Porphyry (232-305)
Reading: Isagoge

    Porphyry was a philosopher from Syria, and he was a pupil of Plotinus, whose teacher was the Alexandrian mystic Ammonius Saccus. In a way, we might credit Porphyry with being the founder of Neoplatonism, because it was he who prepared the lectures of Plotinus for publication in the form of the Enneads ("ennea" is Greek for "nine," he put them into six groups of nine lectures each), and it was he who published very successful defenses of Neoplatonism against old style Platonists, and particularly against traditional Roman objections (e.g. many people found it hard to accept that there is no real distinction between thought and the objects of thought).

    In addition to being responsible for transmitting and popularizing Plotinus, he wrote commentaries on many of the works of both Plato and Aristotle. Unfortunately the only work of this sort that survives is the Isagoge or "Introduction" to Aristotle's Categories. This work had an enormous and lasting impact on philosophy for more than a thousand years. The funny thing is that it may have been even more famous for the questions it does not address, than for the questions it does address. But it will be better to address this issue after discussing what he does talk about.

    Suppose I say that Socrates is 6 feet tall. The philosophical way to say this is to say that I am "predicating" 6 feet of Socrates. The Greek word for "predicate" is "katgore," i.e. "Category." Hence the title of the Aristotelian work that Porphyry is commenting on in the Isagoge. According to Aristotle, there are 10 categories: Substance, Quantity, Quality, Relation, Place, Time, Position, State, Activity, Passivity. In this particular case, the 6 feet I am predicating of Socrates is in the category of Quantity. If I said that "Socrates is sitting," I would be predicating something of Socrates in the category Position; if I said that "Socrates is being prosecuted for impiety," I would be predicating something of Socrates in the category "Passivity." Can you think of an example of predicating something of Socrates in some of the other categories? How about the category of Substance? If I said that Socrates is rational, or Socrates is an animal, I would be predicating something of Socrates in the category of Substance.

    The basic idea of the Categories is very simple. However, it is extremely bold of Aristotle to claim that there are exactly 10 categories, no more and no less. Essentially what Aristotle has done is to claim that all of reality can be summed up in just those 10 categories. This is intended to be an absolutely complete and comprehensive ontological map. As a philosopher, you should try to find counter-examples to this claim. Try to find predicates that don't fit in any of these categories. Let me know if you find any.

    In any case, according to Aristotle, everything real can be located somewhere in the 10 categories. This quite a bold claim to make, and it would be fascinating to see Porphyry discuss it. Unfortunately he doesn't say anything about this aspect of the Categories. But that is not his fault; the fault is with Aristotle. It is notoriously difficult find in Aristotle any adequate defense that just these 10 categories provide a complete ontological map.

    What Porphyry does instead is to focus on what all of the 10 categories have in common: "The Five Predicables:" genus, differentia, species, proprium, accident. My wording is a little different from the text you have, and I would like you to use mine, not the translations you have in the text. What Spade calls "difference" should be called "differentia," the plural is "differentiae;" and what Spade calls "property" should be called "proprium," the plural is "propria." The English word "difference" is too vague, and the English word "property" is too general. Differentiae and propria are very specific things, and it is important not to confuse them. But before I explain what they are, let me just point out one important thing.

    In the other short work of Aristotle's that has always been closely associated with the Categories, De Interpretatione 7 (17a38-b1) Aristotle gives a definition of "universal" and "particular." His definition is as follows:

Some things are universals, others are particulars. By universal, I mean what is naturally predicated of more than one thing; by particular, what is not. Man, for instance, is a universal, Callias a particular.

Go back to the example I started with: Socrates is 6 feet tall. Being 6 feet tall can be predicated of more than one thing, because several different people can be 6 feet tall. That makes the predicate "is 6 feet tall" a universal. What that means, is that the 10 categories, in addition to being an ontological map, give us 10 different kinds of universals.

    This immediately lands us right in the thick of the problem of universals. What is the status of universals? Or, to put the question another way, what is the status of the 10 categories? Do these categories mark real distinctions, or are they just Aristotle's own personal system for keeping things clear? Is this just Aristotle's own personal system of pigeon-holing everything in the universe? Would alternative systems be just as good for others as this one is for Aristotle? If Aristotle is a realist about universals, then he thinks that this list of 10 categories has some reality to it, that it marks natural distinctions. If he is a conceptualist nominalist about universals, then he thinks that this list is just his own personal system for organizing information. If he thinks that this list of 10 categories is useful just for grammarians as a way of cataloging the way people speak and write, then he is a strict nominalist. Although Aristotle does have a little to say about this issue in the Categories (he is some kind of realist), Porphyry avoids all such discussion. He is writing just an introduction, and there are other places where Aristotle says more about this issue, so probably he thought he would reserve his comments on the issue of universals for a different commentary on another work.

