THE MEANING OF TO GENOS TOU EIDOUS MEROS AND TO EIDOS TOU GENOUS MEROS IN ARISTOTLE’S METAPHYSICS Δ 25
In his Metaphysics Δ 25, 1023b24–5 Aristotle juxtaposes to genos tou eidous meros and to eidos tou genous meros by saying that the genus is a part of the form in a different way (allōs) than the form is a part of the genus. The author of the article considers how to interpret the word allōs and argues for the idea that the contrast marked by allōs reveals two different meanings of meros, in each case expressing a different relation of parthood.
PREAMBLE
The exploration of the idea that the genus is a part of the form (to genos tou eidous meros) in a different way (allōs) than the form is a part of the genus (to eidos tou genous meros) in Aristotle’s Metaphysics Δ 25, 1023b24–5 will proceed as follows: (i) the ambiguity marked by allōs will be examined; (ii) the ambiguity of meros will be posited; (iii) the ambiguity of genos and eidos will be dispelled, and (iv) the relations of parthood at work behind the ambiguity of meros will be elucidated.
In this article ambiguity is understood as term’s bearing multiple meanings, and meaning is understood as sense or intension, or concept associated with a term, and it is what determines the referent of the term or the extension, or the object the term is true of. Thus, a term is ambiguous if it has multiple meanings, whether or not it has the same referent. If a term has different referents, then it has different meanings, although a term can have different meanings without having different referents.[1]
THE AMBIGUITY MARKED BY ALLŌS
In the Metaphysics Δ 25 Aristotle distinguishes four ways[2] in which something is called a part:
(1) a part is the result of a division of a quantity, the division being either arbitrary or giving measure, as two is an arbitrary part of three, but not a part which gives measure of three;
(2) parts are the results of a non-quantitative division of a form (i.e. of a genus, namely, a form having forms below itself), as the form, along with other forms, is a part of the genus (to eidos tou genous meros);
(3) parts are the results into which a whole is divided or the constituents out of which it is composed, as both matter and form are parts of something that has the form;
(4) parts are the constituents of a formula (and thus of the form), as the genus (along with the differentia) is a part of the form (to genos tou eidous meros).
Aristotle stresses the difference between the fourth and the second way in which something is called a part by saying that a genus is also called a part of its form, although in a different way the form is a part of its genus (τὸ γένος τοῦ εἴδους καὶ μέρος λέγεται, ἄλλως δὲ τὸ εἶδος τοῦ γένους μέρος, 1023b24–5, trans. Kirwan).
The phrase in a different way (ἄλλως) is crucial here, for otherwise we slip into absurdity. This slip can be easily demonstrated if we assume this principle:
Antisymmetry of Parthood: Two entities which are part of each other are identical.
Let us omit the phrase in a different way and suppose that, unqualifiedly, the genus is a part of the form and the form is a part of the genus. By the Antisymmetry of Parthood, it follows that, if the genus is a part of the form and the form is a part of the genus, then the genus and the form are identical. This result is alarming, since Aristotle would not admit that the genus and the form are identical. It would amount to saying that animal (genus) is identical to man (form). Hence it is not the case that, unqualifiedly, the genus is a part of the form and the form is a part of the genus. If the genus and the form must be distinct and simultaneously it is true that both the genus is a part of the form and the form is a part of the genus, then it must be the case that the genus and the form are parts of each other in a different way.
At first glance, the most evident variant how to interpret the phrase in a different way, viz. the difference between (2) and (4), is to assume that the meaning of genos and eidos shifts. Namely, genos in (2) expresses a distinct concept than genos in (4), and likewise eidos in (2) expresses a distinct concept than eidos in (4). In other words, genus containing the form as a part is distinct from genus being a part of the form, and, similarly, form being a part of the genus is distinct from form containing the genus as a part.
