite pagan, and amounted to little more than the superstitious devotion a football player shows after making a touchdown: "Thank you Jesus for helping me to crush my enemies!"] However, Constantine was the last Roman Emperor to rule over a unified Roman Empire. His children continued the by now endemic civil wars, but by 378 the Eastern half of the Roman Empire settled down and was relatively free from both civil war and external attack. The Eastern Empire lasted until 1453, when Constantinople was captured by Mohammed II. Things were more troubled in Italy, and they continued to deteriorate until 546 when Rome was finally sacked and evacuated. Although Rome had been politically volatile for quite some time prior to this, culturally it still had strong ties with the past. There was a significant break when Rome was sacked. In 529, just 5 years after Boethius' death, Justinian, the Emperor of the Eastern part of the Roman Empire, dissolved Plato's Academy, which had continued in existence since Plato first established it in 385 b.c.e. It was the oldest School in continuous existence. It wouldn't be too far wrong to say that the Medieval era truly began in 546, and that Boethius was the last Classical philosopher in the Greek tradition.
Boethius was born into an Aristocratic Roman family, and he rose through the political ranks to hold the rank of consul, the highest office in the empire, next to that of Emperor. He father had been a consul, and both of his sons served as consuls. Boethius had the best of educations, and it is quite possible that he studied philosophy in Athens. He was a Christian, and he wrote some important theological treatises. His Neoplatonist account of God's existence outside of time was very influential. In addition to this theological works, Boethius set himself the daunting task of translating into Latin all of the works of both Plato and Aristotle, and of writing commentaries on them to help Latins to continue the study of Greek philosophy. Unfortunately he only got around to some of Aristotle's logical works, because he was charged with treason and initially sentenced to exile, but then to death. In prison, awaiting execution, he wrote one of his most famous works, the Consolation of Philosophy. This work is a meditation on life and death, and Philosophy, personified, comes and comforts him. It is actually strange that he finds comfort in Philosophy, rather than in God. This has actually caused many scholars to doubt that he was in fact a Christian. It is conceivable that the theological treatises were not written by Boethius, but simply attributed to him. An intermediate position would be that he was something like the reverse of Augustine. Augustine was a Neoplatonist who converted to Christianity, and intellectually tried to draw Neoplatonism inside the fold of Christianity. Perhaps Boethius was a Neoplatonist who converted to Christianity, and then tried to bring Christianity within the fold of Neoplatonism.
Although Boethius doesn't mention it, the Second Argument is actually quite old. In fact, Plato himself is it's original author. This should tip you off that at least Plato thought the argument was unsound. Actually, this argument was central to the discussion of universals in Plato's time. He gives a version of it in the the Parmenides, and Aristotle gives a version of it (Peri Ideon 84.21-85.3). Aristotle thought the argument was sound, and it was central to his rejection of Transcendent Realism and his acceptance of Immanent Realism. So this is a very important argument. In Aristotle's version, the argument uses the form of humanity as its example, and so in modern discussions the argument is called the "Third Man Argument." Where the third man comes in, we'll see very soon. Plato's version in the Parmenides (132a-b) focuses on the form of the Large. So we could talk about the "Third Large Argument," but since scholars today usually speak of the "Third Man Argument" (TMA), I'll use the form of man.
In Boethius (13), the crux of the argument is stated in a nutshell in the first two sentences. The first part of the next sentence actually begins the argument:
For just as several animals have a certain similar something, yet are not the same, and for that reason their genera are sought out, so too a genus that is in several things, and is therefore multiple, has a likeness of what is a genus.
Take two humans, e.g. Plato and Crito. They are different from each other in many ways. They differ in size, hair length, complexion, and their faces are quite distinctive. However, in one respect, they do share something important in common: they are both humans. Among their many properties, Plato and Crito are unified in that each one of them has the property of being human. We can speak of Plato's humanity and Crito's humanity. Plato's humanity is in Plato, and Crito's humanity is in Crito. This is the "genus that is in several things, and is therefore multiple." Plato's humanity and Crito's humanity are sometimes called "unit properties" or "immanent characters" by modern philosophers.
IC: The properties of things are particulars ("immanent characters").
