Aristotle has just finished claiming that only substances can have contraries predicated of them. He continues the Categories by answering an objection to this claim. Some claim that statements can be true and later become false. Therefore, it seems that statements are a counter-example to his claim.
Nothing like this is to be seen in any other case, unless perhaps someone might object and say that statements and beliefs are like this. For the same statement seems to be both true and false. Suppose, for example, that the statement that somebody is sitting is true; after he has got up this same statement will be false. Similarly with beliefs. Suppose you believe truly that somebody is sitting; after he has got up you will believe falsely if you hold the same belief about him. However, even if we were to grant this, there is still a difference in the way contraries are received. For in the case of substances it is by themselves changing that they are able to receive contraries. For what has become cold instead of hot, or dark instead of pale, or good instead of bad, has changed (has altered); similarly in other cases too it is by itself undergoing change that each thing is able to receive contraries. Statements and beliefs, on the other hand, themselves remain completely unchangeable in every way; it is because the actual thing changes that the contrary comes to belong to them. For the statement that somebody is sitting remains the same; it is because of a change in the actual thing that it comes to be true at one time and false at another. Similarly with beliefs. Hence at least the way in which it is able to receive contraries—through a change in itself—would be distinctive of substance, even if we were to grant that beliefs and statements are able to receive contraries. However, this is not true. For it is not because they themselves receive anything that statements and beliefs are said to be able to receive contraries, but because of what has happened to something else. For it is because the actual thing exists or does not exist that the statement is said to be true or false, not because it is able itself to receive contraries. No statement, in fact, or belief is changed at all by anything. So, since nothing happens in them, they are not able to receive contraries. A substance, on the other hand, is said to be able to receive contraries because it itself receives contraries. For it receives sickness and health, and paleness and darkness; and because it itself receives the various things of this kind it is said to be able to receive contraries. It is, therefore, distinctive of substance that what is numerically one and the same is able to receive contraries. This brings to an end our discussion of substance.
Someone might object and claim that statements are a counter-example. Some statements can be both true and false. For example, “he is sitting” might be true at one time and false later. Beliefs are similar. Someone might believe that “he is sitting” and be right, but later be wrong if he does not change his belief when the person stands up. All of this is true so far. But this case is different from that of substances. When a contrary is predicated of a substance, the substance changes so that the contrary is true of it. When a black substance becomes white the substances changes. It is the same with any other contrary that is truly predicated of a substance. On the other hand, statements and beliefs do not change when contraries are predicated of them. Other things change and make it such that the statement is no longer true. Statements and beliefs are about other things. When that other thing changes, the belief or statement becomes true or false. But the statement and belief does not change at all. So statements and beliefs do not really have contraries predicated in them. A substance does have contraries predicated in them. So while statements have contraries predicated of them because of another thing changes, substances have contraries predicated of them because the substance changes.
Next, Aristotle moves on to a discussion of quantity.