Archive for the ‘Isagoge’ Category

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.

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.

Isagoge: Chapter 4 — Of Property

Tuesday, December 30th, 2008

The remaining chapters are fairly short, and this is no exception. I’ve used the word property in the previous blog posts on the Isagoge; here, Porphyry defines it. The word has four senses:

Property they divide in four ways: for it is that which happens to some one species alone, though not to every (individual of that species), as to a man to heal, or to geometrize:

1. Properties peculiar to a species though not to every member, such as writing blog posts: only human beings do it, but not all human beings.

…that also which happens to a whole species, though not to that alone, as to man to be a biped:

2. Properties shared by all members of the species, but not confined to that species, as being bipedal.

…that again, which happens to a species alone, and to every (individual of it), and at a certain time, as to every man to become grey in old age:

3. Properties shared by all members of the species at some point in their history. This strikes me as a subset of sense #2.

…in the fourth place, it is that in which it concurs (to happen) to one species alone, and to every (individual of it), and always, as risibility to a man; for though he does not always laugh, yet he is said to be risible, not from his always laughing, but from being naturally adapted to laugh, and this is always inherent in him, in the same way as neighing in a horse.

4. Properties shared by all members of a species, and only by members of that species, as the ability to laugh.

Sense #4 is the narrowest sense:

They say also that these are validly properties, because they reciprocate, since if any thing be a horse it is capable of neighing, and if any thing be capable of neighing it is a horse.

Isagoge: Chapter 3:4 — Of Difference

Saturday, December 27th, 2008

In this paragraph, Porphyry wraps up his discussion on the nature of logical difference. I’m not sure it adds much, especially given Thomas’ discussion in De Ente et Essentia, but there are a few interesting points:

Again, they define it (difference) also thus: difference is that which is predicated of many things differing in species in answer to the question, of what kind a thing is, for rational and mortal being predicated of man, are spoken in reply to what kind of thing man is, and not as to the question what is he. For when we are asked what is man, we properly answer, an animal, but when men inquire what kind of animal, we say properly, that he is rational and mortal.

Porphyry made this distinction between “what a thing is” and “what kind of a thing it is” back at the beginning of the Isagoge. Let’s expand on this a bit.

If I point at Socrates, and ask “What is that?” no one is going to answer, “Oh, that’s an animal”. They are going to say, “Oh, that’s Socrates.” If I then ask, “What is Socrates?” I might get the answer “A man.” If I ask, “What kind of a man?” I might get a variety of answers, of which “A philosopher” is probably the best. It’s when I ask “What is man?” that the answer “an animal” becomes appropriate. In other words, the question “What is X?” has a different answer depending on whether X is an individual or a species/genus. In the former case, “X” is a member of its species; in the latter, a member of its genus. And the question “What kind of Y is X?” again has a different answer depending on whether X is an individual or a species/genus.

Regarding the word “mortal”, remember that for Porphyry “mortal” is the difference that distinguishes man from the gods.

For since things consist of matter and form, or have a constitution analogous to matter and form, as a statue is composed of brass, matter, but of figure, form, so also man, both common and specific, consists of matter analogous to genus, and of form analogous to difference, but the whole of this, animal, rational, mortal, is man, in the same manner as the statue there.

Matter is analogous to genus and form analogous to difference. Hmmm. I cannot recall, at the moment, whether Thomas says that form derives from difference or from species; and the word “analogous” here strikes me as somewhat loosey-goosey. I don’t think Porphyry’s using the word quite as Thomas does.

They also describe it thus, difference is what is naturally adapted to separate things which are under the same genus, as rational and irrational separate man and horse, which are under the same genus, animal. Again, they give it in this way: difference is that by which each singular thing differs, for man and horse do not differ as to genus, for both we and horses are animals, but the addition of rational separates us from them; again, both we and the gods are rational, but the addition of mortal separates us from them. They however who more nicely discuss what pertains to difference, say that it is not any casual thing dividing those under the same genus, but such as contributes to the essence, and to the definition of the essence of a thing, and which is part of the thing. For to be naturally adapted to sail is not the difference, though it is the property of man, since we may say that of animals, some are naturally adapted to sail, but others not, separating man from other animals; yet a natural ability to sail does not complete the essence, neither is a part of it, but only an aptitude of it, because it is not such a difference as those which are called specific differences. Wherefore specific differences will be such as produce another species, and which are assumed in explaining the very nature of a thing: and concerning difference this is sufficient.

Of the preceding I found the highlighted sentence to be the most interesting. I’ve often pondered what you do with characteristics that are shared by some but not all animals. Flying, for example, is characteristic of birds, but also of insects; but not of all birds or all insects. A bird, therefore is not a “flying animal”: “flying” is not the specific difference of the species “bird”. Rather, it’s a property of some kinds of bird, and of some kinds of insect.