Boethius mentions that it is because two particular things can have immanent characters which are, in some sense, the same, "for that reason their genera are sought out." This is what drives Socrates' inquiry in dialogues like the Euthyphro, Laches and Charmides. Even though this particular action of prosecuting Euthyphro's father for murder is extremely different from that particular action of pouring a libation to Zeus, nevertheless they both have immanent characters which are, in some sense, the same, i.e. they are both pious acts. For this reason, their genera are sought, in other words, it is for this reason that Socrates goes about looking for the form of piety.
The next step in the argument comes in the next sentence. But this likeness is not one [in number], because it is in several things. Plato's humanity and Crito's humanity are not numerically one thing. They are not numerically identical, they are just qualitatively identical. Stop here and think about this. Perhaps the significance of this would be clearer if I didn't use Plato and Crito, but instead Plato and Evita. One was an ancient Greek male, the other was a modern Argentinian woman. But despite their very serious differences, they have identical properties: they were both human. That can't be an accident. The life Plato lived, and the life Evita lived, were extremely different, but they had remarkable similarities, e.g. they had to eat similar kinds of food, they had to maintain roughly the same body temperature, they had to avoid certain kinds of bodily injuries, and a thousand other similar things. Evita's humanity and Plato's humanity are qualitatively identical, even though Evita's humanity existed at a time when Plato's humanity had been dead and gone for over 2000 years. That can't be an accident, how do you explain it?
The answer comes in the next sentence. For that reason, another genus of that genus is also to be searched for. The realist in this argument explains the remarkable identity in the lives of Evita and Plato by looking for a "genus of that genus," or in other words, by looking for some one thing which is the cause of the similitude. To take a silly example, imagine coming across a pocket watch just lying on the ground. You pick it up and marvel at its craftsmanship. As you walk along, you soon find another pocket watch which looks and functions just exactly like the first one. That can't be a coincidence. They are so exactly similar that there has to be a cause for their similarity. In this case the similarity comes from the person who made them (or the machine that made them). They were made according to exactly the same design by exactly the same watchmaker, or exactly the same machine. That kind of similarity is no accident, this identity which is not numerical, must ultimately be explained by an identity which is similar: there was one single design which was implemented in both that watch and in this watch.
Exactly the same thing is being said of Plato and Evita. What makes them both humans? There must be a single form of Humanity which is shared by both of them. If they were just different from each other, we wouldn't call them both "human." It's no accident that Plato's humanity and Evita's humanity are identical; this unity in diversity must be traced back to some true unity. Because we can lump the many individual humans into one group, there must be a form which unites them. This is the "One Over Many" (OM) assumption.
OM: over a group of many F things, there is one form of F in virtue of which they are F.
Plato's humanity and Evita's humanity are so similar because they got their humanity from one and the same thing: one and the same Form of Humanity. Whenever you have a single group of things which all share some common feature, quality or property, there must be a form of that feature, quality or property.
This seems to be the assumption that drives Plato's early dialogues like the Euthyphro, Charmides and Laches. We distinguish a group of actions as pious actions, and separate them from the impious ones; we distinguish a group of actions as courageous or temperate actions. There must be some principle for these groupings: Socrates wants to know that form of piety, courage and temperance which unites all the virtuous actions and separates them from vicious actions. Why? Why does Socrates want to know the forms of piety, courage and temperance? His interest is not theoretical; his interest is practical. He wants to know what the form of temperance is so that he can be temperate. If I don't know what temperance is, then I couldn't possibly know how to be temperate. If I want to act temperately, piously, courageously, then I have to know what temperance, piety and courage are. If I can't know what they are, then I can never know how to behave virtuously. Virtue becomes a guessing game.
Socrates compares ethics with medicine, so we can extend this from the moral sphere to the medical sphere: virtue is to the soul what health is to the body. Just as we need to know the form of virtue in order to be virtuous, so also we need to know the form of health in order to be healthy. A doctor needs to know what health and sickness are, so that she can make sick people healthy. If I go to the doctor when I don't feel well, I want the doctor to be able to say, "Ah yes, I've seen this condition before and I know how to cure it." I don't want the doctor to say, "Well, I've seen other conditions that remind me of yours, but yours is something separate and distinct form anything I've ever seen before. We can certainly try out what I've done for others, but who knows what that will do!" When the doctor studies patients, she is studying them to discover not just what is wrong with this person here now, but in order to discover the forms of sickness and disease, so that she can cure them wherever and whenever she finds them.
