Thursday, July 31, 2008

Logic I, Lesson 3: The Five Predicables, Pt. 1: Genera & Species


A. The Predicables. Every proposition has a subject and a predicate. The predicates are divided into five basic kinds (which we call "the five predicables") according to how they relate to the subject of the proposition. Predicates name one of the following five aspects of the subject:

  • The genus of the subject of the proposition: "Socrates is an animal."
  • The species of the subject: "Socrates is a man"
  • The subject's specific difference: "Socrates is rational."
  • An essential trait or property (proprium) of the subject: "Socrates is risible (i.e., able to laugh)."
  • An unessential trait or accident of the subject: "Socrates is white."
B. Genus & Species. A genus (plural, "genera") is a class of things that differ in kind--e.g., "animal" is a genus, because it is a class of things (e.g., cats, dogs, cows, etc.) that differ in species. A species is a class of things that differ in number (i.e., many individuals) but not in kind--e.g., "man" is a species, because it is a class of numerous individuals of the same kind. A genus is thus divided into different species and a species is divided into different individuals.

Now, the term "species" can be extended to include narrower genera that fall under broader genera. Therefore, the narrower genera relate to the broader genera as species to a genus and, thus, may be called "species" with respect to their broader genus--e.g., "animal" and "plant," though they are genera (with respect to different species of animal and plant), may themselves be called "species" of "living thing"; "living thing," though a genus with respect to "animal" and "plant," is a species of "body" (i.e., physical substance).

In the end, there will be ultimate genera (summum genus or genus generalissimum) which are not species of any broader genera; there will also be ultimate species (infima species or species specialissima) that are have no species under them, but only individuals.

C. Predication. Whatever is true of the genus is true of the species (but not vice versa), and whatever is true of the species is true of the subject or individual (but not vice versa); therefore, whatever is true of the genus is true of the individual.

From Aristotle's Categories 3 (explanatory notes in brackets):

When one thing is predicated of another [in a proposition consisting of a subject and a predicate], all that which is predicable of the predicate will be predicable also of the subject. Thus, 'man' is predicated of the individual man [e.g., "this individual is a man"]; but 'animal' is predicated of 'man' [e.g., "man is an animal"]. Therefore, it [i.e., animal] will be predicable of the individual man also [e.g., "this individual in an animal"]: for the individual man is both 'man' and 'animal'.

From Porphyry's Isagoge to Aristotle's Categories, 1-2:

[Preface to the Work.] Since it is necessary, Chrysaorius, to know about [the five predicables, namely] genus, specific difference, species, exclusive property, and accident, both for understanding Aristotle’s theory of the categories and for assigning definitions, and generally for questions of classification or demonstration (the study of all of which is most useful), I shall give you a concise exposition, and I shall attempt, briefly and in the manner of an introduction, to approach what the ancients said, leaving alone the deeper questions, but making a few reasonable conjectures about simple ones. [...]

[The Five Predicables.] [O]f predicates [within propositions], some are (A) predicable of one thing alone, as individuals, for instance, "Socrates," and "this man," and "this thing;" but others are (B) predicable of many, as are (1) genera, (2) species, (3) differences, (4) properties, and (5) accidents, predicated in common, but not peculiarly to any one thing. Now (1) genus is such as "animal," (2) species as "man," (3) difference as "rational," (4) property as " risible," (5) accident as "white," "black," "to sit."

[The First Two Predicables: Genera & Species] [G]enus is that which is predicated of many things differing in species, in answer to [questions concerning] what a thing is, e. g. "animal." [...] That is called species also, which is under the genus stated, according to which we are accustomed to call "man" a species of "animal," "animal" being genus, but "white" a species of "colour," and "triangle" of "figure."

Nevertheless, since when we define the genus, we make mention of species, saying "that which is predicated of many things differing in species in reply to [questions concerning] what a thing is," and call species "that which is under the assigned genus," we ought to notice that, since genus is the genus of something, and species the species of something, each of each, we must necessarily use both in the definitions of both.

[Subaltern Genera & Species.] They, therefore, define species thus: (1) "species is what is arranged under genus, and of which genus is predicated in reply to [questions concerning] what a thing is." [They] also [define it] thus, (2) "species is what is predicated of many things differing in number in reply to [questions concerning] what a thing is." This [second] definition [of species], however, belongs to the most specific [species] (species specialissima), and which is species only, but no longer genus also, but the other [definition] will pertain to such as are not the most specific [species] (species specialissima).

Now, what we have stated will be evident in this way: in each category there are certain things most generic, and again, others most special, and between the most generic and the most special, others which are alike called both genera and species, but the most generic is that above which there cannot be another superior genus, and the most special that below which there cannot be another inferior species. Between the most generic and the most special, there are others which are alike both genera and species, referred, nevertheless, to different things.