It can still be the case that the referents of genos and eidos in (2) and in (4) do not change, although the meaning does, i.e. the extension remains the same, despite varying intensions. The extensionalistic reading can be adopted with the proviso that the referents of genos and eidos are universals, e.g. animal and man, since Aristotle remarks that the forms as parts of the genus result from a non-quantitative division (1023b17), which suggests that he is not talking about a set of particulars. The constancy of extension, viz. the idea that the genus in (2) is the same universal as the genus in (4), is compatible with the variability of intensions, viz. the idea that the concept of genus in (2) differs from the concept of genus in (4). The same consideration applies to the form.
But what happens to the concept of part? Does meros both in (2) and in (4) preserve the same meaning? It is argued in this article that it does not. Moreover, it is shown that the distinct concepts of genus and form hinge on the distinct ways something is called a part, and there are distinct meanings of part, because meros expresses different relations of parthood.
It has to be emphasized that part is a predicate expressing a relational attribute (πρός τι), viz. a part does not stand on its own; a part is a part of a whole, just as a slave is a slave of a master and a master is a master of a slave (Cat. 7, 6b29−30). It means that an object which is called a part stands in a relation of parthood to something of which it is a part. Thus, meros does not primarily refer to an object which is called a part; more importantly, meros expresses the relation of parthood in which that object stands. The author of the article claims that for Aristotle there are several such relations of parthood.
In contrast to genos (and to eidos) which has different meanings despite having the same referent, meros has different meanings due to expressing distinct relations of parthood.
THE AMBIGUITY OF MEROS
The general purpose of Book Δ of the Metaphysics is to list the meanings of various philosophically significant terms. The collection of these meanings constituting Book Δ is referred to by Aristotle as τὰ περὶ τοῦ ποσαχῶς (Met. Ζ 1, 1028a11), translated by the phrase on the number of ways in which things are said (Furth 1985).[3] Chapter 25 of Book Δ presents a list of the many ways something is called a part. If Aristotle is taken at his word, distinct entries on the list should indeed be distinct. The reason for setting apart one meaning of meros from another must be grounded in the realization that the nature of parthood is multiplex. By distinguishing the meanings of meros Aristotle proposes the idea that objects called parts are not tied together by a single relation of parthood. Instead, there are various relations of parthood, where each operates according to its own principles and has its own properties. It is assumed here that two relations of parthood are identical if and only if they have the same properties.
By contrast, there is a view that one should avoid postulating a variety of relations of parthood, as it leads to an undue proliferation of them (Koslicki 2008, 158; cf. 2007, 138–9). The ambiguity of meros overthrows the conceptions of parthood, where the two-place predicate part of operates according to a fixed set of principles and thereby is essentially univocal. The ambiguity of meros, then, seems to be less elegant due to the lack of parsimony.
However, if it turns out that the relata do not change, while the relation itself does, the proliferation of the relations is compensated by the reduction of the number of objects to which these relations apply. It is conceivable that the genus and the form remain the same objects, i.e. universals, while the relation of parthood in which they stand varies. In other words, the relata of the parthood relation preserve their identity; what differs is the relation is a part of: A is a part1 of B, and B is a part2 of A. This does not exclude the idea that different concepts could correspond to the same object in different relations. For instance, genus as containing the form as a part and genus as being a part of the form are different concepts, while genus as such remains the same object.
THE MEANINGS OF GENOS AND EIDOS
Both genos and eidos are said in many ways.[4] We are interested in those meanings, as Porphyry puts it when explaining Aristotle’s term genos, which are of account to philosophers (Isag. 2.14‒15, trans. Barnes). First of all, this account requires acknowledging that eidos and genos are correlates – the one does not make sense without the other.[5] If there is a genus, it is a genus of a form, and if there is a form, it is a form of a genus, unless this form itself is the highest genus. Every genus has a form above or below itself, and every form has a genus above or below itself.[6]
The correlative nature of genos and eidos presupposes that the meaning of the one determines the meaning of the other and vice versa. If genos and eidos have several meanings, these also have to be mutually determined. We do not have to look far for the right specification of the meanings of genos and eidos, since the meanings of meros already give us a hint.