OM is extremely important, but it is not enough to generate the "Third Man." The next step is in the next sentence. And when that has been found, then for the same reason as was said above, once more a third genus is tracked down. Where is this "third genus" coming from? He says it comes "for the same reason" as we just saw, so presumably he is referring to OM. To understand this, go back to a question I asked when I first introduced the problem of universals. I put 10 things on the table, and they all have some character in common: penny-ness. So there must be some one form in virtue of which they are all pennies: the Form of the Penny. Now how many entities do I have on the table? Do I have 10 tokens plus the type, making 11 entities all together? The realist appears to be committed to just this. But now what about the form of the Penny, what is it like? Could it look like a nickel? That's absurd. If it looked like a nickel, then how could it be that in virtue of which pennies are pennies? If it really is that in virtue of which pennies are pennies, then it would have to look like a penny, wouldn't it? In fact, wouldn't it have to be a penny itself? Going back to Plato, in the Protagoras at 330c3-e2 Socrates says that the Form of Justice is itself just, and the Form of Piety is itself pious. This is called "Self-Predication" (SP).
SP: the form of F is itself F.
The form of white-ness is itself white; the form of beauty is itself beautiful, in fact, it is the most perfectly beautiful thing there could possibly be.
This is a crucial step in the argument. Let's go back to the argument that led us to the Form of Humanity in the first place. We were led to this form because of OM: we had two individuals who both had the same character: humanity. We said that this couldn't be a coincidence, there must be some one form in virtue of which their humanity was identical. But now because of SP, the form of humanity is itself human. Just like Plato, Crito and Evita, the form of Humanity has the character of humanity. So now we have a new "many" over which there must be a new "one." This changes our diagram.
But now that we have a this next form of humanity, SP is going to kick in to make this next for human also. So now we have yet another group of "many" humans requiring yet a further "one" over them, and we reach Humanity-4. Now you see why Boethius ends this argument by saying "the argument necessarily goes on to infinity, since this procedure has no end." Now we can put the whole argument together. Since the most famous version of this argument is called the "Third Man Argument," (TMA) I'll use "man."
1.
There are many men.
So 2. There are many immanent characters of the
type "man." [IC]
So 3. There is a form of Man. [OM]
4. The form of Man has
the immanent character of the type "man." [SP]
So 5. The form of Man plus the original many men
forms a group of men.
So 6. There are many immanent characters of the
type "man." [IC]
So 7. There is a form of Man over the many men
plus the form of Man. [OM]
8. [Repeat steps 4-7 ad
infinitum.]
So 9. There are an infinite number of forms of
man.
Normally the TMA stops right here. But it is worth pressing the argument one step further. At step 9, why can't the Platonic Realist simply say, "So what?" So there are an infinite number of transcendent forms, big deal! The usual reply is to say that this infinity of form is a metaphysical extravagance, or that it results in a theory which is not parsimonious, or that it violates "Ockham's Razor" (e.g. "plurality must not be assumed without necessity").
But this is a weak objection. One familiar expression of Ockham's Razor is: entities are not to be multiplied without necessity. But it is open to Plato to say that since the infinite regress follows from true assumptions, then we are multiplying entities with necessity. This could very well be a stunning discovery about the nature of the reality. We can't just assume that reality is metaphysically simple. It may very well be that truth is stranger than fiction, and that reality is extremely complex. Remember that the ancient Pythagoreans were stunned by the discovery of what we today call "irrational numbers." It turns out that reality is mathematically far more complicated than they had assumed. Perhaps we are still discovering just how complicated reality truly is.
While this reply certainly is open to Plato, it is not the sort of reply he wants to make. Plato discussed the TMA in the Parmenides because he thought it was a serious problem for his theory. It seems that Plato had two reasons for thinking that the infinite regress of the TMA is a "vicious regress," one is epistemological and the other is metaphysical. Both considerations are central to why Plato believed in real forms in the first place. It all comes back to Socrates.
