Category Archives: Greek Philosophy

Aristotle’s Categories: Predication with Genus and Differentiae

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(See here for the previous posts on the Categories: Chapter 1, Chapter 2)

Aristotle’s philosophical writing, often opaque in style as well as content, can also venture into extended periods of intricate simplicity, innovating complexity and depth from a rather limited set of fixed, technical terms.  This is the case for much of the Categories, and chapter 3 certainly fits this description as well.  In this post, I will be continuing my quasi-commentary on Aristotle’s Categories, now arriving at chapter 3.

Whenever one thing is predicated of another as of a subject (ὑποκειμένου), as many things as are said of the thing being predicated, all of these will also be said of the subject. For example human is predicated of an individual human, and animal is predicated of a human. Therefore animal will be predicated of an individual human also. For an individual human is both a human and an animal.

 

Of the things differing in genus and not being subordinated to one another there are differentiae different in kind (τῷ εἴδει), for example, there are [distinct] differentiae of animal and of knowledge: footed, winged, water-dwelling, two-footed, and none of these is [a differentia] of knowledge. For [one kind] of knowledge does not differ from [another] knowledge by having two feet. Yet nothing prevents there being the same differentiae of the genera subordinate to each other. For the higher genera are predicated of the things said under them, so that as many differentiae as there are of the thing being predicated there will be of the subject as well (Translation mine, Categories 1b10-24). [1]

Aristotle begins this section with the confusingly worded, “Whenever one thing is predicated of another as of a subject (ὑποκειμένου), as many things as are said of the thing being predicated, all of these will also be said of the subject.”  Now the example that follows makes the concept he is addressing here rather clear.  If an individual human is a human, and if a human is an animal, then an individual human is an animal.  In this instance, using Aristotle’s terminology, the subject and the thing being predicated of is “the individual human,” while the thing being predicated is “human.”  (Keep in mind that I use quotation marks not to designate a mere linguistic term, but to clarify and distinguish the objects to which they refer.)

Aristotle next invokes language about genus and differentia (plural, genera and differentiae.)  Assuming that there are such entities we may roughly think of as “kinds of things,” designated as genera, then it follows that these things must be organized and distinguished from each other in some way.  For example, taking animal as a real genus, we can say that there are (at least) two “kinds”: birds and fish.  These two kinds of things, birds and fish, are each a species of the genus animal, and although they belong to the genus animal, birds and fish are distinguished from each other by differing in some salient way.  Possession of this differing property or properties, such as scales or feathers, is what makes the one animal (fish) differ from the other (bird).  Thus these properties are called differentiae.  Since this usage of genus is not to be confused with our modern classifications in biological nomenclature, we can freely apply the term genus to whatever level of kinds of things we wish.  With confidence in being philosophically consistent, in other words, we can also say that in addition to animal, fish is also a genus, with the differentiae of salt-water or fresh-water picking out two other species based on the difference of the type of water inhabited.  What Aristotle warns against in the second half of this text is being sloppy when it comes to distinctions made in one genus that do not apply to another, viz. knowledge and animal, where one applies two-footedness to knowledge.

 

REFERENCES:

[1] Ὅταν ἕτερον καθ’ ἑτέρου κατηγορῆται ὡς καθ’ ὑποκει- (10)
μένου, ὅσα κατὰ τοῦ κατηγορουμένου λέγεται, πάντα καὶ κατὰ τοῦ ὑποκειμένου ῥηθήσεται· οἷον ἄνθρωπος κατὰ τοῦ τι-
νὸς ἀνθρώπου κατηγορεῖται, τὸ δὲ ζῷον κατὰ τοῦ ἀνθρώπου·
οὐκοῦν καὶ κατὰ τοῦ τινὸς ἀνθρώπου τὸ ζῷον κατηγορηθήσε-
ται· ὁ γὰρ τὶς ἄνθρωπος καὶ ἄνθρωπός ἐστι καὶ ζῷον. (15)
τῶν ἑτερογενῶν καὶ μὴ ὑπ’ ἄλληλα τεταγμένων ἕτεραι
τῷ εἴδει καὶ αἱ διαφοραί, οἷον ζῴου καὶ ἐπιστήμης·
ζῴου μὲν γὰρ διαφοραὶ τό τε πεζὸν καὶ τὸ πτηνὸν καὶ τὸ
ἔνυδρον καὶ τὸ δίπουν, ἐπιστήμης δὲ οὐδεμία τούτων· οὐ γὰρ
διαφέρει ἐπιστήμη ἐπιστήμης τῷ δίπους εἶναι. τῶν δέ γε (20)
ὑπ’ ἄλληλα γενῶν οὐδὲν κωλύει τὰς αὐτὰς διαφορὰς εἶναι·
τὰ γὰρ ἐπάνω τῶν ὑπ’ αὐτὰ γενῶν κατηγορεῖται, ὥστε
ὅσαι τοῦ κατηγορουμένου διαφοραί εἰσι τοσαῦται καὶ τοῦ
ὑποκειμένου ἔσονται.

