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Macquarie University
PHIL252 Medieval Philosophy

TAPE 2: BOETHIUS ON PORPHYRY

Before listening to this tape you should read V.E. Watt's introduction to his Penguin translation of The Consolation of Philosophy. In this lecture I will talk about Boethius' other writings, and then I will comment on an extract from his commentary on Porphyry. To follow this lecture you will need either the Readings book, or Richard McKeon (ed.), Selections from Medieval Philosophers (New York: Charles Scribner's Sons).

From the introduction by Watts you will have gathered that Boethius was both a philosopher and a politician. This combination of roles was recommended by Plato and exemplified (imperfectly) in Roman history by Cicero. Cicero also preceded Boethius as a translator of Greek philosophy into Latin. E.K. Rand in his chapter on Boethius in his Founders of the Middle Ages quotes from Boethius' preface to his commentary on Aristotle's Categories, written in the year Boethius was consul. He says:

Although the cares of my consular office prevent me from devoting my entire attention to these studies, yet it seems to me a sort of public service to instruct my fellow citizens in the products of reasoned investigation... I am glad to assume the... task of educating our present society in the spirit of Greek philosophy... this is truly a part of my consular duty...

. As Rand remarks, this is reminiscent of Cicero's preface to his Tusculan Disputations. In the passage Watts quotes in his introduction, p.12, Boethius says he will show that the Aristotelian and Platonic philosophies harmonise, and do not contradict one another, as is widely supposed. This was also Cicero's opinion. He says: "Plato left behind him the peripatetic [Aristotelian] school and the academy, which have different names but agree in substance" (Cicero, Academica II.v). One of Boethius' works is a commentary on Cicero's Topics.

Boethius and Neo Platonism

So Cicero was an important influence on Boethius, but the most important was Plato, who strongly advocated the combination of philosophy with politics. In Republic 473 d Socrates says:

There will be no end to the troubles of... humanity... till philosophers become kings in this world, or till those we now call kings and rulers really and truly become philosophers, and political power and philosophy thus come into the same hands.

In the myth of the cave, Republic 514 ff, those who climb out of the cave and see the real world and the sun must go back down to free the other prisoners still watching shadows. This is politics, properly understood; freeing mankind from delusions, turning them toward reality. In the Republic Plato describes the curriculum for the education of such philosophical rulers. It includes music (Rep. 398 ff), mathematics (524 ff) - including arithmetic, geometry and astronomy - and dialectic (531 ff). These are the subjects of some of Boethius' books (mentioned by Watts, p.13) - his Music, Arithmetic, Geometry (now lost), Astronomy (also lost), and his various works on logic (logic is part of what Plato meant by dialectic). The philosophical schools of Alexandria were following this Platonic curriculum. Boethius' works on these subjects are translations of, or are closely based on, the textbooks used in those schools. In the Alexandrian schools they read Plato, and also Aristotle. According to the neo-Platonists Aristotle's philosophy was for the most part complementary to Plato's, not in serious conflict with it. Porphyry (who edited the works of the founder of neo-Platonism, Plotinus) was especially keen on Aristotle. He wrote an introduction to Aristotle's writings on logic. He also wrote a work entitled, "On the unity of the doctrines of Plato and Aristotle", which would perhaps have been the basis of the book Boethius planned to write to prove the same thesis.

So in effect, when Boethius set out to make Greek philosophy available to his fellow citizens of Rome, he set out to translate the books that were read in the neo-Platonic schools of Alexandria. He completed the textbooks on music, arithmetic, geometry, astronomy, and logic, but he didn't get far in his very ambitious project to translate all of both Plato and Aristotle: he did not translate any of Plato, and only Aristotle's logic which is volume 1 in the 12 volume Oxford translation of Aristotle. But what he did translate was the basis for philosophical education in Europe until the translations of the twelfth century; and those translations would not have been made, or would not have been widely copied and studied, if there had not been a reading public who had been prepared by reading Boethius to take an interest in Greek philosophy.