In the Charmides, when Socrates is looking for a definition of, e.g. the form of, temperance, Charmides' first attempt is to say that temperance is calmness. Socrates then argues that even if many temperate actions are calm actions, there are a great many other cases where a calm action is intemperate. For example, a temperate wrestler wouldn't lost his temper and flail about wildly, but he also wouldn't be calm: he would be quick and decisive. A calm wrestler is not a temperate wrestler because wrestling is not a situation that calls for calmness but for quickness. Calmness is sometimes temperate but sometimes non-temperate, and hence it cannot possibly be what temperance is, it cannot possibly be the form of temperance (Charmides 160b-d).
In the Laches, the second definition Socrates considers is that courage is endurance. He does the same thing here as he did with calmness in the Charmides: in some cases endurance is courageous, but in other cases it is non-courageous. For example, enduring a situation where you ought to make a strategic retreat is recklessness, not courage. Endurance is sometimes courageous but sometimes non-courageous, and hence it cannot possibly be what courage is, it cannot possibly be the form of courage (Laches 192b-d).
The same thing happens in the Republic v. Plato imagines talking to people who deny the existence of forms. He calls these people the "sight-lovers" because they think that the only things that exist are sensible particulars, they are nominalists. He imagines how they would answer the question "What is beauty?" Their only possible answer would be to point out particular beautiful objects and identify what makes each of them beautiful (the "many beautifuls" at 479d3). For example, this bright purple may be what makes this painting beautiful, according to the sight-lovers. The problem with this kind of answer, is that it begs the question. For any sensible particular which is beautiful in one context, it is always possible to find a different context in which it would be non-beautiful, or ugly. For example, take that same beautiful color and put it on the Mona Lisa's nose, and it will not be beautiful. Perhaps it is true that in the first painting, this purple color is beautiful, but the Mona Lisa example compels us to ask the all important follow up question, "Why?" What makes that color beautiful in the first painting, but non-beautiful in the second painting? The sight-lovers haven't really answered the question at all, they have just pushed the answer back a step.
In all of these cases we have what scholars call "The F and Not-F problem," or the "Compresence of Opposites" problem. This particular color is both beautiful and non-beautiful, endurance is both courageous and non-courageous, calmness is both temperate and non-temperate. Sensible particulars cannot explain why anything is the way it is, because the fact that calmness is temperate in this action is itself in need of explanation; the fact that endurance is courage in this particular action is itself in need of explanation; the fact that this color is beautiful in this particular painting is in need of explanation. Since they stand in need of explanation themselves, they cannot themselves be the explanation.
In the Phaedo, emphasizes this point and gives us one of his clearest defenses and explanations of his theory of forms (100b-101e). He begins by stating that there are forms of beauty, goodness, magnitude "and all the rest." He doesn't specify how many forms there are, what sorts of things need forms over them (and that's a problem). The only way we can explain why beautiful things are beautiful is by showing how they "participate" (metechein, 101c) in the form of beauty; the only way we can explain why large things are large is by showing how they "participate" in the form of largeness; the only way we can explain why small things are small is by showing how they "participate" in the form of smallness. For example, he ridicules people who try to explain why one man is taller than another by saying that the first is taller than the other "by a head." The problem is that if the first is taller "by a head," then the second is shorter "by a head," and it must be the same head. But then that same head is making one man taller and the other man shorter. How can one and the same head explain one man's tallness, but another man's shortness? Obviously that is absurd. Tallness and shortness have to do with relative magnitudes, so in order to explain one person's tallness and another's shortness, you have to talk about relative magnitude
Whether Plato is right about all this or not is something I'll leave aside for the moment. What it makes clear is that in Plato's view, forms are causes or explanation, and hence are essential metaphysically and epistemologically. To know that this action is courageous, you need to know what courage it, i.e. you need to be able to give an explanation of why this action, as opposed to some hypothetical alternative, is courageous under these circumstances. Pointing to the fact that the soldier is enduring won't explain why his action is courageous, because that itself stands in need of explanation: why is endurance in that situation courageous? You can't explain the obscure by the equally obscure. So knowledge of the form is epistemologically necessary, but that is because the form itself is metaphysically necessary. You explain why this particular action is courageous by showing what causes it to be courageous, and that is its "participation" in the form of courage.