According to the list (1)−(4) in Met. Δ 25, the meaning of genos in (2) to eidos tou genous meros corresponds to Aristotle’s account in the Topics Α 5, 102a31−2, which is quoted verbatim in Porphyry’s Isagoge 2.16–17: a genus is what is predicated, in answer to ‘What is it?’, of several items which differ in species [i.e. form − εἶδος];[7] for example, animal (trans. Barnes). Porphyry also remarks (ibid. 2.10–13) that we call a genus that under which a species [i.e. form] is ordered (trans. Barnes).
By keeping in mind that genos and eidos are correlates, the appropriate meaning of eidos in (2) is immediately determined. Aristotle talks about the form as being under a genus (Top. Ε 4, 133b10); he says that the form is a subject for the genus and the genus is predicated of it (Cat. 5, 2b19−20). This is manifested in one of the accounts of eidos given by Porphyry as what is ordered under a genus; and: that of which a genus is predicated in answer to ‘What is it?’ (Isag. 4.10–11, trans. Barnes).
The meaning of genos in (4) to genos tou eidous meros in Met. Δ 25 corresponds to the meaning of genos in Δ 28, 1024b4–5 as the first constituent in formulae which is stated in [answer to the question] what a thing is (trans. Kirwan), e.g. the genus animal is stated in answer to what is, for example, man or horse. In this sense, genus is as matter (ὡς ὕλη, Met. Δ 28, 1024b8–9) of its differentia, which, together with the genus, makes up the form. Genus is not exactly hulē but only hōs hulē, for matter strictly speaking belongs to form–matter composites, which is (3) on the list in Met. Δ 25.
Accordingly, the meaning of eidos in (4) is apparent when the form is treated as the object of definition. Since the formula of the form is out of genus and differentia (Top. Ζ 6, 143b19−21), and as the formula is to the thing, so the part of the formula is to the part of the thing (Met. Z 10, 1034b21–2, trans. Furth), hence also the form itself is out of genus and differentia (Met. I 7, 1057b7). Thus, the meaning of eidos in to genos tou eidous meros is what comprises the genus, together with the differentia, as a constituent.[8]
The meanings of genos and eidos in (4) are linked to those in (2), since the referents of genos and eidos in (4) are the same as those in (2). It can be seen via the relations of predication that obtain in both cases. As in (2), so in (4), the genus is predicated of the form,[9] whereas the form is not predicated of the genus (Cat. 5, 2b20−1). It is correct to predicate animal of man and to say that every man is an animal, but it is incorrect to predicate man of animal and to say that every animal is a man (Porph. Isag. 7.6‒8).
THE RELATIONS OF PARTHOOD
To say that the genus is a part of the form in a different way than the form is a part of the genus is to stress that A is a part of B in a different way than B is a part of A. What needs to be explained is the difference between these ways of being a part.
The most straightforward explanation is the following: when the genus is a part of the form (to genos tou eidous meros), the genus composes (σύγκειται) the form along with the differentia, but when the form is a part of the genus (to eidos tou genous meros), the genus is merely divided (διαιρεῖται) into forms by means of the differentiae.[10]
The underlying feature behind a part’s capacity of composing a whole, as opposed to being solely the result of a division of a whole, is its independence from the whole, i.e. ability to exist without the whole. The parts of the form compose the form, because they are independent of the form. The genus animal can exist without the form man, that is, no animal has to be a man. However, the parts of the genus do not compose the genus, because the parts are dependent on it. The form man cannot exist without the genus animal, that is, no man can fail to be an animal.[11]
This reflects a crucial difference in properties of the relation of parthood expressed by meros in (2) and in (4) on the list in Met. Δ 25. That is to say, meros in (4) to genos tou eidous meros expresses a relation of parthood where the parts compose the whole, i.e. the parts are independent of the whole and the whole is dependent on them, whereas meros in (2) to eidos tou genous meros expresses a relation of parthood where the parts only divide the whole and do not compose it, i.e. the parts are dependent on the whole and the whole is independent of them.