Let me say something more about the schools of Alexandria, and about their study of Aristotle. The leading neo-Platonists Plotinus, Porphyry, and Proclus, were strongly opposed to Christianity. Porphyry wrote books against Christianity. These books were destroyed by order of the Christian emperors. What they contained is now known only through quotations by Christians who wrote to refute them. For an outline see Pierre Courcelle's chapter in Arnaldo Momigliano, The Conflict Between Paganism and Christianity in the Fourth Century. Proclus wrote after Constantine's conversion to Christianity and he does not attack it openly. Henry Chadwick writes: "Proclus writes as an enraged pagan, slipping in quiet references to Christianity in a tone of cold anger, as if 'the prevalent opinion' were a kind of intellectual Black Death... " (Chadwick, Boethius, p.17).

So when Christians studied philosophy in the new Platonist schools there were disagreements and controversies. The Christians did not accept that the One, the highest source of reality, was "beyond being" (as Plotinus said: he said this because "a being" has a nature, which implies, he thought, some duality between the nature and what has it - in the One there can be no duality). The Christians did not accept that the highest principle was not a being because in the Bible at Exodus 3:13-14 they read that God's name is "He who is" (in the Greek version, the Septuagint - "I am" in modern translations from the Hebrew). Nothing could be higher than God, so the highest reality cannot be "beyond being". Plotinus had spoken of three "hypostases" superior to the sensible world: the highest is The One (= the Good), below that is Intellect (which is the highest being), below that is the World Soul, and lower still there is our world, containing our souls and intellects. The Christian neo-Platonists rejected the three superior hypostases and held that God is the One, the Good, Intellect and highest Being. While according to Plotinus the other hypostases and the world itself emanated from the One necessarily and eternally, according to his Christian followers God created the world voluntarily a finite time ago. On this last point the Christian John Philoponus wrote a refutation of Proclus on the eternity of the world. On these topics Boethius was a typical Christian neo-Platonist. Those who suggest that his writing a Consolation of Philosophy shows that at the end of his life he was a philosopher and not a Christian do not give enough weight to the fact that his philosophy is a characteristically Christian version of neo-Platonism.

It has sometimes been suggested that conflict between pagans and Christians was the reason why Aristotle's logic and physics were prominent in the curriculum of the schools of Alexandria: study of these works was a good way to begin the study of philosophy without immediately becoming involved in religious controversy. This may have been a reason, but I think the main reason was that these Platonists could see the value of Aristotle's work, and could also see that most of it was compatible with Plato's. And Plato's dialogues and the whole platonic tradition encouraged attention to conflicting theories and arguments; they would not have avoided reading and discussing valuable philosophical works just because they disagreed with Plato. Anyway, for whatever reasons, the neo-Platonists wrote detailed explanatory commentaries on Aristotle's works.

Aristotle's writings needed introductions and explanations. Aristotle wrote some dialogues praised by Cicero, who was a good judge, for their elegant style. But they have not survived except in fragments quoted by other authors. The works that have survived are Aristotle's notes for his lectures in the Lyceum. Or perhaps what we have is some editor's compilation into books of somewhat disorganised and fragmentary collections of notes Aristotle left when he died.

Aristotle, or more likely his editors, arranged his works into a systematic order, which became standard and is still found in editions of Aristotle's complete works. This order resembles the Stoic division of philosophy into its parts. According to the Stoics, philosophy consists of (1) Logic, (2) Physics (in the sense of philosophy of nature), and (3) Ethics. Similarly, Aristotle's complete works include, in order, (1) logic, (2) philosophy of nature, and (3) practical philosophy. Division (2), the philosophy of nature, includes a book entitled Physics, on nature in general, another entitled On the Soul (De Anima), on living nature in general, and various books on particular aspects of nature, including quite a bit of biology (a subject of which Aristotle was one of the founders). These works are followed by the Metaphysics, a study of beings in general and God in particular. Division (3), practical philosophy, includes ethics, politics, poetics and rhetoric. So division (1), the part to read first, was Logic. Aristotle's books on Logic are entitled: Categories, On Interpretation, Prior Analytics, Posterior Analytics, Topics, On Fallacies (De sophisticis elenchis, On Sophistical Refutations). In the neo-Platonic schools they read first Porphyry's Eisagoge (Isagoge) or Introduction, which explained some of the terms the reader encounters in the first book of Aristotle's logic, The Categories.