Hence, Plato can't accept an infinite regress of forms. You can't have an infinite number of different forms all causing this particular action to be courageous, and you can't know why this particular action is courageous if you have to know an infinite number of different forms.
But now I have just given a Platonic objection to the TMA. The key word is "different." You can't explain, and hence know, the courageousness of this act by listing an infinite number of different forms. But there is no problem listing an infinite number of numerically identical forms (listing the same for again and again). If the argument really did show an ever-mounting tower of separate and distinct forms, one on top of the other, that would be an absurdity in the theory of forms. But the argument never proves this. The problem is in step 7.
7. There is a form of Man over the many men plus the form of Man. [OM]
There is a form of Man over the many men plus the form of Man, sure, but the form of Man over the many men plus the form of Man is just the form of Man. It's already there!
Think of it this way. Instead of using the form of man, let me use a different form. In the figure on the right, which objects belong together? Obviously it is the three triangles. Why? Because the properties of triangularity apply to each of them. Much of what you learn by studying one triangle can be transferred over to the other triangles. For example, you know that the square of the hypotenuse is equal to the sum of the squares of the other two sides. That's the Pythagorean Theorem, and it tells you something reliable about every single triangle you come across, past, present or future. Of course there are some differences, because there are three different species of triangle (obtuse, right, acute). But there just is objectively more knowledge that you can gain about one triangle from another than you can gain about one triangle from a pentagon. This is a case of real, objective similarity.
So each of these three triangles has the immanent character of triangularity (IC), and that means there must be a form of triangularity (OM) over this many. What is the form? Answer: closed-three-sided-Euclidean-plane-figure-ness. This form is also triangular: if close-three-sided-Euclidean-plane-figure-ness isn't triangular, then nothing is triangular (SP). So we have the One over the Many, and Self-Predication is true of it. So now we have a new many, the three triangles, plus the form of triangularity, and they need a form over them. What is that form going to be? What immanent character do they all share? Answer: triangularity. So there must be a form of triangularity which they all share. And so there is, the form of triangularity which I just gave you. Here we have successful geometrical explanation and successful geometrical knowledge. If there is an infinite regress here, it is a virtuous, and not a vicious, one.
This argument that Boethius has chosen, is an extremely important one, and it lands us back in the thick of the debate over universals as it was played out in Classical Greece. However, it is not a decisive refutation of Platonic forms in particular, or realism about universals generally.
In the third argument, Boethius shows his philosophical acumen and his intimate familiarity with both the Platonic and Aristotelian texts, because he picks on another absolutely central and absolutely crucial problem with universal which was discussed by both Plato an Aristotle: the problem of "participation."
I mentioned "participation" above when I was talking about Plato's view that forms are both epistemologically and metaphysically necessary. According to Plato, we can know about courage only by having an explanation of what makes courageous actions courageous; just as we can know about triangles only by having an explanation of what makes triangles triangles. The explanation is central both to the metaphysics and the epistemology. But central to the explanation is the relation between the form and the particular. Plato says that beautiful things are beautiful by "participating" (metechei, 100c5) in the form of beauty. The Greek word "metechein" is a compound of the preposition meta, meaning "with" or "among," and the verb "echein" which means "to have." So it could refer to a common possession. This is not a technical philosophical word, it is actually fairly common. Members of a democracy, as opposed to a monarchy, are said to "participate" in political power (Herodotus iii.80); and co-operating with someone or sharing tasks with them is a form of "participation" (Plato, Laws 805d). So Plato is not using a technical term with a precise definition; he is using a common word with only common usage to guide us in understanding the sense. In fact, Plato is well aware of the fact that this central concept of "participation" is vague. At Phaedo 100c9-d8 he says this.
I am not able to understand all these clever explanations. If someone tells me that something is beautiful because it has a lovely color or shape or something else like this, I disregard it because these explanations just confuse me. Instead, without being clever, I cling simply and perhaps foolishly to the claim that nothing except beauty makes something beautiful, either by being present (parousia) or by association (koinnia) or however you want to call it. I don't insist on the exact description, only that it is by beauty that beautiful things are beautiful.
