45 Responses to Objections
45: Responses to Objections To clarify the view described above we shall set out some objections which seem to show that the view is incompatible with the account of Aristotle and his followers.
(1) First, Aristotle scems to say the opposite in the Categories, where he says that a large expanse of white is a quantum only per accidens.' However, if quantity were nothing different from quality, then the white would be a quantum per se. Indeed, it would be a quantity per se.
(2) Again, in the fifth book of the Metaphysics Aristotle says, "Of things said to be quanta accidentally, some are said to be such in the way in which the musical and the white are said to be quanta—by being in that which is a quantum."? But since the white is a quantum only in virtue of the fact that it is in that which is a quantum per se, whiteness is not a quantity.
(3) Again, in the same place Aristotle says, "Some things are said to be quanta essentially and others, only accidentally. Thus, the line is a quantum essentially; whereas the musical is a quantum accidentally."?
(4) Again, in the Categories Aristotle claims that some quantities are such that their parts are connected at some common boundary.' Thus, the parts of the line are connected at the point, the parts of the surface at the line, and the parts of the solid at the surface. Now the parts of a thing are not connected at some different part of the same whole; therefore, the point is to be distinguished from the line, the line from the surface, and the surface from the solid.
(5) Again, in the Posterior Analytics he says that the point is indivisible,> but that property accrues to neither the line nor the surface.
(6) Again, he wants to claim that unity is indivisible and that consequently it is neither the solid, nor the line, nor the surface; neither is it a point; therefore, it is something over and above these things; but since
Responses to Objections unity is not a number it is something over and above number; but the view outlined above runs counter to these remarks.
(7) In the first book of the Physics, he proves, against Parmenides and Melissus, that there are many things by pointing to the fact that both substance and quantity exist." Clearly this proof would fail if substance and quantity were not different things.
But in spite of these objections I think that the position I have outlined, whether true or false, follows from the principles of Aristotle's philosophy.
First it should be noted that the Philosopher uses the terms 'per se' and 'per accidens' equivocally. For the present, it is sufficient to note that in the relevant places, Aristotle does not employ the terms 'per se' and 'per accidens' as generally as he does in the first book of the Posterior Analytics.® On the contrary, he is using the term 'per se' in such a way that a proposition is per sc which is true and has in addition a predicate connoting nothing other than what is connoted in a similar way by the subject. Thus to claim that a proposition per se in this sense is false and that the proposition affirming the existence of the relevant subject is true is to affirm an out-and-out contradiction. Put otherwise, he is claiming that a proposition is per se if part of the definition is predicated of the relevant definition, if the whole definition is predicated of the definition, ifa term is predicatedofitself, or ifa term is predicatedofits synonym. He calls all other propositions per accidens.
Response to (1) This point enables us to handle the first objection; for when he says that a large expanse of white is only a quantum per accidens, the Philosopher means that the following proposition is per accidens: 'The white is a quantum.' It is per accidens since the predicate 'quantum' connotes or signifies that one part of a thing is spatially separated from another part. The subject
'white', however, connotes no such thing. Thus, the predicate 'quantum' is not a part of the definition of'white' nor vice versa. Nevertheless, it is true that the white really and truly is a quantum and, likewise, that it is a quantity.
Thus, the philosopher no more concedes that white is a quantum than that white is a quantity. Just as the white really and truly is a quantum, although only per accidens, so the white is, according to the Philosopher, really and truly a quantity, but again only per accidens. That this is the Philosopher's view is clear from remarks he makes earlier in the same treatise.
Thus, after enumerating the species of quantity and indicating their differences he says "Only the things we have pointed to are properly called quantities; other things are quantities only per accidens. It is in terms of these things that we call other things quantities. We say that a large expanse of white is a quantity since its surface is large."® It is clear from this remark
Responses to Objections that in Aristotle's view the predicate 'quantity' truly applies to things other than those he enumerates. Thus, the white can be called a quantity, although not properly, but only per accidens. Thus he says "It is in terms of these things that we call other things quantities"; and of these other things the name 'quantity' is predicable, although not per se, only per accidens. Of the things Aristotle enumerates, the term 'quantity' is predicable properly and per se; the reason is that 'quantity' is a part of their definition. 'Quantity', however, is not part of the definition of 'white', 'musical', 'men', or 'stone'.
Thus, it should be noted that as regards their significative power, the Philosopher never distinguishes between the two terms 'quantum' and 'quantity', one which is concrete and the other abstract. Whatever he grants as regards one he grants as regards the other. He treats them the same. For him they are synonyms unless the abstract term incorporates some syncategorematic term or some expression significatively equivalent to a syncategorematic term.
Response to (2) We can handle the second text in the same way. The white and the musical are said to be quanta per accidens, since the propositions 'The white is a quantum', 'The musical is a quantum', and others like them are not per se.
