Archive for January, 2009

Isagoge: Chapter 11 — Of the Community and Difference of Species and Difference

Monday, January 26th, 2009

You’d think, given the title of the chapter, that this would another compare and contrast. Not so. What we get instead is a disquisition on combinatorial math. (Feel free to skip to the bottom.)

We have shown then, wherein genus differs from the other four, but each of the other four happens also to differ from the rest, so that as there are five, and each one of the four differs from the rest, the five being four times (taken), all the differences would appear to be twenty. Nevertheless, such is not the case, but always those successive being enumerated, and two being deficient by one difference, from having been already assumed, and the three by two differences, the four by three, the five by four; all the differences are ten, namely, four, three, two, one. For in what genus differs from difference, species, property, and accident, we have shown, wherefore, there are four differences; also we explained in what respect difference differs from genus, when we declared in what genus differs from it. What remains then, viz. in what respect it differs from species, property, and accident, shall be told, and three (differences) arise. Again, we declared how species differs from difference, when we showed how difference differs from species; also we showed how species differs from genus, when we explained how genus differs from species; what remains then, viz. in what species differs from property and from accident, shall be told: these, then, are two differences. But in what respect property differs from accident, shall be discovered, for how it differs from species, difference, and genus, was explained before in the difference of those from these. Wherefore, as four differences of genus with respect to the rest, are assumed, but three of difference, two of species, and one of property with regard to accident, there will be ten (differences altogether), of which, four we have already demonstrated, viz. those of genus, with respect to the rest.

We have five things, genus, difference, species, property, and accident. We’re going to compare and contrast each pair of these; and once we’ve compared and contrasted A with B, we don’t need to compare and contrast B with A. So there are 10 pairs, rather than 20. Woohoo. In the next chapter, I imagine, we’ll get on with comparing and contrasting difference and species.

Isagoge: Chapter 10 — Of Community and Difference of Genus and Accident

Sunday, January 25th, 2009

Genus and accident, compare and contrast:

It is common to genus and accident to be predicated, as we have said, of many things, whether they (the accidents) be separable or inseparable, for to be moved is predicated of many things, and blackness of crows, and of Ethiopians, and of certain inanimate things. Genus however differs from accident, in that genus is prior, but accident posterior to species, for though an inseparable accident be assumed, yet that of which it is the accident is prior to the accident. Also the participants of genus participate it equally, but those of accident do not equally; for the participation of accidents accepts intension and remission, but not that of genera. Besides, accidents primarily subsist about individuals, but genera and species are by nature prior to individual substances. Moreover, genera are predicated of the things under them, in respect to what a thing is, but accidents in respect to what kind of a thing it is, or how each thing subsists; for being asked, what kind of man an Ethiopian is, you say that he is black; or how Socrates is, you reply that he is sick or well.

One of the things about Aristotelian and Thomistic philosophy that I’ve had trouble wrapping my mind around is the notion of cause. I know what the four causes are: the efficient, the material, the formal, and the final, and I even think I mostly understand what they mean. But when I hear the word “cause”, my mind naturally assumes the efficient cause, often without any conscious decision on my part. Porphyry is helping with this, because he keeps pointing out that this is prior or posterior to that: which is equivalent to saying that this a cause of that or that is caused by this. Thus, genus G is a cause of species S within it; and species S is a cause of individual X which has accident A. The question remains, what kind of causes are these?

It seems to me that X is a material cause of A: if Socrates is sick, Socrates is the matter that is sick. X might be the efficient cause of A as well, as when Socrates is sick because Socrates has just chosen to drink a cup of hemlock. S seems to be the formal cause of X; and is G the formal cause of S? I dunno.

The second emphasized statement is also interesting. All beings which participate in a genus, that is, all beings which belong to the genus or of which the genus may be predicated, belong to it equally. All dogs, all cats, and all humans are animals to the same degree. But accidents support “intension and remission”. I’m not sure what he means by that. He might mean that accidents can come and go, but I don’t think so: for individuals which have a particular accident might have it equally, so far as they have it at all, and individuals which don’t don’t. I think he means that one can have an accident to a degree. A cat can be white, but also more or less white. Socrates can be sick, but also more or less sick, sick with a cold, or sick unto death (thanks to the hemlock).