Isagoge: Chapter 3:3 — Of Difference

Wednesday, December 24th, 2008

Next comes a small but confusing paragraph. We’ll take it line by line. Bear in mind that Porphyry has just finished an extended example of specific differences:

These indeed are especially useful for divisions of genera, and for definitions, yet not with regard to those which are inseparable accidentally, nor still more with such as are separable.

In other words, specific differences are useful for definitions, but not the other kinds of differences: those at are separable, and those that inseperable but accidental. As a footnote in the translation says, “accidental definition is, in fact, merely a description”. That is to say, I can describe a dog, or a breed of dog, in great detail but in doing so I haven’t captured the essence of a dog–I haven’t defined what it is to be a dog.

And indeed defining these, they say that difference is that by which species exceeds genus, e. g. man exceeds animal in being rational and mortal,

And again, this is reasonable, bearing in mind that for St. Thomas man is merely a rational animal, for all animals are mortal.

It’s the next bit that confuses me:

for animal is neither any one of these, (since whence would species have differences?) nor has it all the opposite differences, (since otherwise the same thing would at the same time have opposites,) but (as they allege) it contains all the differences which are under it in capacity, but not one of them in energy, and so neither is any thing produced from non-entities, nor will opposites at the same time subsist about the same thing.

I think what’s going on here is this: Porphyry is saying that a species has to have everything that pertains to its genus, and nothing that is opposite to its genus. I suspect that by “capacity” and “energy” Porphyry means something like “potency” and “act” (or possible vice-versa), but I’m not sure. He’s using terminology I’ve not run into before.

Isagoge: Chapter 3:2 — Of Difference

Monday, December 22nd, 2008

Good grief, I’ve been remiss. Time to get back in harness.

In the second paragraph of the chapter 3 of the Isagoge, Porphyry expands on the notion of difference. I think I’m going to have to build some outlines, here.

According then, to the differences which produce another thing do the divisions of genera into species arise, and the definitions arising from genus and such differences are assigned. On the other hand, as to those which only make a thing different in quality, diversities alone consist, and the changes of subsistence of a thing; beginning then, again, from the first, we must say that of differences some are separable, others inseparable, thus to be moved, and to be at rest, to be ill, and to be well, and such as resemble these, are separable, but to have a crooked, or a flat nose, to be rational, or irrational, are inseparable differences.

Thus far, we have the following:

  • Difference
    • In Kind vs. In Quality
    • Separable vs. Inseparable

I am rational; a dog is not. This is a difference in kind. This dog is white; that dog is black. This is a difference in quality.

This dog is a Golden Retriever, but that dog is not. This is an inseparable difference. This dog is currently asleep; that dog is currently chasing a cat. This is a separable difference.

It’s clear that “inseparable” doesn’t mean “unchanging”. Being human, my nose has a shape–at all times, my nose has a shape. Even if my nose is cut off, I am a human being who is lacking a nose. I mean to say, people would notice–it would be as plain as the nose off my face.

Again, of the inseparable, some exist per se, others by accident, for rational, mortal, to be susceptible of science, are inherent in man per se, but to have a crooked or flat nose, accidentally, and not per se. Wherefore, such as are present per se, are assumed in the definition of substance, and effect a different thing, but what are accidental are neither taken in the definition of substance, nor render a thing another, but of another quality.

Aha! I need to adjust my outline.

  • Difference
    • In Kind
      • Essential
      • Inseparable, per se (i.e., a property)
    • In Quality
      • Inseparable, by accident
      • Separable

I’m actually not quite sure about what I have there for differences in kind. It seems to me that when Porphyry talks about differences per se he’s talking about both the specific difference, which is what makes this thing the kind of thing it is, and about other differences–properties, as they are called–which are always there for things of this kind. But I could be mistaken. I’ll note that Rune’s Dictionary of Philosophy defines a property as follows:

In Aristotle’s logic (1) an attribute common to all members of a species and peculiar to them; (2) an attribute of the above sort not belonging to the essence of the species, but necessarily following from it.

Be all that as it may, there’s a further distinction between differences that are inseparable per se and those that inseparable accidentally:

Those too, which are per se, do not admit of the more and less, but the accidental, even if they be inseparable, admit of intention and remission, for neither is genus more and less predicated of that of which it is the genus, nor the differences of genus according to which it is divided. For these are such as complete the definition of each thing, but the essence of each is one and the same, and neither admits of intention, nor remission; to have however a crooked or a flat nose, or to be in some way coloured, admits both of intension and remission.

OK; you’re an animal or you’re not. You’re rational, or you’re not. But your nose can be more or less crooked, more or less pink. I’m puzzled by the words “intention” and “remission” in this context.