Were Plato’s Dialogues Verbatim?

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There are generally a number of questions that come into mind concerning Plato’s chosen literary form, the dialogue; among them why and to what end, for whom and for what occasion.  Yet another realm of interest entirely is the process Plato used when he created his masterpieces of philosophical prose.  Few would consider Plato’s accounts as conversation chronicled for the benefit of future historical contemplation.  Even Plato himself is (paradoxically) averse to the written word in the Phaedrus, in which, among a flurry of allied criticisms, he charges that written words, static and thus muted, are insensitive to the needs of an audience.

Nevertheless, on Plato’s method of composition, there are some interesting tells in the beginning of the Theaetetus.  The dialogue begins with Terpsion and Euclid recounting a conversation Socrates has had with Theaetetus and Theodorus.   A second-hand account is not unusual, of course, as it is employed famously in the Republic, Symposium and Timaeus.  This frequently used technique perhaps is meant by Plato to predispose the reader against any inclination to accept the dialogues as first-hand reports from some embedded reporter.  Whatever their purpose, however, there are a few intriguing aspects of the process of writing that Plato lets us in on.


Plato’s dialogues were meant to be read aloud.

As Euclid is about to relate the story about Socrates, he tells Terpsion that his slave will read out the dialogue.[1]  Reading out loud was common in antiquity, and Plato was certainly well-to-do, if tradition is to be believed, so he would have had slaves, as here in specific, to read out loud from his personal library.


A dialogue was copied down after the fact, and then corrected over time.

Euclid tells Terpsion of this method of composition:

But I wrote down immediately some notes when I came home, and later, as I had leisure, I began to write down as I remembered, and every time I came to Athens, I questioned Socrates on whatever I was unable to recall, and then returning here I corrected it.  So that nearly the whole account has been written down by me (Theaetetus 143a1-5). [2]


A dialogue was meant to come across as dramatic and vital.

Terpsion also says, even though he heard the story from Socrates, that he is going to avoid repeating the dialogue as “Socrates said this was said” and “Socrates then said this happened.”

I wrote it down in this way, not as Socrates relating it to me, as he related it, but talking  with those with whom he told me he was talking….Now in order that the guiding words between the speeches not be vexing in what I wrote, such as “and I said” or “and I remarked,” whenever Socrates spoke, or “he consented” or “he disagreed,” for the interlocutor.  On account of these considerations, I portrayed Socrates himself as talking with them, ignoring such annoyances (Theaetetus 143b4-6, c1-5). [3]

Obviously, it is no surprise that Plato had an eye for dramatic flair, as he is still read today for pleasure, despite intro to philosophy classes’ best efforts to undermine this enduring interest.  But here we have a concession that, at least on some minor level, Plato felt free to omit certain aspects of the dialogue which were tedious, and which tended to draw away from the vivacity with which his dialogues are so closely associated.

Thus, we might be surprised to find, while it is impossible to expect Plato’s dialogues to be word for word, his profession as seen in the Theatetus claims a high degree of trustworthiness and adherence to what we hope were Socrates’ actual words.

 

 

 

 

REFERENCES:

[1] ὁ παῖς ἀναγνώσεται..  (Theaetetus 143b3)

[2] ἀλλ’ ἐγραψάμην μὲν τότ’ εὐθὺς οἴκαδ’ ἐλθὼν ὑπομνήματα,
ὕστερον δὲ κατὰ σχολὴν ἀναμιμνῃσκόμενος ἔγραφον, καὶ
ὁσάκις Ἀθήναζε ἀφικοίμην, ἐπανηρώτων τὸν Σωκράτη ὃ μὴ
ἐμεμνήμην, καὶ δεῦρο ἐλθὼν ἐπηνορθούμην· ὥστε μοι σχεδόν
τι πᾶς ὁ λόγος γέγραπται.