Isagoge: Chapter 9 — Of the Community and Difference of Genus and Property

Tuesday, January 20th, 2009

Compare and contrast. First, we’ll compare:

Both to genus and to property it is common to follow species, for if any thing be man, it is animal, and if any thing be man, it is risible. Likewise to genus, to be equally predicated of species, and to property, (to be equally predicated) of the individuals which participate it; thus man and ox are equally animal, and Anytus and Melitus risible. It is also common that genus should be univocally predicated of its proper species, and property of the things of which it is the property;

So if A is a member of a species S, then we know immediately that A is a member of the genus G to which the species belongs, and that A has all of the properties P of S. Further, not only is G predicated of all species within it, just as P is predicated of all individuals in S, but each is predicated univocally, that is, in exactly the same way. When we say that all men laugh, the term “laugh” doesn’t have different shades of meaning for different men, but it means the same thing for all men. Similarly, when we say that all men are animals, we mean it in the same way for all men.

And now we’ll contrast.

…still they differ, because genus is prior, but property posterior, for animal must first necessarily exist, afterwards be divided by differences and properties.

You can’t have a species until you have a genus, and you can’t have a property until you have a species.

Also genus indeed is predicated of many species, but property of one certain species of which it is the property.


Besides property is reciprocally predicated of that of which it is the property, but genus is not reciprocally predicated of any thing, for neither if any thing is an animal, is it a man, nor if a thing be animal is it risible, but if any thing is a man it is risible, and vice versa.

From this it is clear that Porphyry’s using the word “property” in its narrowest sense, as we saw in Chapter 4.

Moreover, property is inherent in the whole species, of which it is the property, in it alone, and always, but genus in the whole species indeed of which it is the genus, and always, yet not in it alone;


…once more, properties being subverted do not co-subvert genera, but genera being subverted, co-subvert species, to which properties belong; wherefore, also those things of which there are properties, being subverted, the properties themselves also, are co-subverted.

If being A does not have property P of species S, it might still belong to some other species of genus G. But if being A doesn’t belong to genus G, then it clearly doesn’t have property P.

Isagoge: Chapter 8 — Of Community and Difference of Genus and Species

Saturday, January 17th, 2009

Once again, we compare and contrast. Here’s what Porphyry has to say:

Genus and species possess in common, (as we have said,) the being predicated of many things, but species must be taken as species only, and not as genus, if the same thing be both species and genus. Moreover, it is common to them both to be prior to what they are predicated of, and to be each a certain whole; but they differ, because genus indeed comprehends species, but species are comprehended by, and do not comprehend genera, for genus is predicated of more than species. Besides, it is necessary that genera should be presupposed, and when formed by specific differences, that they should consummate species, whence also genera are by nature prior. They also co-subvert, but are not co-subverted, for species existing, genus also entirely exists, but genus existing there is not altogether species; genera too, are indeed univocally predicated of species under them, but not species of genera. Moreover, genera exceed, from comprehending the species which are under them, but species exceed genera by their proper differences; besides, neither can species become most generic, nor genus most specific.

I’m not going to go through this line by line; instead, I’m going to list the points I take away from it.

Aquinas frequently uses the word aspect, as in, “under the aspect of”. I’ve never felt very clear as to just what he means by it, but reflecting on this passage has helped bring me closer to it. An aspect, I take it, is a way of looking at something, a way of analyzing it. Most things can be looked at in different ways.

Now, genus and species have much in common, because all species but the most specific are also genera, and all genera but the most generic are also species. Take animal, for example, which is a species of body, but a genus containing a vast number of species, including Man. But while most genera are species, and most species are genera, it is not the case that genus and species are the same thing. We can consider body as a genus, and as a species, and these are two different aspects.

OK, so what else do we learn from Porphyry?

  • Genus and species are both predicated of many things.
  • They are prior to that of which they are predicated, that is, they are causes in the Aristotelian sense.
  • They are each a certain whole (I’m not at all sure what this means).
  • A genus is prior to the species within it.
  • Equivalently, a genus is predicated of the species within it, but not vice versa.
  • Given genus G and species S within it, G and S co-subvert; I gather that this means that if X is not an S, then it isn’t a G either, and if it isn’t a G, then it isn’t an S.
  • On the other hand, G and S are not co-subverted; which I gather means that if X is an S you know it’s also a G, but if you know that it’s a G you don’t know whether it’s an S or not.