Next we have a detailed example of specific differences that relate to the genus “animal”:

Since then, there are three species of difference considered, some indeed separable, but others inseparable, again, of the inseparable, some are per se, but others accidental, moreover of differences per se, some are those according to which we divide genera into species, but others according to which the things divided become specific:–thus of all such differences per se of animal as these, animated and sensitive, rational and irrational, mortal and immortal, the difference of animated and sensitive is constitutive of the essence of animal, for animal is an animated substance, endued with sense, but the difference of mortal and immortal, and that of rational and irrational, are the divisive differences of animal, for through these we divide genera into species: yet these very differences which divide the genera are constitutive and completive of species. For animal is divided by the difference of rational and irrational, and again, by the difference of mortal and immortal; but the differences of rational and mortal are constitutive of man, but those of rational and immortal of God, those again, of mortal and irrational, of irrational animals. Thus also, since the differences of animate and inanimate, sensitive and void of sense, divide the highest substance, animate and sensitive added to substance, complete animal, but animate and deprived of sense, form plant; since then, the same differences taken in one way become constitutive, but in another divisive, they are all called specific.

So rocks differ from animals in that they are not animate. Plants are animate, but differ from animals in that they are not sensitive–that is, they have no sensitive soul, no powers of sensation. Animals are sensitive but not rational, as men are; and animals are not immortal, as the gods are.

The most interesting bit of the above example is the suggestion that the difference between men and gods is that the gods are immortal. A footnote suggests that Porphyry assumes the Stoic notion of the gods; in any event, this is a facet that St. Thomas did not perpetuate.

Isagoge: Chapter 3:1 — Of Difference

Tuesday, December 16th, 2008

Now, you know and I know that when Thomas speaks of “difference” he means the specific difference, that which distinguishes species from another within the same genus. Man is a rational animal, that is, an animal that is rational; animal is his species genus, and rational his difference.

Porphyry, in his usual way, begins with the common meaning of the word “difference,” and moves on from there.

Difference may be predicated commonly, properly, and most properly:….

So: three kinds of difference: common, proper, and most proper.

….for one thing is said to differ from another in common from its differing in some respect in diversity of nature, either from itself, or from something else; for Socrates differs from Plato in diversity of nature, and himself from himself when a boy, and when become a man, also when he does any thing, or ceases to do it, and it is always perceived in the different ways in which a thing is somehow effected.

In the common sense, this differs from that when, well, this differs from that. I think we get that.

Again, one thing is said to differ properly from another, when one differs from another by an inseparable accident; but an inseparable accident is such as blueness, or crookedness, or a scar become scirrhous from a wound.

That is, when they differ in quality.

Moreover, one is most properly said to differ from another, when it varies by specific difference, as man differs from horse by specific difference, i. e. by the quality of rational.

So specific difference is the most proper use of the term.

Universally then every difference acceding to a thing renders it different, but differences common and proper render it different in quality, and the most proper render it another thing.

Aha! A white dog and a black dog are both dogs, but two things that differ in the most proper way, by a specific difference, are two different kinds of thing. Which is, of course, why it’s called a “specific” difference:

Hence, those which render it another thing are called specific, but those, which make it different in quality, are simply (called) differences, for the difference of rational being added to animal, makes it another thing, (and makes a species of animal,) but difference of being moved makes it different in quality only from what is at rest, so that the one renders it another thing, but the other only of another quality.

So far, so good. I confess, I’m not entirely sure why Porphyry distinguishes above between common and proper differences, but I’m not sure that it matters, either.

Isagoge: Chapter 2:5 — Of the Nature of Genus and Species

Saturday, December 13th, 2008

In this paragraph, Porphyry takes a great while to explain how comprehension and extension vary as you go up and down the chain of genera, species, and individuals. I’m not going to take it apart; you can read it for yourself. I’ll summarize at the end.

Genus then, and species, being each of them explained as to what it is, since also genus is one, but species many, (for there is always a division of genus into many species,) genus indeed is always predicated of species, and all superior of inferior, but species is neither predicated of its proximate genus, nor of those superior, since it does not reciprocate. For it is necessary that either equals should be predicated of equals, as neighing of a horse, or that the greater should be predicated of the less, as animal of man, but the less no longer of the greater, for you can no longer say that animal is man, as you can say that man is animal. Of those things however whereof species is predicated, that genus of the species will also be necessarily predicated, also that genus of the genus up to the most generic; for if it is true to say that Socrates is a man, but man an animal, and animal substance, it is also true to say that Socrates is animal and substance. At least, since the superior are always predicated of the inferior, species indeed will always be predicated of the individual, but the genus both of the species and of the individual, but the most generic both of the genus or the genera, (if the media and subaltern be many,) and of the species, and of the individual. For the most generic is predicated of all the genera, species, and individuals under it, but the genus which is prior to the most specific (species), is predicated of all the most specific species and individuals; but what is species alone of all the individuals (of it), but the individual of one particular alone.14 Now, an individual is called Socrates, this white thing, this man who approaches the son of Sophroniscus, if Socrates alone is his son, and such things are called individuals, because each consists of properties of which the combination can never be the same in any other, for the properties of Socrates can never be the same in any other particular person; the properties of man indeed, (I mean of him as common,) may be the same in many, or rather in all particular men, so far as they are men. Wherefore the individual is comprehended in the species, but the species by the genus, for genus is a certain whole, but the individual is a part, and species |618 both a whole and a part; part indeed of something else, but a whole not of another, but in other things, for the whole is in its parts. Concerning genus then, and species, we have shown what is the most generic, and the most specific, also what the same things are genera and species, what also are individuals, and in how many ways genus and species are taken.