PORPHYRY'S ISAGOGE

So now, as an introduction to Boethius' commentary on Porphyry's introduction, let me give you a brief introduction to Porphyry's introduction and to Aristotle's Categories.

Several of Plato's later dialogues are attempts to work out a definition for something following the method of division. For example, the Statesman is an attempt to define what statesmanship is, and it proceeds by looking for the larger class in which this art is likely to be found and then distinguishing various sub-classes and sub-sub-classes until statesmanship is isolated. The leading character, a stranger, starts with knowledge, divides it into critical and directive, divides directive into that which originates commands and that which passes commands on, divides originative into that which is concerned with production of lifeless things and that which is concerned with the production of living things, divides living things into tame and wild, and so on through a few more stages, and at 266 c arrives at a definition of statesmanship as the art that originates directions for the tendance of wingless bipeds. (As is often the case, Plato argues partly in jest: later academics and Aristotelians defined man as a rational animal, which is more complimentary than "wingless biped".) This definition is then subjected to destructive criticism and the search for a definition starts again, again by trying to distinguish between statesmanship and other similar arts belonging to some larger class.

This process of division could be represented by a diagram, the largest class at the top, lines going down to sub-classes, more lines down to sub-sub-classes, and so on, like a family tree. If you turned the diagram upside down it would look more like a tree, with the largest class as the root and the final sub-divisions as the twigs. The Greek word for a family is genos, Latin genus, which was also the name the philosophers gave to the highest class, genus, in English genus; so the analogy with a family tree is appropriate. The sub-classes of a genus are called "species". In the middle levels of the diagram, each class is both a genus with respect to its sub-classes and a species with respect to the higher class to which it belongs. The top of the diagram is the highest genus and at the bottom are the lowest species, and between are intermediate classes which are both genera and species. (Genera is the plural of genus, the plural of species is the same, species). The definition of a species consists of its genus and what differentiates that species from other species of the same genus. Such a definition is said to be by genus and specific difference.

This sort of diagram is now called "Porphyry's tree", though it could just as well be called Plato's tree or Aristotle's tree. In fact Porphyry does not set out any tree fully, but one that he sometimes alludes to would look like this (I suggest you set it out on paper): substance at the top, divided into corporeal substance and incorporeal substance; corporeal substance divided into animate and inanimate; animate (i.e. living) divided into plant and animal; animal divided into rational and irrational; man is the only species in the "rational" division of animal. So the definition of man by genus and specific difference is "rational animal" - "rational" being the character that differentiates man from other species of the genus animal, or so the ancients believed.

The main purpose of Porphyry's Introduction is to sort out and explain the terms genus, difference, species, definition, property and accident, which the reader will encounter in Aristotle's Categories, and indeed throughout Aristotle's work. Genus, difference, species, and definition I have explained. A "property" is something that is not part of the definition of some species, but is in fact found in all individuals of that species, and not found in individuals of any other species. Note the meaning here of "proper": it means what is peculiar to, what is found only in. Thus "having interior angles adding up to 180 degrees" is a property of triangles as distinct from other rectilinear figures. To have angles adding to 180 degrees is not part of the definition of a triangle (it is defined as a plane figure bounded by 3 straight lines), but all triangles do have interior angles adding up to 180 degrees (this can be rigorously proved), and no other rectilinear plane figure does. An accident is a characteristic found in some members of a species but not in all, and found also in other species: some cats are black, some are not, some black things are not cats; so being black is accidental to a cat. (If only cats, but not all cats, were black, blackness would be a "proper accident" of cats - it would be accidental to a cat but proper to, i.e. found only in, cats.)