CONCLUDING REMARKS
It has been shown that the statement in Aristotle’s Metaphysics Δ 25, 1023b24–5 that the genus is a part of the form in a different way than the form is a part of the genus has to be interpreted in light of the phrase in a different way, which, instead of merely relating it to a change in the meaning of genos and of eidos, has to be tied with a shift in the meaning of meros, which, in turn, relies on the distinction between relations of parthood.
The idea that it is meros that is ambiguous has at least two far-reaching implications. Firstly, it has implications for the interpretation of Aristotle’s theory of parts and wholes. If meros in to genos tou eidous meros differs in meaning from meros in to eidos tou genous meros, then one should rightly ponder whether similar considerations apply to the other ways in which something is called a part in Δ 25, and moreover, one should be cautious of ambiguity with occurrences of meros in other contexts. Secondly, the ambiguity of meros suggests that the understanding of other ambiguous terms listed in Book Δ of the Metaphysics requires more intricate appreciation of their complex nature, which in turn demands aspirations towards an unbiased reading of the text.
BIBLIOGRAPHY
- Aristotelis categoriae et liber de interpretatione. L. Minio-Paluello (Ed.). Repr. Oxford : Clarendon Press, 1966.
- Aristotelis topica et sophistici elenchi. W. D. Ross (Ed.). Repr. Oxford : Clarendon Press, 1970.
- Barnes, Jonathan. Porphyry’s Introduction, Translated with a Commentary. Oxford : Clarendon Press, 2003.
- Furth, Montgomery (Trans.). Aristotle, Metaphysics, Books VII−X, Zeta, Eta, Theta, Iota. Indianapolis : Hackett Publishing Company, 1985.
- Kirwan, Christopher. Aristotle, Metaphysics, Books Gamma, Delta, and Epsilon, Translated with Notes. Oxford : Clarendon Press, 1971.
- Koslicki, Kathrin. Aristotle’s Mereology and the Status of Form. Journal of Philosophy, 103 (12), 2006, 715-36.
- Koslicki, Kathrin. Towards a Neo-Aristotelian Mereology. Dialectica, 61 (1), 2007, 127-59.
- Koslicki, Kathrin. The Structure of Objects. Oxford : Oxford University Press, 2008.
- Magee, John. Anicii Manlii Severini Boethii De Divisione liber: Critical Edition, Translation, Prolegomena, and Commentary. Leiden, Boston, and Köln : Brill, 1998.
- Porphyrii isagoge et in Aristotelis categorias commentarium. A. Busse (Ed.). Vol. 4, bk. 1 of Commentaria in Aristotelem Graeca. Berlin : Reimer, 1887.
- Putnam, Hilary. The Meaning of ‘Meaning’. R. M. Harnish (Ed.). Basic Topics in the Philosophy of Language. Upper Saddle River, NJ : Prentice-Hall, Inc., 1994, 221-74.
- Ross, William D. Aristotle’s Metaphysics, a Revised Text with Introduction and Commentary. 2 vols. Repr. of 1953 corr. edn. Oxford : Clarendon Press, 1958.
- S. Thomae Aquinatis In duodecim libros Metaphysicorum Aristotelis expositio. M. R. Cathala, M. Spiazzi (Eds.). 2nd ed. Taurini-Romae : Marietti, 1971.
ENDNOTES
[1] The meaning of meaning stated here is formulated by Putnam (1994, 222‒5) as the traditional doctrine, which he deems unsatisfactory. In spite of his criticism, this doctrine will do as a crude tool for the purposes of this article.
[2] The meaning of meaning stated here is formulated by Putnam (1994, 222‒5) as the traditional doctrine, which he deems unsatisfactory. In spite of his criticism, this doctrine will do as a crude tool for the purposes of this article.
[3] Besides τὰ περὶ τοῦ ποσαχῶς, Ross (1958, vol. 1, xxv) mentions ἐν ἄλλοις (see, e.g. 1017b9; Θ 1, 1046a5−6) as Aristotle’s way of referring to the contents of Book Δ. Furth (1985) renders ἐν ἄλλοις in 1046a5−6 simply as elsewhere.