[3] ἐγραψάμην δὲ δὴ οὑτωσὶ τὸν λόγον, οὐκ ἐμοὶ Σωκράτη διηγούμενον ὡς διηγεῖτο, ἀλλὰ διαλεγόμενον οἷς ἔφη διαλεχθῆναι… ἵνα οὖν ἐν τῇ
γραφῇ μὴ παρέχοιεν πράγματα αἱ μεταξὺ τῶν λόγων διηγήσεις
περὶ αὑτοῦ τε ὁπότε λέγοι ὁ Σωκράτης, οἷον “καὶ ἐγὼ ἔφην” ἢ
“καὶ ἐγὼ εἶπον,” ἢ αὖ περὶ τοῦ ἀποκρινομένου ὅτι “συνέφη”
ἢ “οὐχ ὡμολόγει,” τούτων ἕνεκα ὡς αὐτὸν αὐτοῖς διαλεγό-
μενον ἔγραψα, ἐξελὼν τὰ τοιαῦτα.

Aristotle’s Categories: Four-fold Division of Being

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In the previous chapter of the Categories we have already discussed homonymy, synonomy, and paronymy.  This section, Chapter 2 of Aristotle’s Categories, sets forth a four-fold system of classification for “things that are,” [1] in addition to introducing a distinction between things that are said “in combination” and things said “without combination.”  Although not without straying interpretations, the distinction between “combined and uncombined” is rather clear, on my view, from the context.  So I will instead be focusing on the four-fold division that takes up the majority of the chapter and the lion’s share of the philosophical difficulty.  Needless to say, however, for the purpose of an explanatory post such as this, I will be sticking to orthodox and traditional interpretations, although of course there are always divergences and minority reports.

Things That Are Said:

 

Of the things that are said, some are said in combination (symploke), while some are said without combination.  Those that are said in combination are such as “human runs,” “human wins.”  Those without combination are such as “man,” “ox,” “runs,” “wins.”

 

Things That Are:

 

A) Of things that are, some are said of an individual subject (tis hypokeimenon), but are not in any subject, such as “human” is said of an individual human, but is not in any subject.

 

B) But some are in a subject, yet are said of no subject.  And by “in a subject,” I mean that which exists in something not as a part and is impossible to be apart from that in which it is.  For example, an individual grammatical knowledge (tis grammatike) is in a subject, but is said of no subject, and individual white is in a subject, i.e. a physical body (for every color is in a body) but it is said of no subject.

 

C) Some are said both of a subject and are in a subject, for example knowledge (episteme) is in a subject, i.e. a soul, but is said of a subject, i.e. grammatical knowledge

 

D) Some are neither in a subject nor said of a subject, for example, an individual person or an individual horse–– for none of these is in a subject nor is it said of a subject.  And generally, things that are irreducible and one in number are said of no subject, but nothing hinders some things from being in the subject.  For, of the things in a subject, the individual grammatical knowledge is one of them (Aristotle, Categories, 1a16-1b9). [2]

First let us discuss what Aristotle means by “in a subject” and “said of a subject.” Since the four-fold division consists entirely in affirming or denying these classifications, resulting in four distinctions, if we understand these two phrases, we are well on our way to understanding all of this chapter.

The In-a-subject Relation

It is best to understand both the in-a-subject and said-of-a-subject distinctions, at a general level, as belonging to relations between things.  So in-a-subject means that if X is in Y, where Y is the subject, we are to understand Y as either a substance proper or, more abstactly, as that thing, whatever it is, which undergoes the process which results in some relation.  X here cannot exist independently from some kind of subject or substance, and that is why it is said to be “in” a subject, for it will not exist “out” of a subject.  Thus the category of things not a subject or substance, here represented by X, are dependent on the subject for their existence.  So in Aristotle’s example, an individual’s grammar-knowledge (his understanding of how language works) is “in” an individual (his mind) because it is dependent on the individual and cannot exist apart from this individual, viz., Grammatical knowledge is in the mind.