Besides genus, difference, species, property and accident there are also individuals, e.g. the individual cats, which all belong to the species cat. Let the individual human beings be named Socrates, Plato, Aristotle, and so on (in medieval texts the names of these famous philosophers were often taken as stand-ins for any proper name, like "Joe Blow") Genera, species etc. are predicable of individuals: Socrates is a man, Plato is a man, Aristotle is a man, and so on. Similarly Socrates is rational, Plato is rational, Aristotle is rational, and so on. Or if these are the names of black cats, Socrates is black, Plato is black, and so on. Recall that a universal is a concept or word that can be predicated of many subjects, and that "to be predicated" means to appear in the predicate of a statement of the form "S is P" - "Socrates is rational". Genera, species, differences, properties, accidents are predicable of many individuals, i.e. they are universals.

ARISTOTLE'S CATEGORIES

Now Aristotle suggests that if you construct (what we call) Porphyrian trees for all the universals, there will be just ten separate trees. These trees (or perhaps just the highest genera) are the ten "predicaments" or "categories". (Greek kategoreisthai, and Latin predicare, mean "to predicate".)

Let me illustrate what he means. Take the term black. "Black" is a universal, predicable of many individuals - many cats, many kettles, and so on. Black is a species of colour, colour is the genus. Colour in turn is a species of quality: there are other sorts of qualities besides colour. That is as far as it goes, Aristotle thinks: Quality is a highest genus, of which black is one of the lowest species.

Another example: take "being to the right of" (Socrates is sitting to the right of Plato): this is a species of spatial relation; there are other kinds of relations that are not spatial (e.g. being more intelligent than). Of all such species relation is the highest genus. Relation does not come under any higher genus.

So Aristotle supposes that if you put all predicable terms under genera, and those genera under higher genera, you will arrive at just ten categories, ten highest genera: substance, quantity, quality, relation, place, time, position, state, action, being acted on. See The Categories, ch. 4.

The other nine categories after substance are categories of accidents, i.e. of predicates a substance may have or may lack without being a numerically different substance. (If you can count things they differ numerically: you [substance] as you become bigger [quantity] or more learned [quality] do not thereby become a numerically different person. Aristotle says: "The most distinctive mark of substance appears to be that while remaining numerically one and the same it is capable of admitting contrary accidents: one and the same colour can't be black and white, but an individual person can be at one time white, at another time black".)

The species, genera and differences in the category of substance express the essence of the thing they are predicated of. The essence is the answer to the question "What is it?" If you say, pointing to Socrates, that this is a rational animal, a man, you are saying what he is. If you say that someone is learned you are answering the question, not "What is he?", but "Of what quality is he?" In English this sounds awkward, but in Latin quale, meaning "of what quality?", and quid, meaning "what?" were equally idiomatic ways of beginning a question. So species, genera and differences in the category or predicament of substance express essence, i.e. answer the question What is this?

Aristotle distinguishes between primary and secondary substance. Secondary substances are certain of the universals, primary substances are individual things. Not all universals are secondary substances; some stand for qualities, quantities, etc., and these are not secondary substances, but some universals stand in some way for the substances of things, and these are secondary substances -- for example "animal", "man", "rational". Socrates (and I don't mean the name, but the actual person) is a primary substance, substance in the primary or basic sense. Aristotle says: "Primary substances are the entities that underlie everything else, and everything else is either predicated of them or present in them". Universals of whatever category are "predicated of" individual beings like Socrates: Socrates is a man (man being secondary substance), Socrates is tall (quantity), Socrates is wise (quality), Socrates is older than Plato (relation) and so on. By "present in" Aristotle means that the realities to which terms signifying accidents refer exist only in individual substances: Socrates' tallness exists in Socrates, his wisdom is present in him, and so on. The realities to which the words and concepts in the nine categories of accidents refer have no independent existence - they are the quantities, qualities, relations etc. of substances. Primary substance is not predicable of a subject and not present in a subject: it is the subject. You can say "This is Socrates", but here the predicate is the name Socrates, not the very person: only words or concepts, not things, can be predicates.