    This is good news for us. Since we are focusing on the problem of universals, and the Isagoge doesn't have much to say about it, we don't have to spend much time on Porphyry. Nevertheless, Porphyry's choice to focus on the Five Predicables was very smart. As an introduction to the problem of universals, the Five Predicables is an excellent choice. So let's spend a little bit of time on them.

    Go back again to my first example: Socrates is 6 feet tall. This is one of those predicates that you can say "just happen" to belong to Socrates. Socrates doesn't have to be 6 feet tall, he could be 5-9 or 5-11. In fact, earlier in his life, Socrates was 5-9, and earlier than that he was 5-8, and so on. How tall you are can change, even though you persist. Because your height is a predicate or property you can just happen to have, or just happen to lack, it is called an "accidental" property. In a way, it is an accident that you have it. If Socrates had smoked when he was a kid, it may have stunted his growth and he might never have made it to 6 feet. Lots of Socrates' properties are accidental, being pale, being a philosopher, having a beard, being in the agora, being the teacher of Plato and so on are all accidental properties of Socrates.

    Now that you know what an accidental property is, in a way you have some idea of the other four predicables: they are all non-accidental properties. Your genus, differentia, species and propria are all non-accidental. So now think; can you come up with a property Socrates has that is not an accident? Can you think of a property Socrates has that he couldn't just happen to have or just happen to lack? Can you think of a property that is a necessary prerequisite for being Socrates? Aristotle's central and favorite example of such a property is rationality. The reason he chooses rationality is because he thinks that by definition, all human beings are rational animals. His taxonomy is in the chart. It is no accident that Socrates is a rational being, because Socrates is a human, and by definition, all humans are rational. Actually this chart is useful because it sums up three of the Five Predicables: "Animals" at the top is Socrates' genus, "Rational" below it is Socrates' differentia, and "Human" is Socrates' species. I will give definitions for all of these in a moment, but there is just one last Predicable we need to see.

    A proprium is the only kind of property we don't have. To understand propria, try to figure out what is missing so far from our list of predicables. With the genus, differentia and species we have your essence, or nature. You define what something is by listing its genus, differentia and species. The accidents give you accidental properties the thing doesn't have to have. What's left? We've covered the essential properties and the accidental properties? Isn't that complete? If not, then what is left over would have to be non-accidental, and at the same time, non-essential. Does that make any sense? Could there be a property that you have which is not essential to you, but it is no accident that you have it? Could you have a property which is not a part of your essence, but which nevertheless is not something you could just happen to have or lack?

    The two most famous examples of propria are hinnibility in horses, and risibility in humans. "Hinnibility" is the ability to neigh or whinny. It is no accident that Mr. Ed that horse is hinnible, and yet it is not a part of Mr. Ed's essence that he be hinnible. Hinnibility is a necessary concomitant of his essence, or a necessarily entailment of his essence, or a necessary symptom of his essence, but it is not a component of his essence. Hinnibility follows from, but is not a part of the essence of a horse.

    The same goes for risibility in humans. Risibility is the ability to laugh at a joke. The reason that the ability to laugh at a joke requires the ability to understand a joke, which requires rationality, which is a part of our essence. This part of our essence makes it no accident that we are risible, although risibility is not actually a component of our essence.

    This covers all the bases. Not only do all predicates fall within the 10 categories, inside each of the 10 categories, all predicates fall under one of the Five Predicables. Every property is either a genus, a differentia, a species, a proprium, or an accidental property.

    Now it is time to give you definitions of all these. Just for completeness, I've compared Porphyry's list with Aristotle's. The definitions are sometimes Aristotle's, sometimes Porphyry's, sometimes a combination.

    At (22) Porphyry applies the Five Predicables to a specific case. He takes the category of Substance, and delineates its differentiae and species, all the way down to the particular individuals in the category. One complication in the tree is that, as Porphyry points out at(71), both genus and species are predicated of many things. How then are they distinct? The answer is that species and genus are relative terms, except at the extreme top and the extreme bottom. For example, Body is a species with respect to Substance, but it is a genus with respect to Animal. The very top is called "the most general genus" or the Summum Genus. The bottom is called "the most specific species" or the Infima Species. Nothing can be under the Individuals, because they are not predicables: Socrates is not predicated of anything, other things are predicated of him.