In short, the species is predicated of every individual in the species; the genus is predicated of every species within it, and so on up the chain. Thus, Socrates is a man, an animal, a body, and a substance.

It’s tempting to think of genera and species as mathematical sets: a species is the set of all individuals in the species, a genus is the set of all individuals in the species, and so forth, and indeed this is the way modern logic encourages us to think. But to do so is to confuse genera and species with their extensions: remember that the extension of a genus or species is precisely the individuals of which the genus or species is predicated. But genera do not contain individuals; they contain species. And in addition to extension, each genus and species has a comprehension, that is, a meaning. The extension of the species Man is all men precisely because all men are rational animals. Individual men belong to the species because they fit the defining criteria; a species is not an arbitrary set of individuals.

Given that, we can say that every genus has a wider extension than any species within it, and every species has a more precise–indeed, more specific–comprehension than its genus.

Isagoge: Chapter 2:4 — Of the Nature of Genus and Species

Friday, December 12th, 2008

So, how many genera and species are there? First, there are the ones in the middle:

Now, the media of the extremes they call subaltern species and genera, and admit each of them to be species and genus, when referred indeed to different things, for those which are prior to the most specific, ascending up to the most generic, are called subaltern genera and species. Thus, Agamemnon is Atrides, Pelopides, Tantalides, and lastly, (the son) of Jupiter,….

OK; we talked about this kind yesterday. Why go on about it now?

…yet in genealogies they refer generally to one origin, for instance, to Jupiter; but this is not the case in genera and species, since being is not the common genus of all things, nor, as Aristotle says, are all things of the same genus with respect to one summum genus.

Aha! In a genealogy (aha! genus; genealogy. D’oh!) there’s one genus that’s most generic. But there is no single genus to which all beings belong. Why? Because “being” is a term of courtesy:

Still, let the first ten genera be arranged, as in the Categories, as ten first principles, and even if a person should call all things beings, yet he will call them, so he says, equivocally, but not synonymously, for if being were the one common genus of all things, all things would be synonymously styled beings, but the first principles being ten, the community is in name only, yet not in the definition also belonging to the name: there are then ten most generic genera.

Substances are different than quantities, which are different than qualities, which are different than relations, etc. We call all of these things “beings” by courtesy, in that they can all be objects of thought, but clearly “whiteness” is a different class of thing than “dog”. Per Aristotle, there are ten distinct kinds of thing, the ten Categories, and hence ten most generic genera. There are ten trees, with the Categories as starting points.

On the other hand, the most specific they place in a certain number, yet not in an infinite one, but individuals which are after the most specific are infinite; wherefore, when we have come down to the most specific from the most generic, Plato exhorts us to rest, but to descend through those things which are in the middle, dividing by specific differences; he tells us however to leave infinites alone, as there cannot be science of these.

OK, there are a finite number of most-specific species, what we might call species proper; why, necessarily, a finite number? But individuals within species are infinite. Again, why? And per Plato, we should think about the genera and species and not waste any time on individuals, because there cannot be any certain knowledge of these….because, evidently, the number of them is infinite. Of course, we know that Plato regarded the Ideas (which would correspond, presumably, to the genera and species) as really real, and the things we perceive with our senses as less so, and I presume this dictum has something to do with that. Aristotle and Thomas disagree.

In descending then, to the most specific, it is necessary to proceed by division through multitude, but in ascending to the most generic, we must collect multitude into one, for species is collective of the many into one nature, and genus yet more so;….

Oh, right, that’s where division comes from. When I take a concept and make a distinction, I’m logically dividing the concept. Anyway, yes, genera have greater extension than the species within them.

….but particulars and singulars, on the contrary, always divide the one into multitude, for by the participation of species, many men become one man; but in particulars and singulars, the one, and what is common, becomes many; for the singular is always divisive, but what is common is collective and reductive to one.

Again, I see the Platonic hand here. Particulars, like “Some men have black hair,” clearly divide the one essence, human nature, into a multitude of individual men. But in what sense can we possibly say that a singular, like Socrates, we divide human nature into a multitude?