Category Archives: Ancient Greek Philosopher

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.

Philosophical Humility, or, Admitting I Don’t Know What I Don’t Know

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I have seen many a conscientious reader of Plato smirk when considering Socrates’ plea that he knows one thing, he knows nothing.  We are in on the joke, I think many people believe; Socrates is much more clever than I and certainly more enlightened than the characters, in comparison real rubes, he systematically dismantles in the dialogues.  Socrates, under the hallowed authority of this confession, is a figure to whom we give lip service as the fount of all western education: be humble, accept your limitations, pursue the truth, and recognize that learning is never complete.

Nevertheless, Socrates is critical not only of a lack of knowledge, but also that erroneous “knowledge,” the misinformation, to which he also unwittingly adheres.  In the Gorgias, he goes so far as to say this.

I therefore, would cross-question you with pleasure, if you are the kind of person I am. But if not, I would let it be. Of what kind am I? Of those who are pleased to be refuted if I say something untrue, and with pleasure I would refute if someone said something untrue, and in fact I am not less pleased being refuted than refuting. For I think it is a greater good to be refuted, by as much greater it is a good to rid oneself of a great evil than to rid someone else of it. For I do not think that a thing could be such an evil for a man, as much as having a false opinion concerning the things about which our discussion is about (Gorgias 458a1-b1). [1]

Far from being shameful, Socrates thinks it is a actually a good to be refuted rather than a harm, and he prefers this to refuting someone else!

In light of this Socratic admission, I have thought how it applies to students who are hesitant to admit, in a classroom setting, and in one way or another, that they do not know.  However insofar as this is a legitimate fear, I assume that students have done their due diligence in homework, readings and independent thought on the subject. If they have not completed all of these preparatives, then these students are not candidates for Socratic humility, admitting they know what they do not know, but are simply poor students.

Thus I take it as a given, that if one is a prepared student, it is a philosophical good to admit what and when one does not know, for this is THE propaedeuctic.  Of course, these are also applicable to discussions of ancient philosophy in non-academic settings, and may even be useful generally when there are group intellectual discussions.

Fear of Appearing Stupid

I am sure we can all relate to this.  We are hesitant to speak up in class because we think our comment too obvious, or our question too stupid.  I have found that personally, as a participant and as a teacher, that an attitude of patient charity towards every single comment and question leads to more confidence in the questioner and more frankness in the answer.  Yet I am not a proponent of the idea that there are no stupid questions.  Rather, I think whether a question is stupid or not, the questioner should be a position in which he is encouraged to ask the stupid question, and not feel intellectual pain over it, while still being lead toward more intelligent questions.

Fear of Academic Worth

Another obstacle to Socratic humility is fear of having one’s academic worth undermined if one does not know the answer to a question or asks for clarification on background information owing to lack of knowledge.  As jockeying for the glory of the admiration of one’s peers is always in play in a classroom, I think, then acknowledging one’s ignorance in even minor issues often is an obstacle to learning and academic growth.

Fear of Preparedness

This I think is the most difficult of the fears.  For I think that if a student actually is prepared, but is hesitant to speak up in such a way because it might imply she is not prepared, this too is an obstacle to Socratic humility and to learning.  One way for a student to overcome this fear, is to couch his confession of ignorance (on whatever item of knowledge it is) in the context of expressing knowledge which is illustrative of the fact that the student does not some things, just not all, on this subject.

In conclusion, I think it is apparent that these are not only fears of the individual, but also expectations that the group can, in the snide inner voice we like to imagine we do not have, impose on an individual.  “Oh, you don’t know X about Y on Z, then you must not be very bright.”  “You need clarification on this, are you serious!”

 

 

 

REFERENCES:

[1] (a.) ἐγὼ οὖν, εἰ μὲν καὶ σὺ εἶ τῶν ἀνθρώπων ὧνπερ καὶ ἐγώ,
ἡδέως ἄν σε διερωτῴην· εἰ δὲ μή, ἐῴην ἄν. ἐγὼ δὲ τίνων
εἰμί; τῶν ἡδέως μὲν ἂν ἐλεγχθέντων εἴ τι μὴ ἀληθὲς
λέγω, ἡδέως δ’ ἂν ἐλεγξάντων εἴ τίς τι μὴ ἀληθὲς λέγοι,
οὐκ ἀηδέστερον μεντἂν ἐλεγχθέντων ἢ ἐλεγξάντων· μεῖζον (5)
γὰρ αὐτὸ ἀγαθὸν ἡγοῦμαι, ὅσῳπερ μεῖζον ἀγαθόν ἐστιν
αὐτὸν ἀπαλλαγῆναι κακοῦ τοῦ μεγίστου ἢ ἄλλον ἀπαλλάξαι.
οὐδὲν γὰρ οἶμαι τοσοῦτον κακὸν εἶναι ἀνθρώπῳ, ὅσον δόξα
(b.) ψευδὴς περὶ ὧν τυγχάνει νῦν ἡμῖν ὁ λόγος ὤν.