[This] may become clear [by way of example] in one category. "Substance" indeed, is itself a genus; under this is "body" [i.e., physical substance], under "body" is "living body," under which is "animal"; under "animal" is "rational animal," under which is "man,"* under "man" is Socrates, Plato, and particular men. Still, of these, "substance" is the most generic [genus] (summum genus), and that which is genus only; but "man" is most specific [species] (species specialissima), and that which is species only; yet "body" is a species of "substance," but a genus of "living" body, also "living body" is a species of "body," but a genus of "animal"; again, "animal" is a species of "living body," but a genus of "rational animal," and "rational animal" is a species of "animal," but a genus of "man," and "man" is a species of "rational animal,"* but is not the genus of particular men, but is only the species [to which they belong], and every thing prior to individuals being proximately predicated of them, will be species only, and no longer genus also. As then, "substance" being in the highest place, is most generic [genus] (summum genus), from there being no genus prior to it, so also "man"--being a species after which there is no other species, nor any thing capable of division into species, but individuals (for Socrates, Plato, Alcibiades, and this white thing, I call individual)--will be species alone, and the last species, and as we say the most specific [species] (species specialissima).

[*NB. Porphyry is wrong in saying that "man" is a species of "rational animal." In fact, "man" and "rational animal" are the same thing, the latter being the definition of the former. However, he accurately explains the general logical principle of the subordination of species and genera.]

Yet the media [i.e., the intermediate genera/species] will be the species of such as are before them, but the genera of things after them, so that these have two conditions, one as to things prior to them, according to which they are said to be their species, the other to things after them, according to which they are said to be their genera.

The extremes [i.e., the summum genus and the species specialissima], on the other hand, have one condition, for the most generic [genus] (summum genus) has indeed a condition as to the things under it, since it is the highest genus of all, but has no longer one as to those before it, being supreme, and the first principle, and, as we have said, that above which there cannot be another higher genus. Also, the most specific has one condition, as to the things prior to it, of which it is the species, yet it has not a different one, as to things posterior to it, but is called the species of individuals, so termed as comprehending them, and again, the species of things prior to it [i.e., its genera], as comprehended by them, wherefore the most generic genus (summum genus) is thus defined to be "that which being genus is not species," and again, "that above which there cannot be another higher genus"; but the most specific species (species specialissima), as "that which being species is not genus", and "that which being species we can no longer divide into species"; and also "that which is predicated of many things differing in number, in reply to [questions concerning] what a thing is."

Now, the media of the extremes they call "subaltern species and genera," and admit each of them to be species and genus, when referred indeed to different things, for those which are prior to the most specific, ascending up to the most generic, are called "subaltern genera and species." [...]

[Predication: Genus, Species, and Individual.] Genus then, and species, being each explained as to what it is, since also genus is one, but species many, for there is always a division of genus into many species, genus indeed is always predicated of species, and all superior of inferior, but species is neither predicated of its proximate genus, nor of those superior, since it does not reciprocate. For it is necessary that either equals should be predicated of equals, as "neighing" of "a horse," or that the greater should be predicated of the less, as "animal" of "man," but the less no longer of the greater, for you can no longer say that "animal" is "man," as you can say that "man" is "animal."

Of those things however whereof species is predicated, that genus of the species will also be necessarily predicated, also that genus of the genus up to the most generic; for if it is true to say that Socrates is "a man," but that "man" is "an animal," and that "animal" is "a substance," it is also true to say that Socrates is "an animal" and "a substance." At least, since the superior are always predicated of the inferior, species indeed will always be predicated of the individual, but the genus both of the species and of the individual, and the most generic of the genus (or the genera, if the media and subaltern be many) of the species, and of the individual. For the most generic is predicated of all the genera, species, and individuals under it, but the genus, which is prior to the most specific species, is predicated of all the most specific species and individuals; but what is species alone of all its individuals, but the individual of one particular [thing] alone. Now, an individual is called "Socrates," "this white thing," "this man who approaches," "the son of Sophroniscus" (if Socrates alone is his son), and such things are called individuals, because each consists of properties of which the combination can never be the same in any other, for the properties of Socrates can never be the same in any other particular person; the properties of "man," indeed, (I mean of him as common) may be the same in many, or rather in all particular men, so far as they are men. Wherefore the individual is comprehended in the species, but the species by the genus, for genus is a certain whole, but the individual is a part, and species both a whole and a part; part indeed of something else, but a whole not of another, but in other things, for the whole is in its parts. Concerning genus then, and species, we have shown what is the most generic, and the most specific, also what the same things are genera and species, what also are individuals, and in how many ways genus and species are taken.
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