Concerning the chapter "On species," the question is whether the definition of species -- "Species is what is predicated of many items differing in number" -- is appropriately given.

1 It appear that it is not:

For according to Porphyry, since genus and species are correlatives, "one must make use of each in defining the other." ⁽¹⁾ But nothing is stated in this definition that expresses the correlative, namely genus. Therefore, it is a bad definition of species.

2 Moreover, this definition also holds of genus, as is evident, given that "differing in species" implies "differing in number."

3 Moreover, there are not many definitions [of one and the same item], according to Aristotle in Topics VI [4, 141^a31-^b1], just as there are not many essences. For if there were, an item would not be definible. Therefore, since species is appropriately defined as "what is subordinated to a designated genus," it is not appropriately defined by this definition.

4 Moreover, the definition "subordinated to a genus" implies that a species is per se capable of being a subject; therefore, it is not per se predicable. ⁽²⁾ Therefore, the other definition is false, since opposites are not present in one and the same item per se.

5 One view ⁽³⁾ is that relative opposites can be present in one and the same item, although not with respect to the same item, since with respect to the same item they are opposites. Now what is predicable with respect to individuals is capable of being a subject with respect to a genus.

6 An objection to this view: If what is related to a genus is appropriately defined through the genus, then it is related to the genus per se. It is also related to the individuals through which it is defined in this second definition [given in n. 4]. Therefore, one and the same item is said twice relatively, which is contrary to what Aristotle says in Metaphysics V [15, 1021^a31-^b2].

7 Moreover, as to the main question: This definition does not separate species from definition.

8 Moreover, species is not a predicate, according to Aristotle in Topics I [4, 101^b24-26]. Therefore, it is badly defined on the basis of "being predicated."

9 Porphyry argues for the opposite view. ⁽⁴⁾

10 Arguments both for and against the view in question, as well as objections, could be given here is very much the same ways as above [q. 15, nn. 1-11], where the question concerned the definition of genus.

11 It must be said that the definition is appropriate, in just the same ways as I argued above [q. 15, n. 19] concerning the definition of genus.

12 To the first argument [n. 1] it is said that species is said relatively to genus, and so it is necessary that some definition of species be given in which genus is included. That definition is "Species is what is subjected to a designated genus." But species has another relation to individuals, not according to which it is related to the genus -- since Porphyry denies that the extremes have two relations in this way ⁽⁵⁾ -- but according to which it is a species. And for that reason it must have another definition that relates it to individuals.

13 A reply to the second argument [n. 2] was given above, in question 17 [nn. 7-10].

14 To the third argument [n. 3] it is said that are not many definition of one absolute item of which there is a definition that expresses its being in itself. But species is per se related to two items.

15 An objection to this reply: Even if that were true, species would have just the two definition, since it would have just one relating it to individuals and just one relating it to genus. But Porphyry gives two definitions [see n. 4] relating it to genus. For he says [n. 9] that this designation, namely, being predicated of many, is proper to the most specific species, "but there will be others, and not of the most specific species." So there are at least two other definitions of species besides this one.

16 One approach ⁽⁶⁾ is to concede this point and to say that species can have a twofold relation to genus: one as it is ordered beneath the genus, and another as the genus is predicated [enuntiatur] of a species in a proposition. The definition "Species is what is subordinated to a designated genus" is given in the first way; "Species is that is of which the genus is predicated in eo quod quid" is given in the second way.

17 An objection to this approach: The Categories is more immediately ordered to De interpretatione than Porphyry's book is. But in the Categories no determination is made concerning simples insofar as one is predicated of another -- otherwise it would be redundant for De interpretatione to determine that noun and verb signify simples under those notions. Therefore, much less is species defined here as genus is predicated of it.

18 Here it can be conceded that Porphyry offers only one definition relating species to genus. And then the notion "what is subordinated to a genus" is expounded through what follows, namely, "of which [the genus is predicated in eo quod quid]." When he says "there will be others, not of the most specific species," he means other statements that make the species known [notificationes], not other definitions, since on the basis of a certain diversity they make the species known secundum quid. For an exactly similar diversity could be found by relating the species to individuals, and yet only one definition of species is given on the basis of that relation.

19 The reply to the fourth argument [n. 4] was given above [n. 5].

20 To the argument against this reply [n. 6] it can be said that species is not related to both genus and individuals merely on account of diverse items that are accidental to itself -- for if that were the case, it would not be defined in terms of either of them, just as human being is not [defined in terms of double], even if a human being is accidentally double. ⁽⁷⁾ Rather, it is related to both essentially and per se. As for the claim that "the same item is not related twice," Aristotle understands this to mean that an accident is not related to its subject, as he indicates in the text where he says "it is not understanding [because it is related] to the one who understands and to the intelligible." ⁽⁸⁾ So understood, this claims is not contrary to what was said above.

21 ⁽⁹⁾ Alternatively, one ought to say ⁽¹⁰⁾ that one and the same item is not related primarily to diverse items, but it can be related per se to diverse items. Species is related primarily to one item through its definition but per se to another item according to the definition of its genus. For a relative according to its genus is relative per se, since it includes in its essence that through which it is a relative. For it is impossible that an absolute essentially includes a relative in its essence. In this way, species according to its proper definition is said with respect to genus; but according to the definition of its genus, i.e. universal, it is said relatively to those items of which it is predicated, since "to be said of" belongs to it qua universal. ⁽¹¹⁾

For example: the double according to itself is related to the half, but according to its genus it is related to the fractional. ⁽¹²⁾ Still, the analogy is not perfect, since in the latter case, but not in the former, the correlative of the genus contains the correlative of the species. For this reason the first definition of species is the proper definition according to itself, since it is given on the basis of its first correlative; the second definition is given later, since it is more relevant to the inquiry at hand. For it is proper to species qua universal.