According to Aristotle, words may be univocal, equivocal or analogous (Aristotle does not use the term "analogous", though medieval Aristotelians do; instead of "analogous" he says "predicated according to prior and posterior"). Equivocal means ambiguous, having many unrelated senses; e.g. "pen" can mean a writing implement or an enclosure for holding animals, and these senses are quite unrelated. A univocal word has just one sense. There aren't too many words like that; perhaps the names of tools of trade, like screwdriver or hammer are examples. A term used analogously has a basic sense and other senses somehow related to the basic sense. For example, "healthy" in its basic sense is a state of an animal body; a healthy tan is a sign of health in the basic sense, a healthy lifestyle is a cause of health in the basic sense - "healthy" is not being used in a merely equivocal way, because the senses are not unrelated.

The ten categories can be regarded as modes of being, that is, different ways in which it can be said that something is something ("being" is sometimes a noun, as when we say that God is a being, but it can also be the present participle of the verb "to be", of which "is" is a form). But the ten categories are not species of being. Aristotle says that being is not a genus. This is because any possible differences are also themselves modes of being, and a genus cannot be predicated of its own differences (we could not say that "rational is an animal"). (See Aristotle, Metaphysics B.3, 988 b23-27.) According to Aristotle "being", since it is not a genus, is applied to the ten categories in different senses - it is an ambiguous or equivocal term. But it is not simply equivocal. Substance is being in the basic sense (and by "a being" we mean a substance); the other modes of being - being tall, being learned, being to the right of, and so forth, are being in secondary or derived senses. See Metaphysics N.2, 1089 a6. The nine accidental kinds of being are being because they have some relation to substance - they express the quantities of substance, the qualities of substances, the relations of substances, and so on - "of substance" indicates a relation to substance. So in the senses of "being" there is priority and posteriority - being in the sense of substance is the prior sense, being in the sense of this or that other category is a posterior sense.

The same is true of "the Good". According to Aristotle, criticising Plato, there cannot be an Idea or Form of Good, because the many goods are not good in the same sense. In N.E., I.6, 1096 a15 ff Aristotle says:

The term "good" is used both in the category of substance, and in that of quality, and in that of relation, and that which exists by itself, i.e. substance, is prior in nature to the relative (for the latter is like an offshoot or accident of being)... there could not be a common Idea set over all these goods. Further, since "good" has as many senses as "being" (for it is predicated both in the category of substance as of God and of reason [God is good], and in quality, i.e. of the virtues [justice is a good quality], and in quantity, i.e. of that which is moderate, and in relation, i.e. of the useful, and in time, i.e. of the right opportunity, and in place, i.e. of the right locality, and the like), clearly it cannot be something universally present in all cases and single [as a Form or Idea is supposed to be]; for then it could not have been predicated in all the categories but in one only.

So being, and also anything predicable in all the categories of being, like good, is not a genus, does not have one Form or Idea.

BOETHIUS ON PORPHYRY

This should give you an idea of the contents of Aristotle's Categories and of Porphyry's Introduction to the Categories. Let us go on now to look at Boethius' commentary on the preface to Porphyry's book. You will often need to stop the tape to find the words I refer to.

Open McKeon's Selections at p. 70 (Readings at handwritten p.11). Fifteen lines down the first page, change "related with human souls" to "acquired by human minds". (It might be useful to make a marked strip of paper as a ruler.) On the top line of p.71, change "judgment to perception" to "the judgment of perception". Third line of p.72, change "genus" to "race", and on line 5 change "explains" to "disentangles". Change "how" on p.72 lines 16 and 25 to "of what quality". Read paragraph 1, down to p.72 line 27.

This is an outline of some points of Aristotle's account of the soul. All living bodies have a soul. A plant has a vegetative soul that enables it to grow. An animal has a "sensitive" soul, which includes a vegetative part and also has powers of sense, memory and imagination. A human being has a rational soul, which does what plant and animal souls do and also analyses and develops sensations and imaginations into knowledge.

The point of the next paragraph is to show the need to study logic. Philosophy has two ends or purposes mainly, to know the natures of things and to decide what should be done (deciding what should be done is what he means by "that that which moral gravity may later perform may come to be known beforehand", p.73.1-2). These parts were called physics (which studies the nature of things) and ethics (or "speculative" and "practical" - these terms are used in the last two lines of p.75). But before physics and ethics the ancient philosophers put logic. Read paragraph 2. Notice "topic" (p.74.23); topos is the Greek word for place. Aristotle's Topics is a survey of the different "places" to look for arguments to prove various sorts of conclusions - a repertory of possible lines of argument.

