Tag Archives: ontology

Aristotle’s Categories: Predication with Genus and Differentiae

Posted on by

(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.

I command you to ponder these things- Parmenides

Posted on by

“It is necessary that saying and thinking actually are. For being exists, and
nothing does not exist. I command you to ponder these things. For I shut you out from this first inquiry; moreover since it is from this, on which mortals who know nothing wander, being two headed. For helplessness keeps straight the wandering mind in their breasts: and the dumb and likewise the blind are carried around, astounded and confused people, for whom being and non-being are considered the same thing and not the same thing, and their (i.e. of the dumb and blind) path turns back” (DK Frag. 6 :1-9).”

Χρὴ τὸ λέγειν τε νοεῖν τ΄ ἐὸν ἔμμεναι· ἔστι γὰρ εἶναι,
μηδὲν δ΄ οὐκ ἔστιν· τά σ΄ ἐγὼ φράζεσθαι ἄνωγα.
Πρώτης γάρ σ΄  φ΄ ὁδοῦ ταύτης διζήσιος <εἴργω>,
αὐτὰρ ἔπειτ΄  πὸ τῆς, ἣν δὴ βροτοὶ εἰδότες οὐδέν
πλάττονται, δίκρανοι·  μηχανίη γὰρ ἐν αὐτῶν
στήθεσιν ἰθύνει πλακτὸν νόον· οἱ δὲ φοροῦνται.
κωφοὶ ὁμῶς τυφλοί τε, τεθηπότες, ἄκριτα φῦλα,
οἷς τὸ πέλειν τε καὶ οὐκ εἶναι ταὐτὸν νενόμισται
κοὐ ταὐτόν, πάντων δὲ παλίντροπός ἐστι κέλευθος.

With the consideration that Parmenides wrote in hexameters, and that such works were often recited in public, and that Parmenides himself is portrayed by Plato as being present at such a recital of one of his own students [1], I approach this particular fragment differently than if it were merely a philosophical treatise, void of cultural context.
Saying, by existing, is a thing.  The “being-ness” of words is casually assumed by their very use, yet their use qua existence is unreflectively maintained, absent the awareness which appreciates even the possibility of the existence of words.  This “being-ness” of words is re-iterated for the uncognizant by the very fact that Parmenides is speaking words at them, at the audience.  We are incapable of thinking of non-existence.  For any thinking involves the thinking of a thought as thing, a thing which must exist to be a thing.  If it is thought, it is not a nothing, but a something, even if that something is merely a thought (i.e. a unicorn).  We can not think of non-being, for if we could, it would be a being we were thinking of, not non-being.

Therefore all is being.

 

[1] ἀναγιγνώσκειν οὖν αὐτοῖς τὸν Ζήνωνα αὐτόν (Parmenides 127c)
“Zeno himself was reading to them…”  A few lines later Parmenides comes in to hear the end of the reading.

Parmenides, expressibility and pure being

Posted on by

In my previous post I translated Parmenides fragment 8. Among the most perplexing frustrations, and trust me, there are many in an ancient epic hexameter poem, was the phrase I translated as, “Thought and that thing on account of which thought exists are both the same thing. For not without being, within which thought has been expressed, will you discover thinking.

I had previously struggled to understand what the sentiment was which Parmenides was conveying.  On reflection, and perhaps with an appreciation for the midnight startle I woke up with pondering this sentence over and over again, and moreover, with the over-familiarity I have gained in having translated this sentence “into being”, I now think it rather a straightforward, but not obvious argument.

If there were no existence, nothing existing at all, we would not be able to express anything, for that very expression of something would itself be existing, (because it is something) and then something would, in fact, exist.  The fact that something is verbally expressed demonstrates that something exists, namely at least the expressed and the expresser.  In this sense they are the same thing.

Does Descartes simply steal a version of this argument away from Parmenides, or adapt it?  “I think, therefore I am”, is closely akin to “I speak, therefore I am”, or perhaps more basically, “It is expressed, therefore it exists.”

Any Cartesians out there have a thought (and who also exist)?