22 To the fifth argument [n. 7; cf. q. 12, nn. 19, 15-16] it can be conceded that definition is not a universal distinct from species as far as this present treatment of universals is concerned.

Alternatively: Species is not predicated in quid, but in quid-quale, since it does not have unqualifiedly one mode of being predicated, but two, like genus and difference, of which it is composed.

23 The reply to the sixth argument [n. 8] was given in question 12 [nn. 18-19].

[Question 22: Is "Many men are one man" true?]

The question is about the truth of "Many men are one man."

1 It appears that it is true:

The following inference is valid: "By participation in the species, many men are one man; therefore, many men [are one man]." According to Porphyry, ⁽¹³⁾ the antecedent is true; therefore, so is the consequent. Proof of the inference: Nothing is restricted by another unless it is placed with it on the part of the same extreme. ⁽¹⁴⁾ "By participation in the species" is placed in the antecedent on the part of the subject, and "one" is not. Therefore, 'one' is not restricted in the antecedent.

2 Moreover, when something is related to others unqualifiedly and secundum quid, if something is added that determines it secundum quid, it stands only for [what it is related to secundum quid]. 'One' is related to one-in-number unqualifiedly and to one-in-species secundum quid. Therefore, in the proposition at issue, when the name of the species, man, is added, it will stand for unity of species, and in this way the proposition is true. Therefore, the proposition is true unqualifiedly.

3 Moreover, according to Aristotle in Metaphysics V [6, 1016^b4-6], "Universally, insofar as certain items admit no division, in that respect they are one." The many men admit no division with respect to man, since the form of man is in them univocally. Therefore, they are one man.

4 Moreover, each of them is one man; therefore, the whole lot of them are one man. The antecedent is true, since any given one of them is singular. Proof of the inference: The opposite of the consequent -- namely, "Only one man is one man" -- is incompatible with the antecedent, "Each [man is one man]," since in the antecedent 'one man' is attributed to the subject for at least two.

5 Arguments for the opposite view:

7 It must be said that 'one' can be taken categorematically, and in that way it signifies a difference of being. This is how Aristotle speaks of 'one' in Metaphysics V [6, 1017^b10-1020^a6] and X [1-3, 1052^a15-1054^b3], and he divides it accordingly into many modes in Metaphysics V. At the end, however, in the chapter "On one," ⁽¹⁵⁾ he puts forward four modes to which all the previous modes are reduced: one in number, in species, in genus, and in proportion. If the categorematic 'one' is related equivocally to these four, then the proposition at issue still has to be distinguished [into different senses] according to the equivocation of the categorematic 'one', and in three of those senses it is true. It is false in the fourth sense - that is, where 'one' is taken as 'one in number'.

8 On the other hand, if (as is perhaps more true) 'one' is related to these four as to unqualifiedly and secundum quid (which appears to be the case from what Aristotle says in Metaphysics V, and from the fact that from 'one in number' follows 'one in species' and, further, 'one in genus' and 'one in proportion', and not vice versa, as though there is a lesser character [ratio] of unity in what is one in species than in what is one in number, and in what is one in genus than in what is one in species), then what one should say is that the proposition is false insofar as 'one' is categorematic. For since nothing is added here to limit it to unity secundum quid, 'one' stands only for one-in-number, which is one unqualifiedly.

9 Alternatively, 'one' is taken as syncategorematic, ⁽¹⁶⁾ and in this way it expresses a mode of understanding the term for a determinate supposite, but indeterminately. And 'man', taken in this way for its supposit, is not in its subject. So in that way the proposition is false. For there is nothing in the subject in virtue of which one man could be confused and taken for diverse [men], since conjunction does not confuse [the conjuncts]. For if it did, "Two and two are two" would be true in the composed sense. But that is false, since in the composed sense "Two and two are four" is true. And from these two claims it follows that four are two, which is impossible. Therefore, one of the premises is false in the composed sense, in which they imply that conclusion.

10 As for the first argument [n. 1], I reject the inference. As for the proof, I say that that determination is to be understood in the predicate, as follows: Many men are one man by participation in the species, that is, by participating in the species.

11 To the second argument [n. 2] I say that the determinable does not restrict the determination, but vice versa -- and especially not to 'secundum quid'. Thus, in 'dead man', 'dead' does not stand secundum quid, even though it sometimes restricts man to supposits. For in 'white man' 'white' stands only for white in man. [Someone please explain this argument to me.]

12 To the third argument [n. 3] I say that the inference "they are undivided with respect to man, or (in other words) with respect to the form of man; therefore, they are one man, or an undivided man" is invalid. For in the antecedent man is signified as having the nature of a determination with respect to one, whereas in the consequent man is signified as determinable.

13 As for the fourth argument [n. 4], I reject the inference. As for the proof, I say that what is put in the place of the consequent, if it is one in the same way as in "This man and that man are one man," is true in the divided sense. And its opposite is not "Only one man" but "Not many men," which is perfectly compatible with the antecedent. For in this proposition the predicate is denied of many taken through the mode of many; in the other proposition that same predicate is affirmed of many taken through the mode of one. For in the original proposition the predicate is [applied] distributively to this man and that man -- after all, "each" is a sign of distribution -- whereas in the other proposition it is [applied] jointly to both.