Tag Archives: 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.

The Perceptive Daisy: I See You, I See You Not

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Thus far in the Theaetetus Socrates, Theodorus and Theaetetus have begun to discuss the nature of knowledge, discussing the Protagorean (and simplistic) ‘man is the measure’ tagline as a prompt to their first candidate: perceiving is knowledge.[1]  What does Socrates mean, or more properly, what does he take Theaetetus to have accepted, by “perceiving is knowledge?”  One thoughtful and easily producible experiment on this thesis is offered by Socrates at 165a, to which I will now turn.

 Socrates: In fact I say this is the most incredible question, and I think it is something like this: is it possible for the same man to know what he knows and not to know what he knows?

 

Theodorus: What then do we reply, Theaetetus?

 

Theaetetus: It is impossible, I think.

 

Socrates: It is not impossible, if you make seeing knowing. How would you deal with the inescapable question, trapped inside a well, so to speak, when some intrepid person asks you, placing his hand on one of your eyes, “Do you see my cloak with your covered eye?”

 

Theaetetus: I will deny I see it with this eye, but with the other I say I can see it.

 

Socrates: So then, do you both see and not see the same thing?

 

Theaetetus: Indeed–– yet in this specified way.

 

Socrates: Yet I did not arrange the question in this way nor did I ask how, but whether that which you know is also that which you do not know. But now what you do not see you appear to see. And you happened to agree that seeing was knowing and not seeing was not knowing. Therefore from these things consider how it turns out for you.

 

Theaetetus: Yet I do consider that it is at odds with what I hypothesized (Translation mine, Theaetetus 165a2-d1). [2]

(Not all Platonic experiments on the eye are so compelling or provocative. Notably in the Timaeus, I think, it is given out as proof that light emanates from the eye on the grounds that if you squeeze it a light is seen!)

I really am attracted to this little scenario, especially in light of the current investigation as to whether perception is knowledge.  Perhaps I am taken in by the simple novelty of the experiment, attributing too much to it–– for example, Cornford seems to dismiss it as a “cavil” and sophistry unfair to Protagoras’ position.  Yet what is going on philosophically when the eye is covered?

Assuming that perceiving is knowledge, say we then proceed to cover one eye and look at an eye chart with our uncovered eye.  Socrates says this shows that we both know and don’t know, since we both see (with one eye) and don’t see (with the other eye).  This seems like an easy position to refute, even from a Platonic standpoint.  Elsewhere Socrates says that the eyes are merely instruments and that the soul is that which really sees; so in this case the soul, qua self, would know, yet could not be said to not know.

However, playing along, what does covering one eye and seeing with the other prove if perceiving is knowing?  That we neither know nor not know?  This seems absurd.  That we know?  Yet we also do not know, with the eye that is covered.  That we don’t know?  Yet we do know with the eye that is uncovered.  Perhaps then, it is a proof that we don’t know whether we know or don’t know, since we perceive that we both see/know with one eye and don’t see/know with the other, and to perceive is to know.  This then would be a self-defeating belief, it seems.

Furthermore, stepping away from the confines of this dialogue for a moment: is this a proof that seeing does not occur in the eye(s), but in the mind, and thus one explanation for how or why Plato created a distinction between the instruments of the self (body) and the self itself (soul)?

 

 

REFERENCES: 

[1] Starting at about 165a
[2] ΣΩ. Λέγω δὴ τὸ δεινότατον ἐρώτημα, ἔστι δὲ οἶμαι
τοιόνδε τι· “Ἆρα οἷόν τε τὸν αὐτὸν εἰδότα τι τοῦτο ὃ οἶδεν
μὴ εἰδέναι;”
ΘΕΟ. Τί δὴ οὖν ἀποκρινούμεθα, ὦ Θεαίτητε; (5)
ΘΕΑΙ. Ἀδύνατόν που, οἶμαι ἔγωγε.
ΣΩ. Οὔκ, εἰ τὸ ὁρᾶν γε ἐπίστασθαι θήσεις. τί γὰρ
χρήσῃ ἀφύκτῳ ἐρωτήματι, τὸ λεγόμενον ἐν φρέατι συσχό-
μενος, ὅταν ἐρωτᾷ ἀνέκπληκτος ἀνήρ, καταλαβὼν τῇ χειρὶ
(c) σοῦ τὸν ἕτερον ὀφθαλμόν, εἰ ὁρᾷς τὸ ἱμάτιον τῷ κατειλημ-
μένῳ;
ΘΕΑΙ. Οὐ φήσω οἶμαι τούτῳ γε, τῷ μέντοι ἑτέρῳ.
ΣΩ. Οὐκοῦν ὁρᾷς τε καὶ οὐχ ὁρᾷς ἅμα ταὐτόν;
ΘΕΑΙ. Οὕτω γέ πως. (5)
ΣΩ. Οὐδὲν ἐγώ, φήσει, τοῦτο οὔτε τάττω οὔτ’ ἠρόμην
τὸ ὅπως, ἀλλ’ εἰ ὃ ἐπίστασαι, τοῦτο καὶ οὐκ ἐπίστασαι.
νῦν δὲ ὃ οὐχ ὁρᾷς ὁρῶν φαίνῃ. ὡμολογηκὼς δὲ τυγχάνεις
τὸ ὁρᾶν ἐπίστασθαι καὶ τὸ μὴ ὁρᾶν μὴ ἐπίστασθαι. ἐξ
οὖν τούτων λογίζου τί σοι συμβαίνει. (10)
(d) ΘΕΑΙ. Ἀλλὰ λογίζομαι ὅτι τἀναντία οἷς ὑπεθέμην.

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.