This is, of course, a big problem. If forms are going to be the key to metaphysical and epistemological explanation, then their explanatory role ought to be made clear. Unfortunately, Plato doesn't do that for us in the dialogues. I suppose his attitude was, "Hey, if you really want to know, come to my lectures!"
Well, this can be turned right around on Plato as an objection to a realist theory of universals, and that is exactly what Boethius does in the Third Argument. Here it is.
1. A
universal is common to many, but not
(a)
piecemeal, or
(b)
over time, or
(c)
by non-constitutive relation.
2. Whatever is common
is common in at least one of those ways.
So 3. A universal cannot exist.
Logically speaking, this argument is a simple modus tollens: if universals exist, then something could be common in some mysterious fourth way, but there can be no such mysterious forth type of commonality, hence universals can't exist.
Plato knew this was a problem, and he explicitly raised it in the Parmenides (131a-d). There he uses the form of the Large. You might say that large things "participate" in the form of the Large by having pieces of the form of the Large. But what could a "piece of a form of the Large" be? Could some pieces be larger than others? Could there be a small piece of the form of the Large?
He tries out the suggestion that the form of the Large is "present" with all the large things in the way that a day is simultaneously present to all the things that exist on that day. The problem is that this seems to be like the way in which an open parachute can be "present" to a number of people under it: only a piece of the parachute is really over a particular individual, and so we are back again to cutting up forms into pieces. Plato never reaches an acceptable solution in the Parmenides, but again, this may simply be a case of exoteric vs. esoteric doctrine: "Hey, if you really want to know, come to my lectures!"
There is one more important problem related to "participation," but since it is also relevant to Boethius' First Argument against universals, I'll raise it in relation to that argument. In addition, I think that the response Plato can make to the First argument, also gives him a response to the Third Argument.
The First Argument Boethius gives against the reality of universals cuts absolutely to the heart of the theory of universals, and it also provides an excellent example of Medieval syllogistic argumentation. In ¶11 Boethius gives us the minor premise, in ¶12 he gives us the major premise and the conclusion to the argument. Here it is.
1. A
universal cannot be one.
2. Everything that
exists is one.
So 3. A universal cannot exist.
In the course of giving the central argument, Boethius gives a subsidiary syllogism in support of the first premise, the minor premise. Here it is.
1a.
A universal is, as a whole, in many things simultaneously.
1b. [Everything that
is, as a whole, in many things simultaneously, cannot be one.]
So 1. A universal cannot be one.
This cuts right to the heart of the problem of universals because it focuses in on the central phenomenon to be explained: apparent unity in diversity. How is it that all these different, particular individuals happen to be all the same? How is it that although Plato and Crito are two separate and distinct individuals, nevertheless they are so much the same? The realist answers, "because they both participate in one and the same form, there is a One over the Many, which explains their unity in diversity."
The problem is that this unity seems to be impossible. Metaphysically speaking, there couldn't be any such real unity as the realist asks us to imagine. Why? Because, as the last sentence of ¶11 says, "it cannot happen that although it is a whole in several things at one time, nevertheless in itself it is one in number." Let's take this apart piece by piece.
If you say, "I've got one thing, but it is both here and over there," you are not making sense. You can't have one and the same thing be in two different places. Or can you? Suppose I have an apple, and I say it is here in this room. Would it necessarily be a contradiction if I say that the apple is not here in this room, but over there in a completely different room way across campus? No. If it was here now, but there later, there is no impossibility. So we need to bring time into the discussion.
You can't have one and the same thing can be in two different places simultaneously. Or can you? Is it possible for me to be in more than one State (of the United States) simultaneously? Is it possible for me to be both inside and outside the room simultaneously? Suppose I say that the room is here (the ceiling) and simultaneously there (the floor). I can be both inside and outside of the room simultaneously if I stand in the doorway, just like if I stand at "Four Corners" I can be simultaneously in Utah, Colorado, Arizona and New Mexico. What we need is the concept of "total position" of something in both space and time.