The talk of genera comprehending species and species not comprehending genera bugs me. As I understand it, the comprehension of a genus or species is what it means; the extension of a genus or species is the collection of beings of which it is predicated. The comprehension of man is wider than that of animal because it takes the comprehension of animal and adds rational to it; whereas the extension of man is narrower than that of animal because all men are animals but not all animals are men.

That latter appears to be what Porphyry is saying, or in other words, that animal includes man, and other species, but man doesn’t include animal in the same way. But I don’t see that this use of “comprehend” aligns with the description I’ve just given.

Isagoge: Chapter 7 — Of the Community and Distinction of Genus and Difference

Sunday, January 11th, 2009

I confess, I’ve been bogging down in Porphyry, not because he’s hard as because he’s dull; and I’ve been spending time on other books. But I want to finish the things I start, especially in this arena, so once more into the breach!

So: Genus and Difference, compare and contrast. Let’s go.

It is common to genus and difference to be comprehensive of species, for difference also comprehends species, though not all such as the genera; for rational, though, it does not comprehend irrational, as animal does, yet it comprehends man and divinity, which are species. Whatever things also are predicated of genus as genus, are predicated of the species under it, and whatever are predicated of difference as difference, will be also of the species formed from it.

Discounting the species “divinity”, as we’ve had to do in the previous parts of the Isagoge, this is straightforward. All species of animal are animals; all species rational beings are rational. Thus, genus and difference both comprehend species. Given that a species is the combination of a genus and a difference, this only makes sense.

When we say that they both comprehend species, what does that mean?

For animal being a genus, substance is predicated of it as of a genus, also animated, and sensible, but these are predicated of all the species under animal, as far as to individuals. As moreover, rational is difference, the use of reason is predicated of it, as of difference, yet the use of reason will not be predicated of rational only, but also of the species under rational.

Simply, I can predicate animal of all animal species; I can predicate rational of all rational species.

This too is common, that when genus or difference is subverted, the things under them are also subverted, for as when animal is not, horse is not, nor man, thus also, when rational is not, there will be no animal which uses reason.

Right. If I can’t predicate animal of a being, I can’t predicate any animal species of it; and if I can’t predicate rational of a being, I can’t predicate any rational species of it.

So, now, what are the differences?

Now, it is the property of genus to be predicated of more things than difference, species, property, and accident are, for animal (is predicated) of man and horse, bird and snake, but quadruped of animals alone, which have four feet; again, man of individuals alone, and capacity of neighing of horse alone, and of particulars. Likewise, accident of fewer things: yet we must assume the differences by which the genus is divided, not those which complete, but which divide the essence of genus.

Genus is predicated of more things than difference–than any difference within that genus, anyway. (A genus like animal is simply a species defined by the parent genus and difference, e.g., animate body; and so the difference animate will have the same extension as animal. But the extension of rational is clearly much less than the extension of animal. The same is true of species, property, and accident.

Moreover, genus comprehends difference in capacity, for of animal one kind is rational, but another irrational, but differences do not comprehend genera. Besides, genera are prior to the differences under them, wherefore they subvert them, but are not co-subverted with them. For animal being subverted, rational and irrational are co-subverted, but differences no longer co-subvert genus, for even if all of them should be subverted, yet we may form a conception of animated, sensible substance, which is animal.

The genus comprehends all of the differences within it, that is, all of them include the genus within their meaning; but none of the differences comprehend the entire genus. And if I should say, this being is not a member of this genus, then I’ve said that none of the differences in this genus can be predicated of it, but not the other way around. The genus still has meaning and can be conceived of, even in all of the differences which apply to it are denied.

Yet more, genus is predicated in reference to what a thing is, but difference in reference to what kind of a thing it is, as was observed before; besides there is one genus according to every species; e. g. of man, animal (is the genus), but there are many differences, as rational, mortal, capable of intellect and science, by which he differs from other animals. Genus also is similar to matter, but difference to form: however since there are other things common and peculiar to genus and difference, these will suffice.

Here, he seems to be using difference in the wider sense, not merely as the specific difference.

How useful it is to know any of the above is, I can’t say.

Maritain’s Introduction to Philosophy

Wednesday, January 7th, 2009

I’ve posted an (extremely brief) review of Jacques Maritain’s Introduction to Philosophy over at my other blog.

