Category Archives: Aristotelianism

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.

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.

Aristotle’s Case Against Vegetarianism: Predator and Prey

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If it is a given that man is an animal, as is so famously articulated in Aristotle’s famous dictum that man is a social animal, then there should be no good reason to exclude ideas which, in general, are meant to apply to man as an animal, from animals.  So in the case of vegetarianism: if there is an argument suitably argued against vegetarianism for animals qua animals then it will apply to man insofar as he is an animal as well.

This is the case in an interesting passage from the first book of Aristotle’s Politics.

For some animals, when they are created, at the outset bring forth with them in the process of creation (τοῖς γεννωμένοις) so much nourishment as is adequate until the time when the animal itself is able to provide for itself; for example those animals which have larvae or eggs. As many animals as give birth to live young, they have nourishment in themselves for a given time, the substance called milk.  So that clearly one must think that [there is nourishment] for the things which have been created (γενομένοις), plants on account of animals and the other animals for the sake of humans.  The tame animals are for the use and nourishment of mankind, while the wild ones, if not all, most of them, are on account of nourishment and help, in order that clothes and other tools come to be from these.  And therefore, if nature does nothing in vain or without a purpose, it is necessary that nature made all of these on account of humans (Translation mine, Aristotle, Politics, 1256b10-22) [1]

Aristotle, not uncharacteristically, is running together lines of thought, arguments and assumptions.  He begins from the idea that in nature when an animal is in the process of being former, it is supplied by nature with some form of physical sustenance, such as an egg providing not only a type of shelter but also some nutrition for the growing embryo.  To Aristotle, this is a universal feature for animal life; even in the case of animals which give birth to live young, their mothers are capable of lactation to provide this same sustenance in a different manner.  Thus, the thinking goes, when an animal is past the initial stage of life, nature would likewise still provide it with nourishment as when it has reached the point of maturity.

Latent within this passage is the idea that once nature has delivered an animal into its full physical maturity, it will have come to possess capabilities to procure food by its own means.[2]  Thus, there is still a need for food, but the initial form of food, such as a lactating mother, is not longer present for the animal.  The animal feels the urge to continue feeding, and in Aristotle’s mind, it has a natural instinct to seek those things which will best suit its appetite.  Among those things are both plants and animals.  Thus vegetarianism is ruled out, albeit Aristotle does need some detail work in explaining the nuances of this idea in full.

Lastly, there is the point made about nature doing nothing in vain.  What does he mean in applying that thought in this case?  (1) Either that nature does not bring an animal into maturity to just let it die since it has no way to get food (e.g. a human baby dies because it cannot find food); but this would be absurd.  (2) Or nature does not bring an animal into existence for it not be used in the proper way (i.e. cows are made for hamburgers, for leather, and for milk) (3) Or both, to put it somewhat directly, the predator and prey are made for a purpose, and both fulfill their roles.

REFERENCES:

[1]  καὶ γὰρ κατὰ τὴν ἐξ ἀρχῆς γένεσιν τὰ μὲν συνεκ- (10)
τίκτει τῶν ζῴων τοσαύτην τροφὴν ὥσθ’ ἱκανὴν εἶναι μέχρις
οὗ ἂν δύνηται αὐτὸ αὑτῷ πορίζειν τὸ γεννηθέν, οἷον ὅσα
σκωληκοτοκεῖ ἢ ᾠοτοκεῖ· ὅσα δὲ ζῳοτοκεῖ, τοῖς γεννωμένοις
ἔχει τροφὴν ἐν αὑτοῖς μέχρι τινός, τὴν τοῦ καλουμένου γά-
λακτος φύσιν. ὥστε ὁμοίως δῆλον ὅτι καὶ γενομένοις οἰη- (15)
τέον τά τε φυτὰ τῶν ζῴων ἕνεκεν εἶναι καὶ τὰ ἄλλα ζῷα
τῶν ἀνθρώπων χάριν, τὰ μὲν ἥμερα καὶ διὰ τὴν χρῆσιν
καὶ διὰ τὴν τροφήν, τῶν δ’ ἀγρίων, εἰ μὴ πάντα, ἀλλὰ
τά γε πλεῖστα τῆς τροφῆς καὶ ἄλλης βοηθείας ἕνεκεν, ἵνα
καὶ ἐσθὴς καὶ ἄλλα ὄργανα γίνηται ἐξ αὐτῶν. εἰ οὖν ἡ (20)
φύσις μηθὲν μήτε ἀτελὲς ποιεῖ μήτε μάτην, ἀναγκαῖον
τῶν ἀνθρώπων ἕνεκεν αὐτὰ πάντα πεποιηκέναι τὴν φύσιν.

[2]  Unsurprisingly, Aristotle will include hunting among the means.