The Total Position of x =df the totality of x's four-dimensional area (counting time as the 4th dimension).
Sometimes people refer to a thing's total position as its "space-time worm." If you think of your career through life as being composed of your three dimensional area at each moment of your existence, each moment of your existence will be another segment of the "space-time worm" that is the totality of your life, or your "total position." [To picture this in your mind, think of a special effect in a movie where you see fading trails of cars or people as them move, kinda like the slime that a slug leaves as it oozes through the muddy garden. Now imagine those trails somehow remaining very faint but visible, carrying on each segment a time stamp of when you were there. At the end of your life, we might step back and look at the whole planet Earth and see the space-time trail of metaphysical slime that was your life.]
Now back to the argument. Spatio-temporal particulars, like you and I, have unique total positions. What makes no sense is to say that I have one thing here with two distinct total positions. But that is precisely what would be true of universals, if they existed. Humanity exists in me and it also exists in all of you. My humanity has my total position, and your humanity has your total position, which is distinct from my total position. That is what doesn't seem to make sense. How can the form of Humanity exist wholly in you and wholly in me? Real universals seems to violate the familiar doctrine that you can't be in two places at one time (informal version), or (formal version) one thing cannot have two distinct total positions.
An initial panic response to this deep objection would be to say that the universal doesn't itself enter wholly into distinct particulars, rather each particular "participates" in the universal by getting a piece of it. But we already saw when we discussed "participation" that this doesn't seem to make sense. This is like trying to eat your cake and have it too. We want to "eat our cake" in the sense that we want pieces of the form to be sliced out of the form, and consumed into the various particulars that "participate" in it. But we don't want this slicing up to diminish the form itself. We want to form to remain wholly itself, unchanged from what it was originally. But as we saw above, this doesn't seem to make sense. We can't have our cake and eat it too; if we eat it up, its in pieces; and if we don't want it in pieces, it can't be eaten.
What is worse, is that if we chop up the forms like this, we are ruining the theory of universals from the foundation. The theory of universal forms is supposed to tell us the answer to the question of how different particulars can all have something in common. If we answer the question by splitting up forms into pieces, then we simply replace the question of how different particulars can all have something in common with the question of how different "pieces of forms" can all have something in common. Clearly we have made no headway in solving the problem of universals and particulars if we have simply replaced the first question with the second.
This is a problem for the idea of "Immanent Characters." If you think of the form of Humanity as being chopped up into you and me and every other particular human, then you are striking at the very foundation of what the theory of real universals is supposed to be doing. According to the realist theory of forms, there is a real unity amidst diversity. But if what you want is a real unity which makes Plato and Crito the same, in spite of the fact that they are distinct particulars, then why say they are the same by possessing two different things (the two "Immanent Characters") which are the same? Why the middle man? Now instead of explaining why Plato and Crito are the same, we are explaining why Plato's humanity and Crito's humanity are the same. We don't seem to make any metaphysical headway by appealing to "Immanent Characters." We are just delaying our answer to the question. Why not just state right out to begin with that Plato and Crito are the same because they both "participate" in one form: the form of Humanity?
This gives the Platonist a very simple reply to the Third and First Arguments. The doctrine that you can't be in two places at one time (informal version), or (formal version) one thing cannot have two distinct total positions, is a doctrine which applies to particulars. In fact, this is what seems to be so particular about particulars: the fact that they each have unique total positions seems to be what makes each particular the particular it is. Plato's simple reply is just to say that this doctrine doesn't hold true of universals: that's why they're universals! Philosophical reflection, and scientific study has shown us that there is a structure to reality that is regular and repeated. It didn't have to be this way, but it turns out that it is. Just as the Pythagorean Theorem is precisely true of every single triangle, regardless of size, regardless of the measurements of its angles; so also the basic principles of humanity are true of every single human being, regardless of race, color, creed, gender or sexual orientation.
Think of the stunning discovery of the periodic table of the elements. The table wasn't developed until the second half of the 19th century. It was developed because chemists began to notice repeated patterns in various elements. Reality didn't have to be like this, but it is. Just as every triangle has three sides, so also every chunk of gold has a certain cluster of basic properties which are repeated identically in every chunk of gold. There is a limited number of elements because reality just does happen to repeat them again and again.