Isagoge: Chapter 6 — Of Things common and peculiar to the Five Predicates

Monday, January 5th, 2009

This chapter is both simple and straightforward:

Having discussed all that were proposed, I mean, genus, species, difference, property, accident, we must declare what things are common, and what peculiar to them. Now it is common to them all to be predicated, as we have said, of many things, but genus (is predicated) of the species and individuals under it, and difference in like manner; but species, of the individuals under it; and property, both of the species, of which it is the property, and of the individuals under that species; again, accident (is predicated) both of species, and individuals. For animal is predicated of horse and ox, being species, also of this particular horse and ox, which are individuals, but irrational is predicated of horse and ox, and of particulars. Species however, as man, is predicated of particulars alone, but property both of the species, of which it is the property, and of the individuals under that species; as risibility both of man, and of particular men, but blackness of the species of crows, and of particulars, being an inseparable accident; and to be moved, of man and horse, being a separable accident. Notwithstanding, it is pre-eminently (predicated) of individuals, but secondarily of those things which comprehend individuals.

In short:

  • Genus is predicated of:
    • The species within it: Man is an animal.
    • The individuals within it: Socrates is an animal; Trigger is an animal.
  • Species is predicated of:
    • The individuals within the species: Socrates is a man.
  • Difference is predicated of:
    • The species of which it is the difference: Man is rational.
    • The individuals within that species: Socrates is rational.
  • Property is predicated of:
    • The species of which it is a property: Man can laugh.
    • The individuals within that species: Socrates can laugh.
  • Accident is predicated of:
    • The species of which it is an inseparable accident: Crows are black.
    • Individuals: This crow is flying.

Isagoge: Chapter 5 — Of Accident

Saturday, January 3rd, 2009

Here’s what Porphyry has to say about the term accident:

Accident is that which is present and absent without the destruction of its subject. It receives a two-fold division, for one kind of it is separable, but the other inseparable, e. g. to sleep is a separable accident, but to be black happens inseparably to a crow and an Ethiopian; we may possibly indeed conceive a white crow, and an Ethiopian casting his colour, without destruction of the subject.

They also define it thus; accident is that which may be present and not present to the same thing; also that which is neither genus, nor difference, nor species, nor property, yet is always inherent in a subject.

None of this should come as a surprise to anyone reading this blog. However, this is a reasonable place to mention something I learned yesterday, as I continue to work through Maritain’s Introduction to Philosophy: the term accident has a slightly different meaning in logic than in metaphysics. In logic, accident is one of the five predicables, along with genus, difference, species, and property; in metaphysics, as I understand it, the term includes the logical accidents, but also the logical properties.

Tunnel Vision

Thursday, January 1st, 2009

There are times when I really feel like the proverbial ten blind men studying the elephant. I focus on one thing, and miss how it is connected to everything else, or focus on one sense of a word and miss the richness inherent in it. Today, though, a number of things came together, and my thanks are due to Jacques Maritain’s Introduction to Philosophy, which was the proximate cause.

I’ve spent a great deal of time recently focussed on the notion of essence, and in particular the essence of a substance, and on essence as that which the intellect apprehends. Socrates is a man; that is his essence, and when I contemplate Socrates, “man” is what I apprehend.

This is all true, but the full picture is ever so much richer than that. Let us contemplate, not Socrates, but someone known personally to me. My father, for example. You can contemplate your father. When I contemplate my father, what do I apprehend?

Here’s the first thing I’ve been ignoring. As intelligible, my intellect apprehends essence; but as existing, my intellect apprehends substance. So the first thing, really, that I apprehend when I see my father is my father as a substance, something that exists in itself. He has identity. He is a real thing, a person, he has his own identity that continues through time. And then, as intelligible, I apprehend his essence, that he is a man.

But I know much more about my father than that. If that were all I could apprehend, there’d be no reason to honor my father over any random man in the street. But substance isn’t all that exists, and it isn’t the only thing that has essence.

In addition to his substance, my father also has many accidents, beings that exist within him, that exist with the support of his substance. That’s where the “sub” in “substance” comes from: substance stands under the accidents and supports him. Thus, my father is smart, strong, skilled, possessed of various experiences and relationships including that of being my father; these are accidents, but they are significant accidents. In point of fact, most of what makes my dad important to me are these accidents. Though they are not substances, my intellect can apprehend them as beings existing in the substance is my father. And these beings have essences; our relationship as father and son, for example, is a being in the genus of relation.

I can and do apprehend a vast constellation of beings and essences when I contemplate that single substance, my father. What a great and glorious thing that is!