Paragraph 3 (which I have cut off at the bottom of p.75) discusses the question whether logic is part of philosophy or merely a tool used by philosophy. (In the standard edition of Aristotle's work the books of logic made up a volume called the Organon or tool, instrument.) Boethius decides that logic is both part of philosophy and an instrument used by the other two parts.

In the paragraphs I have omitted Boethius tells the reader what Aristotle's Categories is about and what Porphyry's Introduction to the Categories is about, and how useful these books are.

This brings us to paragraph 10, on p.90. Read to halfway down p.91. In the quotation from Porphyry there are three questions. Write (1) in front of "they subsist or whether they are placed in the naked understanding alone". Write (2) in front of "they are corporeal or incorporeal", and (3) in front of "they are separated from sensibles or placed in sensibles". The second and third questions arise if the first of the alternatives is chosen for the first, i.e., that they subsist - notice the words just before (2), "whether, subsisting" - you might put a comma before and after subsisting, to mean "whether, if they do subsist,...". Now insert corresponding numbers: (1) at the beginning of the fourth line from the bottom of p.91; (2) at p.92.6, before "But even"; (3) at p.92.20, before "For there remains". Put a mark at p.93.1, "These questions", and read up to that mark.

A few comments. At p.91, 3rd line from the bottom, "established in the nature of things" means "is to be found in reality". In Latin the phrase "In rerum natura", literally "in the nature of things", just means "in the world", without any special emphasis on nature. Near the bottom of p.92 he is referring to things like lines and triangles: geometry does not treat these as bodies - the fact that the line is drawn with white chalk on a blackboard is of no significance for Geometry; yet such things as lines and triangles do not actually exist except in bodies.

This brings us to the top of p.93. Some corrections: At 93.4 insert "in such a way" in front of "that I may neither"; at 93.8 change "ambiguity" to "doubtfulness". Put a mark at 94.26, "But if genera", and read to there.

Some comments. Put brackets round the passage from 93.28 "Yet if there are genus and species but they are multiplex" down to 94.7 "since no end of the process occurs". In this bracketed section Boethius argues that a genus or a species must be one in number: if you were counting the beings in the universe you would give a genus or species just one number. Before the bracketed section he argues that if a genus or species is common to the many species or individuals of which it is predicated then it can't be one in number, and can't exist; after the bracketed section (down to p.94, line 22) he argues that if it is one then it can't be common. In short: if common then not one, if one then not common. From each of these two "if" statements it follows, since a genus or species is common, that it is not one. And if it is not one, then it can't exist. To sum up the whole passage: a genus must be one in number; but since, contradictorily, it can't be one in number, it can't exist.

Let's look at the bracketed section. Suppose the genus "animal" were not a unity - suppose there were many genera of animals. But since all the animals are called animals because they are in some way alike, corresponding to this general likeness and to the name "animal" that they all have there will be a comprehensive genus animal, additional to the many genera of animals: and if that is also not one but many, there will be another genus animal above that, and so on in infinitum. (This argument is reminiscent of the "third man" argument found in Plato's Parmenides at 131e ff, though it is not quite the same argument.) So each genus, and by similar argument each species (e.g. lion), must be one and not many.

But how can a genus be one? The whole nature of the genus must be in each of its many species. Take lions and tigers as species of animal: the whole nature or definition of animal, whatever that is - say living body having sense perception - is found in both species: it is not as if lions are living bodies and tigers have sense perception, both are living bodies having sense perception, and similarly all the other species of animals fully satisfy the definition, all have the whole of the nature of animal. Now if the whole "form" or idea of the genus is participated or shared in by each of many species, it cannot be numerically one thing. This is a point made in Plato's Parmenides at 130e ff. Re-read p.93.

