LESSON 4

Ways in Which One and Many Are Opposed

  Chapter 3: 1054a 20-1055a 2

             833. One and many are opposed in many ways, and one of these is the opposition between one and many as between something indivisible and something divisible; for many means either what is divided or what is divisible, and one means either what is undivided or what is indivisible.

             834. Hence, since we speak of four modes of opposition, and one of these two opposites is expressed privatively, they will be contraries and not contradictories or relative terms (313).

             835. And what is one is described and made known in reference to its contrary, and what is indivisible in reference to what is divisible; for what is many and is divisible is better known to the senses than what is indivisible. Hence what is many is prior in intelligibility to what is indivisible, because of sensory perception.

             836. And as we have already indicated in our division of contraries, same, like and equal relate to what is one; but diverse, unlike and unequal relate to what is many.

             837. Now things are said to be the same in several ways; for in one way we say that a thing is numerically the same; and in another way we say that it is the same if it is one both in its intelligible structure and numerically; for example, you are the same as yourself in both form and matter. Again, things are the same if the intelligible structure of their primary substance is one, as equal straight lines are the same, and equal quadrangles which are equiangular, and also many other things; but in these cases equality is unity.

             838. Things are like if, while being the same in an unqualified sense or without a difference as regards their substance, they are the same in species; for example, a larger square is like a smaller one. And this likewise holds true of unequal straight lines, for these are like but not the same in an unqualified sense. And some things are said to be like if, while having the same form and admitting of difference in degree, they do not differ in degree. And other things are like if the same affection belongs to both and is one that is the same in species; for example, both what is whiter and what is less white are said to be like because they have one species. And other things are said to be such if they have more of sameness than diversity, either absolutely, or in regard to those attributes which are more important; for example, tin is like silver in being white, and gold is like fire in being red or yellowish.

             839. It is evident, then, that the terms diverse and unlike are used in many senses; and that other or diverse is used in a way opposite to the same. Hence everything in relation to everything else is either the same or diverse. And things are diverse in another sense if their matter and intelligible structure are not one; thus you and your neighbor are diverse. A third meaning of this term is that found in mathematics. Hence for this reason everything is either diverse or the same as everything else, i.e., everything of which men predicate unity and being. For other is not the contradictory of the same, and this is why it is not predicated of non-beings (but they are said to be "not the same"), but it is predicated of all beings; for whatever is by nature a being and one is either one or not one. Hence diverse and same are opposed in this way.

             840. But different and diverse are not the same. For that which is diverse and that from which it is diverse need not be diverse in some particular respect, because every being is either diverse or the same. But that which is different differs from something in some particular respect. Hence there must be some same thing by which they differ. Now this same thing is either a genus or a species; for everything that differs, differs either generically or specifically: generically, if they have no common matter and are not generated from each other, like those things which belong to a different figure of predication (60), and specifically, if they have the same genus. Genus means that by which both of the things that differ are said to be without difference in substance. But contraries are different, and contrariety is a kind of difference.

             841. That this assumption is correct becomes clear by an induction; for all these contraries seem to be different, and they are not merely diverse, but some are generically diverse and others belong to the same category, so that they are contained in the same genus and in the same species. The kinds of things which are generically the same and those which are generically diverse have been established elsewhere (445).

COMMENTARY

             1983. After having treated of one considered in itself, here the Philosopher deals with one in comparison with many; and this is divided into two parts. In the first (833:C 1983) he treats one and many and their concomitant attributes. In the second (842: C 2023) he establishes what is true about the contrary character of one and many; for the investigation of this involves a special difficulty ("But since it is possible").

             The first member of this division is divided into two parts. In the first part he shows how one and many are opposed. In the second (836:C 1999) he considers their concomitant attributes ("And as we have").

             In regard to the first he does three things. First (833), he indicates how we should understand the opposition between one and many. He says that, although one and many are opposed in many ways, as will be made clear below, none the less one of these ways, and the most important one, concerns one and many insofar as they are opposed as something indivisible is opposed to something divisible, because this mode of opposition pertains to the proper notion of each.

             1984. For the essential note of plurality consists in things being divided from each other or in being divisible. He says "divided" because of the things which are actually separated from each other and which are for this reason said to be many. He says "divisible" because of the things which are not actually separated from each other but come close to being separated, for example, moist things such as air and water and the like, of which we use the term much because they are easily divided; thus we speak of much water and much air.

             1985. But the formal constituent of unity or oneness consists in being indivisible or in being undivided; for the continuous is said to be one because it is not actually divided, although it is divisible.

             1986. Hence, since (834).

             Second, he makes clear to what kind of opposition the aforesaid manner of being opposed is ultimately reduced. He says that, since there are four kinds of opposition, one of which is based on privation, it is evident that one and many are not opposed as contradictories or as relative terms, which are two kinds of opposition, but as contraries.

