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Substance Cannot be Measured

Aristotle has just shown that substance has no contraries. He continues the Categories by showing that substance cannot be measured.

Substance, it seems, does not admit of a more and a less. I do not mean that one substance is not more a substance than another (we have said that it is), but that any given substance is not called more, or less, that which it is. For example, if this substance is a man, it will not be more a man or less a man either than itself or than another man. For one man is not more a man than another, as one pale thing is more pale than another and one beautiful thing more beautiful than another. Again, a thing is called more, or less, such-and-such than itself; for example, the body that is pale is called more pale now than before, and the one that is hot is called more, or less, hot. Substance, however, is not spoken of thus. For a man is not called more a man now than before, nor is anything else that is a substance. Thus substance does not admit of a more and a less.

It is not possible for a substance to be measured. Aristotle has already shown that primary substance is more of a substance than secondary substance. He has also shown that primary substances are all equally substance and that secondary substances are all equally substance. This is a different claim. Aristotle is claiming that no particular man is more or less human than another man. In general no particular example of a secondary substance is more or less of that secondary substance than another. This is different from something such as being pale or being beautiful. Some people are more pale than others or less beautiful than others. This means that it is not possible for a substance to be more or less of the substance that it is.

If it were possible for something to be more or less, then it might be possible to assign a number and measure it. Since this is not possible, it is not possible for substance to be measured. The reason for this is found in the previous claim of Aristotle that substances are equal. This does not prevent secondary substances from being counted.

Next, Aristotle shows that substances can have contraries added to them.