    But remember that the Five Predicables apply to every category, not just to the category of substance. Porphyry doesn't mention and examples, but here is one that Aristotle gives in Categories 6. In the category of Quantity, there are discrete quantities and continuous quantities. Aristotle says that time is a continuous quantity. The surfaces of bodies are also continuous quantities. Notice that there is no Subaltern Genus name for the discrete quantities. This is important because Aristotle's categories are not intended to be categories for the words we use in our everyday life. The categories are a philosophical or scientific tool for identifying the structure of reality. As scientists, we have discovered that there is a significant distinction between discrete quantities and continuous quantities, and so our language doesn't already have a word for this subaltern genus, there ought to be one, so we should feel free to make one up. This is just like entomologists making up names for species of insects they discover. If it is truly distinct from insects already studied, then even though a word for them doesn't exist, we ought to come up with one in order to refer to it more easily.

    Now bring back all Five Predicables. Take the number 6. You can now give the genus, species and differentia of the number 6. Can you think of any accidents of the number 6? Here is one: the number 6 is the number I chose to use as my example of a discrete quantity which is mathematical. Can you think of a proprium of the number 6? It is the sum of 4 and 2, and it is the only number that is the sum of 4 and 2. This is one of its properties, it is not a part of the essence of what it is to be the number 6, but it is also not a property which is just happens to have and could just happen to lack. This is a proprium of the number 6.

    One final point. How many feet tall is Socrates? 6 feet. Being a discrete quantity is an essential property of the number 6. Does that mean that being a discrete quantity is an essential property of Socrates? No. What quantity Socrates happens to have is an accidental property of his; the only essential properties you have come strictly from your species, differentiae and genus.

    Now for the all important three questions. Now that you know what the Five Predicables are, and now that you have some concrete examples in mind, it's time to address the status of those predicable. Here are the three questions (Isagoge (2)):

(A) Are genus and species real or are they situated in thought alone?
(B) If they are real, are the corporeal or incorporeal?
(C) If they are real, do they have a separate existence from particulars?

These are the three central issues regarding universals. The first question asks whether Realism or Nominalism is true. The second question asks whether, if Realism is true, real universal are "abstract entities" or "concrete entities." The third question ask whether, if Realism is true, real universals are Transcendent or Immanent.

    The main reason why it is so difficult to discuss the problem of universals is that somuch of the discussion is abstract. To help you get into the problem, let me give you some concrete examples. To begin with, here (on the next page) are two modern day Porphyrian Trees. They are both for biological taxonomies for human beings, but they are significantly different.

    Notice the difference in these taxonomies. The traditional taxonomies lumps all the "Great Apes" together and puts them in the same family. Humans are put in a separate family. The distinguishing differentia is supposed to be brain size. Although elephants and whales have larger brains in absolute size, if you calculate brain size relative to body weight, the primate brain is the largest of all mammals. Among primates, using the same relative calculation, our brain is three time the size of the average non-human primate brain. [But it is not just a monkey brain that got bigger. Our prefrontal cortex (responsible for attention span, some kinds of memory, linguistic skills and perhaps other intellectual and social functions) is 200% larger than that of other primates, but our motor cortex is about 30% smaller than that of other primates.] This seems to be one of those cases where the very large distinction drawn between us and the other primates is exaggerated because we want to think that we are so special. The grouping here is driven by some egotistical desire we have to set ourselves apart from all the other animals. This grouping is not driven by reality, by nature itself, but strictly by our desires.

    This is an example of a distinction which is "situated in thought alone." This is a mind-dependent distinction. It's like the difference between real money and play money. Real money is money only because we have a cultural practice of accepting certain pieces of paper as legal tender, but not accepting others as legal tender. But in reality is all just paper. The only distinction is in our heads.

    But compare the traditional grouping with the genetic one. Many taxonomists now argue that we ought to use the latter grouping, regardless of what that may do to our egos. Doesn't that suggest that we are capable of setting aside our own desires, and our own pre-conceived notions, and, as Plato said, "carve nature at its joints?" 98.4% of our DNA is identical to that of chimpanzees. That is a difference of only 1.6%. The difference between human and gorilla DNA is only 2.3%. Usually that close a genetic tie is found only among different species of the same genus. Isn't that a real similarity?

    Or consider the taxonomy of ladybugs. In everyday experience, ladybugs are pretty round bugs with red backs and black spots. But scientists don't use the coloration as the basis for classification. They classify them on the basis of structural features. The family Coccinellidae is a member of the order Coleoptera (the Beetles). One of the structural features that sets them apart from other beetles is the fact that they have only 3 tarsal segments (that means that their "feet" are divided into only 3 segments, as opposed to the 4 segments that many other beetles have in their "feet"). Identified in this way, not all lady bugs are red with black spots. The Ashy Gray Ladybug is ashy gray with black spots. Some ladybugs don't have any spots at all. On the other hand, there is a species of Leaf Beetle (Crioceris duodecimpunctata) which looks very much like a lady bug: it's red with black spots. The big difference, though, is that it actually has 4 tarsal segments, rather than 3, like the ladybugs. This raises an important taxonomic question.