You could object to this very simple answer by asking what happens to the form of humanity I die. Does it die too? The problem with this objection is that it is still thinking of universals as if they were particulars. When I die, all that happens is that humanity is no longer being exhibited by me. It is still being exhibited by others. How can that be? Answer: humanity is a universal, not a particular.
In (37), Boethius points out that in this commentary he has followed Aristotle's view because he is writing a commentary on Porphyry's commentary on Aristotle's Categories. Boethius himself accepted the existence of Platonic (Transcendent) Universals in addition to Aristotelian (Immanent) Universals. Actually, it had been standard philosophical practice to assume that the philosophies of Plato and Aristotle were completely harmonious, and formed one complete philosophical system. So in this commentary, Boethius doesn't try to defend the existence of Transcendent Forms, just Aristotelian Immanent Forms.
The theory he gives is relatively simple. I put it into two stages. For the first stage, look at (31). Boethius says that species is a "thought gathered from the substantial likeness of individuals that are unlike in number." In other words, we recognize qualitative identity in numerical (quantitative) diversity. Remember our triangles. The three triangles are all different from one another (obtuse, right, acute), but they are all the same in that they are triangles: closed, three-sided, Euclidean plane figures. The definition of a triangle is the Form of Triangle. It is what all triangles have in common; it is the "substantial likeness" amidst numerical diversity.
That is stage one. Stage two is stated in (26).
For there are several kinds of things that have their being in others, from which they either cannot be separated at all or, if they are separated, there is no way they can subsist. To make this clear by a widely known example, a line is something in a body. And what it is it owes to the body. that is, it keeps its being through the body. This is explained as follows. If it is separated from the body, it does not subsist. Who by any sense faculty ever grasped a line separated from a body? But the mind, when it grasps in itself confused and mixed up things from the senses, distinguishes them by its own power and thought.
A line cannot subsist without being the line of something. A grin cannot subsist without being a grin of some lips. In other words, some beings are ontologically dependent upon other beings. You can't see them walking around the world stripped of the thing they ontologically depend upon. You can't see a grin floating in the air without any lips there to be doing the grinning. Nevertheless, the fact that grins are ontologically dependent upon lips doesn't mean we can't understand grinning separately from lips. All we have to do is to pay attention to the grinning, and forget about the lips that are doing the grinning. Forget about whether the lips are thick or thin, if they are human lips or chicken lips, if they are covered in lipstick or chapstick, if they are grotesquely misshapen or kissably-perfect. Our minds have the ability to focus upon certain things and ignore certain other things. That is abstraction.
To re-cap the two stages: First, we notice qualitative similarity among numerical diversity, and second, we abstract the qualitative similarity out of the qualitative and numerical diversity, and that is how we isolate universals. The universals cannot exist separately from the things that have them, but we can understand them separately from the things that have them. In other words, the universals are not transcendent, they don't subsist, they are immanent. If all lips vanish from the face of the earth, then all grins vanish from the face of the earth.
The important thing to remember about this is that it is a form of realism. Boethius is here accepting that universals really exist; he is just denying that they subsist. In other words, humanity really does exist, and it really does unite us. We all participate in the form of humanity in the sense that we are all human beings, and the fact that we are all humans is a real fact about us. This is not an arbitrary grouping, it is not a subjective way of organizing information; we really are truly and objectively human beings. Just as surely as the Pythagorean Theorem applies to all triangles, whether they be obtuse, right or acute, and regardless of their size, so also the basic principles of human medicine apply to absolutely every human being regardless of race, color, creed, sex, or anything else. Humanity is a repeated, real feature of the world.
Just one final thing I'd like to point out before leaving Boethius. According to Boethius, we can notice similarity before knowing the form in virtue of which similar things are similar. Little children can spot that the triangles are all similar, and the pentagon is dissimilar, even before knowing the definition of a triangle. Similarity is similarity in some respect, and the realist's quest is to discover the respect of similarity, i.e. the universal which is shared by the many particulars, and which makes them all similar, i.e. of the same species. Abelard disagrees.