             1987. That they are not opposed as contradictories is evident because neither of them applies to non-being, for non-being is neither one nor many. But the second member of the contradiction would have to apply to being as well as to non-being. That they are not opposed as relative terms is likewise evident, for the terms one and many are used in an absolute sense.

             1988. And although he had said that one and many are opposed as what is indivisible and what is divisible, and these appear to be opposed as privation and possession, none the less he concludes that one and many are opposed as contraries; for the opposition between privation and possession is the basis of the opposition between contraries, as will be made clear below (848:C 2036). For one of the two contraries is always a privation, but not a pure privation; otherwise it would not share in the nature of the genus, since contraries belong to the same genus. Each of the two contraries, then, must be a positive reality, even though one of them shares in the nature of the genus with a certain deficiency, as black in relation to white, as has been stated above (831:C 1967). Therefore, since unity does not signify a pure privation, for it does not designate the mere lack of division but the very being which is undivided, it is evident that one and many are opposed not as pure privation and possession but as contraries.

             1989. And what is one (835).

             Third, he answers an implied question. Because he had said that one is related to many as what is indivisible to what is divisible, and what is indivisible seems to be the privation of what is divisible since privation is subsequent to possession or form, it seems to follow that one is subsequent to many, although he had said above (821:C 1939) that one is the principle of many, from which it becomes known.

             1990. In order to see the solution of this difficulty, then, it must be borne in mind that things which are prior and better known by nature are subsequent and less well known to us, because we derive our knowledge of things from the senses. Now the first things to be perceived by us are composite and confused things, as is said in Book I of the Physics; and this is why the first things to be known by us are composite things. But simpler things, which are prior and more intelligible by nature, are known by us only derivatively; and this is why we define the first principles of things only by the negations of subsequent things; for example, we say that the point is what has no parts; and we know God by way of negations inasmuch as we say that God is incorporeal, unchangeable and infinite.

             1991. Accordingly, even though what is one is prior by nature to what is many, yet in our knowledge it is defined and gets its name from the privation of division. This is why the Philosopher says that "what is one is described," i.e., named, "and made known," i.e., understood, "in reference to its contrary," just as the indivisible is known from the divisible. And for this reason many things are able to be perceived more easily than one thing; and what is divisible is able to be perceived more easily than what is indivisible, not in the order of nature but because of sensory perception, which is the foundation of our knowledge.

             1992. But a twofold difficulty arises with regard to those things which the Philosopher is expounding. The first concerns his statement that one and many are opposed as contraries. For this appears to be impossible, because unity is the basis of plurality, whereas one of two contraries does not ground the other but rather destroys it.

             1993. Hence it must be noted that, since contraries differ formally, as is said below (888:C 2120), when we say that things are contraries, each of them is to be taken insofar as it has a form, but not insofar as it is a part of something having a form. For insofar as body is taken without the soul, as something having a form, it is opposed to animal as the non-living is opposed to the living. But insofar as it is not taken as something complete and informed, it is not opposed to animal but is a material part of it. We see that this is likewise true of numbers; for insofar as the number two is a kind of whole having a determinate species and form, it differs specifically from the number three; but if it is taken insofar as it is not made complete by a form, it is a part of the number three.

             1994. Therefore insofar as unity itself is considered to be complete in itself and to have a certain species, it is opposed to plurality; because what is one is not many, nor is the reverse true. But insofar as it is considered to be incomplete as regards form and species, it is not opposed to plurality but is a part of it.

             1995. The second difficulty has to do with the statement that plurality is prior in intelligibility to unity; for, since the concept of plurality or multitude involves unity, because a plurality is nothing else than an aggregate of units, if unity is subsequent in intelligibility to plurality, it follows that the notions of unity and plurality involve circularity, i.e., in the sense that unity is intelligible in terms of plurality and vice versa. But circularity of definition is not admissible in designating the intelligible structures of things, because the same thing would then be known both to a greater and to a lesser degree. This is impossible.

             1996. The answer to this difficulty, then, must be that nothing prevents one and the same thing from being prior and subsequent in intelligibility according to different traits which are considered in it. For in multitude it is possible to consider both multitude as such and division itself. Thus from the viewpoint of division multitude is prior in intelligibility to unity; for that is one which is undivided. But multitude as multitude is subsequent in intelligibility to unity, since a multitude means an aggregate of units or ones.

             1997. Now the division which is implied in the notion of that kind of unity which is interchangeable with being is not the division of continuous quantity, which is understood prior to that kind of unity which is the basis of number, but is the division which is caused by contradiction, inasmuch as two particular beings are said to be divided by reason of the fact that this being is not that being.