    Here is a rival taxonomy for ladybugs. Instead of categorizing them by the number of tarsal segments, why not categorize them by color? If you are a nominalist about taxonomy, then in your view it doesn't really matter if we use the previous taxonomy or this one. For example, the authors of The Peterson Field Guide to Insects claim that "The arrangement of animals into these categories is arbitrary: it is the opinion of the specialist that determines the limits of a category." If it really is arbitrary, then this is just as good as the other taxonomy. However, there is a problem with the claim that the division is "arbitrary." Just two paragraphs before this claim that the division is arbitrary, the authors say this (emphasis added).

    Zoologists classify animals chiefly on the basis of structure: those with certain structures in common are placed in one group and those with other structures are put in other groups. These groups are divided and subdivided. The result is a system of categories, each with certain structural features in common, and a name.

    According to the very same authors, there is a commonality shared by all and only the members of a single group. The groupings, then, can't be totally arbitrary.

    But I suppose they could say that once the zoologist has selected the basic structures to group things, there is nothing arbitrary about the grouping; however, the selection of basic structures is itself arbitrary. But that doesn't seem to be the case. Here is what these authors say about the most important grouping: the species.

    The species is the basic category; it is a kind of animal. That is, it consists of individuals fundamentally similar in structure which interbreed to produce offspring but do not ordinarily interbreed with other groups.

    The species category is not one that is based on arbitrarily selected criteria, some structures that this zoologist wanted to use, but other zoologists didn't want to use. The species is based upon a grouping that is really significant: ability to interbreed and pass along genetic material. If groupings were truly arbitrary, then brown cows and brown spiders could form a single species. But clearly that's nuts. The capacity for passing along genetic material seems to be a real feature of the world, and recognizing the groups that have that capacity seems to be "cutting nature at its joints." In other words, biological taxonomy, at least at the level of species, seems to make a strong case for the existence of real groupings based on real commonality, i.e. real universals.

    So in answer to Porphyry's first question, whether genus and species are real or are "situated in thought alone," there is reason to think that perhaps at least with species, they are real. At the very least, by now you should have some fairly concrete idea about how nominalists and realists will differ.

    The second question is whether, if genus and species are real, they are corporeal. Another way philosophers ask this question is to ask whether universals are "abstract" or "concrete" entities. Here are the definitions.

An entity is abstract = it has properties, but no spatio-temporal properties.
An entity is concrete = it has spatio-temporal properties.

Strictly speaking, nominalists have to reject this question altogether, because they deny any real existence to universals. Nevertheless, it is possible for a nominalist to give a reductive analysis of universals. For example, a nominalist who is a conceptualist might say that talk about universals is really talk about concepts, which are ideas in people's minds (or "souls" as Porphyry would say.) Consequently, a conceptualist nominalist might say that universals are abstract entities.

    Alternatively, a nominalist paradigmatist might say that talk about universals is really talk about the resemblance of things to some concrete, particular, paradigmatic object. In this way the nominalist can say that a universal is a concrete entity.

    The same two options are open to the realist, but for different reasons. A transcendent realist, like Plato, can say that universals (Platonic Forms) have an eternal existence which is independent of space and time. An immanent realist, like Aristotle, can go either way. He can say that the universal is concrete, it is just that it is a scattered concrete entity, i.e. scattered in all of its concrete instances. Alternatively, an immanent realist can say that the universal itself is abstract, only its instances are concrete.

    Finally, the third question asks whether genus and species have an existence which is separate from particulars. In other words, the third question is whether genus and species subsist.

    subsistence = ontologically separate existence, existence as a basic subject as opposed to existence as a modification or property of a subject

    Look at Boethius (26). Boethius asks, "Who by any sense faculty ever grasped a line separated from a body?" Think of it this way. A true line in the mathematical sense, is a one-dimensional thing: it has length, but no width or depth. Consequently, it can't exist on its own. You can talk about the line that is formed by the edge of the desk, or the line in between two slabs of concrete on the sidewalk, but mathematical lines don't exist on their own: they don't subsist. Just as the Cheshire cat's grin only exists when its lips curl, so also a line exists only when some concrete physical object has a relatively straight edge. Only Plato accepts the subsistence of universals.