They are not propositions in which a part of a definition is predicated of its definitum. When it is said that they are quanta because they are in something, 'to be in' is not used in the sense of real inherence, but in the sense of predication. Thus, 'The white is a quantum' is true only because the surface which is predicated of 'white', is a quantum; for this is true: "The surface is a quantum', but 'white' is predicated of 'surface' and vice versa; therefore, 'The white is a quantum' is true.
Response to (3) We can also handle the third text in this way. Some things are said to be quanta per se—the line, the solid, etc; for the following propositions are per se: 'The line is a quantity', 'The solid is a quantity', etc. Other things, however, are quanta per accidens since propositions like the following are per accidens: 'The white is a quantity' and 'The musical is a quantity'.
Response to (4) In response to the other passage from the Categories, Aristotle does not mean that the parts of quantities exhibiting relative position join at some boundary which is totally distinct from those parts; for in Aristotle's view no subject could be specified for such a boundary. Further, it would have to be in some genus per se, since it could not be construed as a part of something in a genus. The boundary then must be a quantity or a substance or a quality or .
. but each of these is false. On the contrary the Philosopher only means that one part of such quantities is extended to another part, in such a way that nothing lies between those parts. This, indeed, is the reason
Responses to Objections such quantities are called continuous quantities; their parts mutually extend to each other in such a way that did they not reach each other, one continuous quantity would not be formed by them.
The difference between continuous and discrete quantities according to Aristotle is that with discrete quantity it makes no difference whether the things which constitute the discrete quantity are in different places and, similarly, whether something else is between them. Thus, that two men be two, it is irrelevant whether something is between them; for they are two when they are one hundred leagues from each other or when they are next to each other. Nor is the predication of the term 'two' of the two men altered by their moving cither closer or farther apart. Indeed, if they were simultaneously in the same place, they would be two, just as if they were not in the same place. Things are quite different in the case of continuous quantity. Quantities can be continuous with each other only if nothing is between them. They must be in different places, extend to each other, and constitute something that is numerically one. Otherwise they are not continuous, for if they did not constitute something numerically one, if they did not mutually extend to each other, or if they were not distinct in location and position, they would not be continuous. But none of these features are required in the case of discrete quantity. For this reason Aristotle says that "their parts are connected at some common boundary;"?°that is, they are extended to each other and they are not in the same place, so that were there an indivisible thing, it would limit both of them. But this is not so in the case of discrete quantity, for its parts do not necessarily extend to each other. Indeed, they can constitute a quantity when something is between them as much as when nothing is. And it is for this reason that Aristotle says that the parts of a continuous quantity have a position relative to each other. That they be part of a continuous quantity, it is necessary that they be spatially separated one from another, so that it is possible to say that one part is here; another, there; a third, there; and so on. No such spatial separation is required for discrete quantities as was noted earlier. Thus, matter and form are really two things even though they are not spatially separated.
Response to (5) The response here is that when the Philosopher says that the point is indivisible, he is merely employing the jargon of a renowned position, or he is speaking conditionally saying that the point would be indivisible if it were something different from quantity. Or by the proposition 'The point is indivisible', he means this proposition 'One part of a continuous quantity extends to another without any divisible thing between them'. Likewise, by by the proposition 'The parts of a line are connected at some common
Responses to Objections boundary', he means 'The parts of a line are extended to each other without any third thing lying between them'.
Response to (6) Here the Philosopher does not mean that unity is something lacking parts because for him nothing in this world lacks parts. When he says "Unity is indivisible," he means to say, "That which is one is not many." I have argued that this is his meaning in the second book of my commentary on the Physics. In the interests of brevity I will not pursue the point here.
Response to (7) The reply here is that when the Philosopher claims that since substance and quantity exist there are many things, he is not arguing from the fact that substance is distinct form quantity, but from the fact that it is impossible for something to be a quantum if it does not contain a plurality of parts. Thus, it is necessary that if substance and quantity exist there are many things, for quantity requires a plurality of parts. That is all the Philosopher needs to show the ancients wrong.
Thus, I hold it to be Aristotle's view that nothing existing in this world is indivisible except perhaps the indivisible intellective soul. He also wanted to claim that everything is either a substance or a quality. If he should sometime be found saying that substance is not quantity o1 that quality is not quantity, he means that the propositions 'Substance is quantity' and 'Quality is quantity' are not per se. The reason they are not per se is that the name 'quantity', if it be taken for 'continuous quantity', connotes that one part of a thing is spatially separated from another. The names 'substance' and 'quality', however, connote no such thing. I claim, therefore, that the view of Aristotle and many other authors was that no quantity is an object distinct from substance and quality and similarly, that the point, the line, the surface, and the solid are not things essentially different from each other.
But those who hold the view that is common among recent writers would say that the point is something different from the line, that it is that which joins the parts of a line; that the line is something different from the surface, that it is that which joins the parts of the surface; and that the surface is something different from the solid, that it is that which joins its parts...
On their view number also is something different from things enumerated. It is an accident existing in those things. Likewise, speech is something different from the uttered word and its quantity. They would make the same point as regards place and time, that they are things different from each other and from all the aforesaid things.