             1998. Therefore what we first understand is being, and then division, and next unity, which is the privation of division, and lastly multitude, which is a composite of units. For even though things which are divided are many, they do not have the formal note of a many until the fact of being one is attributed to each of the particular things concerned. Yet nothing prevents us from also saying that the notion of multitude depends on that of unity insofar as multitude is measured by one; and this already involves the notion of number.

             1999. And as we have (836).

             Here he indicates the attributes which stem from unity and plurality; and in regard to this he does two things. First, he gives the attributes which naturally stem from unity and plurality. He says that sameness, likeness and equality flow from unity, as has been pointed out above in Book V (446:C 911), where he divided or distinguished the various senses in which things are said to be contrary; for those things are the same which are one in substance; those are like which are one in quality; and those are equal which are one in quantity.

             2000. And the contraries of these, diverse, unlike and unequal, pertain to plurality. For those things are diverse whose substance is not one; those are unlike whose quality is not one; and those are unequal whose quantity is not one.

             2001. Now things (837).

             He now explains the various senses in which these terms are used; and in regard to this he does two things. First, he shows how the modes of those attributes which accompany unity differ from each other. Second (839:C 2013), he does the same thing for those attributes which accompany plurality ("It is evident").

             In regard to the first part he does two things. First, he explains the various ways in which things are said to be the same; and second (838:C 2006), those in which they are said to be like ("Things are like"). He does not make any distinctions as regards equality, however, because there are not many ways in which things are said to be equal, unless perhaps in reference to the various kinds of quantity.

             2002. He accordingly gives (837) three ways in which the term same is used. For since same means one in substance, and substance is used of two things, namely, of the supposit itself and of the nature or species of a thing, the term same is used of three things: either of the supposit alone, as this white thing or this musical man, assuming that Socrates is white or musical; or of the nature of the supposit alone, that is, its intelligible expression or species, as Socrates and Plato are the same in terms of humanity; or of both together, as Socrates is the same as Socrates.

             2003. Hence, the Philosopher, in giving these three ways in which the term is used, says that the term same is used in many senses. In one sense it means what is numerically the same, which we sometimes express by the term itself, as when we say that Socrates is a man and that he himself is white. For since the pronoun itself is reflexive, and a reflexive term brings back the same supposit, wherever the term itself is used it signifies that the supposit is numerically one and the same.

             2004. A thing is said to be the same in another sense if it is one not only by the oneness of the supposit, as this wood and this white thing, but if it is the same both in its intelligible structure and in number, as you are the same as yourself both specifically and materially, inasmuch as matter, which is the principle of individuation is taken for the supposit, and species is taken for the nature of the supposit.

             2005. Things are said to be the same in a third sense when "the intelligible structure of the primary substance," i.e., of the supposit, is one, even though there is not one supposit. And these things are the same specifically or generically but not numerically. He gives an example of this in the case of quantity, according to the opinion of those who claimed that quantities are the substances of things; and according to this opinion many straight lines are regarded as many supposits in the genus of substance, and the measure of a line is considered to be its species. This opinion maintains, then, that many straight lines are one, just as distinct supposits are one which have one specific nature in common. And since mathematicians speak of lines in the abstract, for them many equal straight lines are considered as one. And in a similar fashion many "equal quadrangles," i.e., figures which have four angles and are equal in size and "equiangular," i.e., having equal angles, are considered to be the same. And in such things as these equality provides the unity of their specific nature.

             2006. Things are "like" (838).

             Here he reveals the different ways in which things are said to be like, and there are four of these. The first corresponds to the third way in which things are the same; for since that is the same which is one in substance, and that is like which is one in quality, the basis of likeness must be related to the basis of sameness as quality to substance. And since he has used equality to designate oneness of substance, he uses figure and proportion to designate quality.

             2007. It should also be noted that, since quality and quantity are rooted in substance, it follows that wherever there is oneness of substance there is oneness of quantity and quality, although this oneness or unity does not derive its name from quantity and quality but from something more basic, namely, substance. Hence, wherever there is oneness of substance we do not speak of likeness or of equality but only of identity.

             2008. Diversity of substance, then, is required for likeness or equality. This is why he says that some things are said to be like even though they are not absolutely the same as to the species of their substance (provided that they are also not without difference in their underlying subject, which is called the supposit) but are specifically the same in some way. Thus a larger quadrangle is said to be like a smaller one when the angles of one are equal to those of the other and the sides containing the angles are proportional. It is evident, then, that this likeness is viewed from the standpoint of oneness of figure and proportion. And in a similar way many unequal straight lines are not the same in an absolute sense even though they are like.

             2009. It can also be noted here that, when there is unity in regard to the complete concept of the species, we speak of identity. But when there is no unity in regard to the whole concept of the species, we speak of likeness; so that if someone says that things which are generically one are like, then those which are specifically one are the same, as the examples given above would seem to indicate. For he said that equal straight lines and equal quadrangles are identical with each other, whereas unequal quadrangles and unequal straight lines are said to be like.