Highlight 93.26, "for everything which is, is because it is one" - a characteristic neo-Platonic statement (compare Consolation of Philosophy, 105.29; Proclus, Elements of Theology, tr. E.R. Dodds, (Oxford: Clarendon Press, 1963), proposition 13 in Supplement, p.106; and Supplement, p.92, point 5). Stop the tape to follow those references up. If everything is because it is one, then if a genus or species cannot be one thing it cannot exist.

The section before the bracketed section argues that if a genus or species is common it cannot be one. Now on p.94 after the bracketed section he argues that if it is one it can't be common. Re-read down to the mark before "But if genera". Highlight 94.21 "the substance". Animality is part of the substance of a lion: it is part of what it is as an independent being, a substance. If it belonged to it like a spectacle belongs to all the spectators it would not be part of what a lion is.

So far Boethius has argued against the first alternative in Porphyry's first question (on p.91). Now in the section beginning "But if genera" he argues against the second: that "they are placed in the naked [bare] understandings alone". An amendment to the text: p.94.29-30, between the dashes, read "what is taken from no subject is empty, for an idea cannot be made from no subject". Put a mark at 95.7, before "Thus", and read to the mark.

Comment. The translator has used "idea" in this passage to translate "intellectus", which previously he had translated as "an understanding". Don't take it in the sense "idea" has in Plato's philosophy but as "idea" in the modern sense, a thought in someone's mind. The argument here is this: If genera etc. are thoughts, then either they derive from no object (and this is ruled out "for an idea can not be made from no subject"), or they derive from things as they really are, or from things otherwise than as they really are; if from things otherwise than as they really are then genera etc. are false thoughts; if from things as they are, then after all genera etc. are found in the world and we are back with the first alternative, the position argued against on pp.93-4. To put all this in other words: if we don't get our classifications of things from the world in any way at all, then they are altogether empty. If they are in some way based on the world but do not accurately reflect the way it really is, then they are false or misleading. (Some people these days do say that our classifications are arbitrarily imposed on the world -- I don't know how they think they know that: Boethius would say that if this is so then classification falsifies.) If our ideas of genera and species are based exactly on the way things are, then there are genera and species in reality.

A small amendment to the text at 95.10-12. Read: "must be set forth concerning the five predicables aforementioned with the care of disputation", i.e., with logical skill, since we are dealing with an apparently impossible problem. Read to the end of paragraph 10.

Para. 10 illustrates what is sometimes called the aporetic method of ancient philosophy, practised also in the middle ages. Aporos in Greek means "without passage" (our word "pore" comes from poros, aporos is the negative). An aporia is a situation from which there seems to be no way out: whichever way you turn there is some obstacle. In the aporetic method the first stage in discussing a topic is to construct such a situation, and then of course you try to find a way out. Whichever way you turn there is an obstacle: to each possible answer there is some objection. See in the printed introductory lecture, footnote 19. Another metaphor is the "knot": Aristotle says, "For those who wish to get clear of difficulties it is advantageous to discuss the difficulties well: for the subsequent free play of thought implies the solution [literally "untying"] of the previous difficulties, and it is not possible to untie a knot of which one does not know. But the difficulty in our thinking points to a 'knot' in the object; for in so far as our thought is in difficulties, it is in like case with those who are bound; for in either case it is impossible to go forward" - i.e. they are in an aporia; Metaphysics III.1, 995 a27 ff. Boethius refers to the "knot of doubt" at 93.9.

So what is the knot he has tied us in, in pp.93-4? A genus or a species must be one, because if it is multiple there will be a genus comprehending its multiplicity - and it that is not one, there will be an infinite series of genera. But on the other hand a genus or a species cannot be numerically one thing, because then it could not be, simultaneously and as a whole, part of the substance of the many things that come under it. And if it is not numerically one, it does not exist in the world. But then, if it doesn't exist in the world but only in our minds it must be either empty, if it is in no way based on things in the world, or misleading, if it is based on things in the world but not as they really are. The solution or untying of this knot will be to reject the last assumption: concepts or thoughts formed from things but not being in all respects as those things are need not be empty or misleading.