[4] There is no list of the meanings of eidos, whereas in Met. Δ 28 we can find a list of the meanings of genos, which, however, does not include all the meanings of genos used by Aristotle.
[5] Aristotle does not explicitly say that genos and eidos are correlates, but this idea can be derived from his talk about relatives (τὰ πρός τι) in Book 7 of the Categories.
[6] The highest genus is not a form of a genus above itself, and the last form is not a genus of a form below itself; the intermediate genera are forms of the highest genus and genera of forms below them (see Porph. In Cat. 83.20–3).
[7] It is traditionally accepted that εἶδος in Aristotle is translated by two names, i.e. form or species, depending on the context of use. In the context where the relations of εἶδος and γένος are operative, the rendering of εἶδος is species, whereas form as a translation of εἶδος is used to contrast it with matter (ὕλη) when talking about form-matter composites. This brings out the affinity of εἶδος to μορφή ‒ shape or appearance. From time to time Aristotle employs μορφή to designate the formal aspect of form-matter composites, although μορφή is a rarer occurrence than εἶδος. The author of the article translates εἶδος consistently as form (following Kirwan 1971), since Aristotle himself uses εἶδος in both contexts.
[8] It is not uncontroversial whether genus literally is a constituent of the form. Koslicki (2006, 728 n. 32; cf. 2008, 158) rightly points out that form should not be identified with definition (of which genus is a constituent), since a definition is a linguistic entity, whereas a form is what is described by it. At the same time, it cannot be denied that Aristotle endorses correspondence between the parts of the definiens, i.e. the terms of the definition, and the parts of the definiendum (Met. Z 10, 1034b21–2). In that case, there is no way to circumvent the fact that something in the form, i.e. a constituent of the form, is picked out by each term of the definiens. Since a form is delimited within a genus by a differentia, there is no reason why one should not concede that in a way the form consists of genus and differentia.
[9] In fact, both constituents of the form can be predicated of the form. The differentia can be predicated of the form, e.g. rational can be predicated of man, when the differentia is form-producing (εἰδοποιός), i.e. when it composes the form together with the genus (Top. Ζ 6, 143b8–9). However, the differentia cannot be predicated of the form, when it serves to divide the form (qua genus) into subordinate forms, e.g. rational cannot be predicated of animal, for animal is not composed as a form by the differentiae that divide it (see Porph. In Cat. 85.21–8).
[10] The same idea is voiced also in Boethius’ De Divisione 39.1‒2 when it is stated that in division the genus is a whole, in definition a part (trans. Magee). What is emphasized is that definition resembles the composition of a whole (ibid. 39.5, trans. Magee), it is as if parts of some kind are constituting a whole (ibid. 39.2‒3, trans. Magee), namely the form (i.e. species in Boethius’ terminology, 39.20), but in division the whole, namely the genus, is merely resolved into parts. In Medieval terminology (see, e.g. Aquinas In Met. lib. 5 l. 21 n. 13), a genus having the form as a part is a universal whole (totum universale) predicated of its form as of a subjective part (pars subiectiva), whereas a genus being a part of the form is, along with the differentia, an integral part (pars integralis) of the form, which in this case is an integral whole (totum integrale).
[11] The dependence of the parts on the genus and the independence of the genus from its parts are affirmed also in De Div. 13.36‒14.1: [I]f the genus is destroyed the species immediately perish, but … if a species is destroyed the genus consists inviolate in its nature (trans. Magee).
* Raksts «THE MEANING OF TO GENOS TOU EIDOUS MEROS AND TO EIDOS TOU GENOUS MEROS IN ARISTOTLE’S METAPHYSICS Δ 25″ oriģināli publicēts Antiquitas Viva 4. sējumā, 2014., 58.-66. lpp. Autores agrākais uzvārds – Muižniece. Pārpublicēts ar autores un LU Apgāda piekrišanu.