             2010. Things are said to be like in a second sense when they have in common one form which admits of difference in degree although they participate in that form without difference in degree; for example, whiteness admits of greater and lesser intensity, so that, if some things are equally white without any difference in degree, they are said to be like.

             2011. Things are said to be like in a third sense when they have in common one form or affection but to a greater or lesser degree; for example, a thing which is whiter and one which is less white are said to be like because they have "one form," i.e., one quality.

             2012. Things are said to be like in a fourth sense when they have in common not merely one quality but many, as those things which are said to be like because they agree in more respects than they differ, either in an absolute sense, or in regard to certain particular attributes; for example, tin is said to be like silver because it resembles it in many respects. And similarly fire is like gold, and saffron like red.

             2013. It is evident (839).

             Here he treats the attributes which naturally accompany plurality. First, he considers unlikeness and diversity; and second (840:C 2017), he treats difference ("But different").

             He accordingly says, first (839), that, since the terms same and diverse and like and unlike are opposed to each other, and since the terms same and like are used in many senses, it is evident that the terms diverse and unlike are used in many senses; for when one of two opposites is used in many senses, the other is also used in many senses, as is said in the Topics, Book I.

             2014. But omitting the many senses in which the term unlike is used, since it is quite apparent how the senses of this term are taken in contrast to those of the term like, he gives three senses in which the term diverse, or other, is employed. First, the term diverse refers to everything that is other in contrast to the same; for just as everything that is itself is said to be the same, and this is the relation of identity, in a similar fashion everything that is diverse is said to be other, and this is the relation of diversity. Hence everything is either the same as or other than everything else. Second, the term diverse, or other, is used in another sense when the matter and intelligible structure of things are not one; and in this sense you and your neighbor are diverse. The term is used in a third sense in mathematics, as when unequal straight lines are said to be diverse.

             2015. And since he had said that everything is either the same as or other than everything else, lest someone think that this is true not only of beings but also of non-beings, he rejects this by saying that everything is either the same as or other than everything else in the case of those things of which the terms being and unity are predicated, but not in the case of those things which are non-beings. For same and diverse are not opposed as contradictory terms, of which one or the other must be true of any being or non-being; but they are opposed as contraries, which are only verified of beings. Hence diversity is not predicated of non-beings. But the phrase not the same, which is the opposite of the same in a contradictory sense, is also used of non-beings. However, same or diverse is used of all beings; for everything that is a being and is one in itself, when compared with something else, is either one with it, and then it is the same, or it is capable of being one with it but is not, and then it is diverse. Diverse and same, then, are opposites.

             2016. But if someone were to raise the objection that diversity and sameness do not apply to all beings, since sameness is a natural consequence of oneness of substance, and diversity is a natural consequence of plurality of substance, we should have to answer that, since substance is the root of the other genera, whatever belongs to substance is transferred to all the other genera, as the Philosopher pointed out above regarding quiddity in Book VII (582:C 1334).

             2017. But "different" (840).

             Then he shows how difference and diversity differ. He says that diverse and different mean different things; for any two things which are diverse need not be diverse in some particular respect, since they can be diverse in themselves. This is evident from what has been said above, because every being is either the same as or other than every other being.

             2018. But that which differs from something else must differ from it in some particular respect. Hence that by which different things differ must be something that is the same in things which do not differ in this way. Now that which is the same in many things is either a genus or a species. Therefore all things that differ must differ either generically or specifically.

             2019. Those things differ generically which have no common matter; for it has been said above, in Book VIII (704:C 1697), that although matter is not a genus, still the essential note of a genus is taken from a thing's material constituent; for example, sensory nature is material in relation to the intellectual nature of man. Hence anything that does not possess sensory nature in common with man belongs to a different genus.

             2020. And since those things which do not have a common matter are not generated from each other, it follows that those things are generically diverse which are not generated from each other. It was also necessary to add this because of the things which do not have matter, such as accidents, so that those things which belong to different categories are generically diverse, for example, a line and whiteness, neither one of which is produced from the other.

             2021. Now those things are said to be specifically diverse which are the same generically and differ in form. And by genus we mean that attribute which is predicated of two things which differ specifically, as man and horse. Moreover, contraries differ, and contrariety is a type of difference.

             2022. That this assumption (841).

             Then he proves by an induction what he had said above about the formal note whereby things differ, because all things that are different seem to be such that they are not merely diverse but diverse in some particular respect. Some things, for instance, are diverse in genus; some belong to the same category and the same genus but differ in species, and some are the same in species. What things are the same or diverse in genus has been established elsewhere, namely, in Book V of this work (456:C 931).