Put a mark at 97.10 in front of "Since genus and species", and another mark at 97.24 in front of "But this likeness". Amend 97.10 "Since genera and species" to: "Therefore, when genera and species are thought, then their likeness is gathered... ". Go back and re-read 92.28-93.1 (from "but others, although they are incorporeal..."), and then read para. 11 down to the first mark.

Boethius regards a mathematical object like a line as an incorporeal even though it exists only in a body (cf. 96.9-10, "all incorporeal things of this sort"). Such an object can be thought without reference to any body: in geometry we do not care whether the line is drawn in chalk on a blackboard or in pencil on paper. And this way of thinking does not falsify, it merely leaves out. Similarly we can think of the genus animal, as a living body capable of sense perception, leaving out whether the animal has fur, feathers or scales, four feet or two or none. Read on to the second mark. Some comments. On (97.13-14) "From individual men unlike each other": in thinking of the species man we leave out such differences as colour, sex, size and so on, and consider only the ways in which all members of the species are alike. On (97.22) "Unlike in number": numerically different, though alike in specific or generic nature - if we imagine counting all the individual members of the species they will be assigned different numbers even if they are otherwise exactly similar. So just as lines do not exist except in bodies, so genera and species exist only in individuals, but are thought in separation from the differences in which the individuals are unlike - at least numerical differences if the members of the species are exactly alike. On (97.20) "Thought universals": in our thought the genus is a universal, because it can be predicated of each of the many individuals - "This is an animal", "that is an animal", "the other is an animal" and so on. But as animality exists not in thought but in the real world, it is not universal but is in each individual something individual: this animal's animality exists in it. Read down to 98.12, "Plato, however". The individual animality existing in this animal is perceived in sensation, animality as predicable of many is understood by the intellect. "Genera and species subsist in one manner but are understood in another" (98.8): they subsist individually in sense-perceptible things, they are understood as predicable of many, with the distinguishing differences left out of the concept. Read the rest of para.11. The doctrine he has been explaining is Aristotle's as expounded by the peripatetic commentator Alexander of Aphrodisias (as he says at the beginning of para.11). Plato thought that each species or genus - or in his own words each Form or Idea - subsists as numerically one thing separate from all the individuals that share in it, and that these Forms are the objects of understanding. Boethius himself and Porphyry are Platonists, but after all they are introducing Aristotle. Read para.12. The first four lines are the next bit of Porphyry's text. The reference at 99.13 is not to himself, Boethius, but to an earlier writer, Boethus.

So re-read paragraphs 1, 10 and 11 and think it all over. In a few weeks time we will read Peter Abailard's commentary on the same passage of Porphyry.

Moderate realism

Historians of philosophy describe the theory of universals Boethius presents here as "moderate realism". Plato's theory they call "realism", meaning not that the sensible world is real (which is what "realism" means in modern philosophy), but that the ideas or forms are real, each of them being numerically one real entity existing in separation from the many sensible things that participate in it. Most medieval philosophers were moderate realists, some were realists or Platonists. The "moderate realist" view does not dispute that the forms or natures of things are real, but rejects the doctrine that each form is one and exists separately from the things which have it. Rather, each form exists multiplied in sensible things, but it can be "abstracted" or "drawn out" of sensation by the mind as a single concept predicable of many, a universal. The one form (not numerically one, but in some other way the same form) exists in many things and also as a concept in the mind: but it does not exist separately from things and minds.

In the fourteenth century William of Ockham took a different view. He does not deny that forms are real - a real form exists in each of the many individuals. But instead of saying that these are the same form, he says that the many forms of the many things resemble one another, and because they do resemble one another each of them can be referred to by the one sign-type, such as a word or a concept. At different times Ockham entertained two theories about the concept: in the earlier theory he held that the concept itself resembles the things it can signify, like a picture of them; in the later theory he held that the concept is a mental entity or act that can stand for things without picturing them, as a red lion outside a pub signifies that this is a pub without resembling a pub. On both of these theories there are concepts in the mind, and words in language, that can signify or refer to stand for any member of a set of resembling things. He does not deny that the forms of individuals truly resemble one another, or that their forms are real; what he denies is that it is the one form that exists both multiplied in the things and as a universal in the mind.