The Said-of-a-subject Relation

While the in-a-subject distinction concerns a subject or substance and its independent status (in contrast to the dependent relation of a non-subject or non-substance), the said-of-a-subject relation pertains to an individual and a universal, or in slightly different wording, to an individual and a species or genus.  Returning to one of Aristotle’s examples, the term human (as a species) is “said of” an individual human, viz., Socrates is a human.

The Four-fold Division Simplified

Now that we have discussed the in-a-subject relation and the said-of-a-subject relation, we can apply these distinctions to the text above to get four categories into which (presumably) all things fit.

A) Essential Universals: Universals (or species and genera) in their relation to substances. E.g. “Human” in “Socrates is human.”
B) Accidental Particulars: Particulars, but not substances. E.g. An individual grammatical knowledge in a person.
C) Accidental Universals: Universals (or species and genera) in their relation to things other than substances. E.g. Knowledge is said both of grammatical knowledge (i.e. grammatical knowledge is knowledge) and is in a subject, i.e. a mind.
D) Primary Substances: Particulars that are substances. E.g. An individual such as Socrates or a particular horse, e.g. Secretariat

 

 

REFERENCES:

[1] Although the division is four-fold, there are actually 6 possibilities; however two of these possibilities are contradictions: “in a subject and not in a subject” and “of a subject and not in a subject.”

[2] Τῶν λεγομένων τὰ μὲν κατὰ συμπλοκὴν λέγεται, τὰ
δὲ ἄνευ συμπλοκῆς. τὰ μὲν οὖν κατὰ συμπλοκήν, οἷον
ἄνθρωπος τρέχει, ἄνθρωπος νικᾷ· τὰ δὲ ἄνευ συμπλοκῆς,
οἷον ἄνθρωπος, βοῦς, τρέχει, νικᾷ.
Τῶν ὄντων τὰ μὲν καθ’ ὑποκειμένου τινὸς λέγεται, ἐν  (20)
ὑποκειμένῳ δὲ οὐδενί ἐστιν, οἷον ἄνθρωπος καθ’ ὑποκειμένου
μὲν λέγεται τοῦ τινὸς ἀνθρώπου, ἐν ὑποκειμένῳ δὲ οὐδενί ἐστιν·
τὰ δὲ ἐν ὑποκειμένῳ μέν ἐστι, καθ’ ὑποκειμένου δὲ οὐδενὸς
λέγεται, —ἐν ὑποκειμένῳ δὲ λέγω ὃ ἔν τινι μὴ ὡς μέρος
ὑπάρχον ἀδύνατον χωρὶς εἶναι τοῦ ἐν ᾧ ἐστίν,— οἷον ἡ τὶς (25)
γραμματικὴ ἐν ὑποκειμένῳ μέν ἐστι τῇ ψυχῇ, καθ’ ὑπο-
κειμένου δὲ οὐδενὸς λέγεται, καὶ τὸ τὶ λευκὸν ἐν ὑποκειμένῳ
μέν ἐστι τῷ σώματι, —ἅπαν γὰρ χρῶμα ἐν σώματι,— καθ’
ὑποκειμένου δὲ οὐδενὸς λέγεται· τὰ δὲ καθ’ ὑποκειμένου τε
(1b.) λέγεται καὶ ἐν ὑποκειμένῳ ἐστίν, οἷον ἡ ἐπιστήμη ἐν ὑπο-
κειμένῳ μέν ἐστι τῇ ψυχῇ, καθ’ ὑποκειμένου δὲ λέγεται
τῆς γραμματικῆς· τὰ δὲ οὔτε ἐν ὑποκειμένῳ ἐστὶν οὔτε καθ’
ὑποκειμένου λέγεται, οἷον ὁ τὶς ἄνθρωπος ἢ ὁ τὶς ἵπ-
πος, —οὐδὲν γὰρ τῶν τοιούτων οὔτε ἐν ὑποκειμένῳ ἐστὶν (5)
οὔτε καθ’ ὑποκειμένου λέγεται·— ἁπλῶς δὲ τὰ ἄτομα καὶ ἓν
ἀριθμῷ κατ’ οὐδενὸς ὑποκειμένου λέγεται, ἐν ὑποκειμένῳ δὲ
ἔνια οὐδὲν κωλύει εἶναι· ἡ γὰρ τὶς γραμματικὴ τῶν ἐν ὑπο-
κειμένῳ ἐστίν.