Division Into Two

I pointed out in the last post that Parmenides is mistaken in maintaining the absolute unity of all being. But the refutation was simply from experience. One can still ask about the real reason for this. Why is being not absolutely one in the way he supposed?

Distinction consists in the fact that one thing is not another. But why is it not the other? We can find two kinds of distinction in things, material and formal.

Material distinction consists in the fact that one thing is not another, even though the things are of the same kind. Thus one man is not another man. Formal distinction consists in the fact that one thing is not another thing because they are different in kind, as for example a dog is distinct from a man, or as blue is distinct from green.

It is quite difficult to understand the existence of material distinction, and I will not try to explain it at this time. But formal distinction always happens because of some opposition between the forms in question. And opposition results from things that are opposite to one another, while opposites come in pairs. Consequently formal distinction always results first into a division into two, although the things which are divided into two may possibly be divided again.

We can illustrate this with the way that St. Thomas divides a text into parts. For example, in his commentary on the Gospel of St. John, discussing the wedding at Cana, he says:

Above, the Evangelist showed the dignity of the incarnate Word and gave various evidence for it. Now he begins to relate the effects and actions by which the divinity of the incarnate Word was made known to the world. First, he tells the things Christ did, while living in the world, that show his divinity. Secondly, he tells how Christ showed his divinity while dying; and this from chapter twelve on. As to the first he does two things. First, he shows the divinity of Christ in relation to the power he had over nature. Secondly, in relation to the effects of grace; and this from chapter three on. Christ’s power over nature is pointed out to us by the fact that he changed a nature. And this change was accomplished by Christ as a sign: first, to his disciples, to strengthen them; secondly, to the people, to lead them to believe (2:12). This transformation of a nature, in order to strengthen the disciples, was accomplished at a marriage, when he turned water into wine. First, the marriage is described. Secondly, those present. Thirdly, the miracle performed by Christ. In describing the marriage, the time is first mentioned. Hence he says, “On the third day there was a wedding,” i.e., after the calling of the disciples mentioned earlier. For, after being made known by the testimony of John, Christ also wanted to make himself known. Secondly, the place is mentioned; hence he says, at Cana in Galilee. Galilee is a province, and Cana a small village located in that province.

Every division here is into two except when he talks about the description of the marriage, saying, “First, the marriage is described. Secondly, those present. Thirdly, the miracle performed by Christ.” But it is easy to see that he divides into three here in order to omit a distinction that would not be very helpful, namely the division between describing the background to the miracle and describing the miracle itself. The background is then divided once again into the marriage and into those present.

Thus, in theory every formal division is into two. But in practice in can happen that it is sometimes useful to divide into three, and in rare cases larger numbers. This happens first of all when some divisions are obvious and can be skipped over, as is the case here with St. Thomas. Second, the division into beginning, middle, and end is usually best left as a division into three, even though in principle the beginning can be divided against the rest. Finally, cases which consist of a list are best left as such, as when I mention seven interesting things that happened to me yesterday. Basically such cases are cases of material distinction, not formal; here is one interesting thing, here is another, and here is still another.

For additional illustration, we may divide the above paragraph:

  1. Statement of the theoretical principle: every formal division is into two.
  2. Discussion of practical exceptions.
    1. General statement regarding exceptions: sometimes it is useful to divide into larger numbers.
    2. Consideration of various cases.
      1. Consideration of cases which in fact contain formal distinction.
        1. The general case in which some divisions are omitted.
        2. The special case of beginning, middle, and end.
      2. Consideration of cases in which material distinction is involved instead.
        1. Description of such cases: situations where we basically have a list.
        2. Explanation of such cases: the fact that they consist in material distinction.

Someone may argue that such an explanation of a text is artificial, and that the author was not thinking of such a breakdown of his text, and consequently that it cannot be a true explanation. But the reality is that it does not matter whether he was thinking of it or not. If his text is in fact coherent, it will have such an explanation, and one that is basically most correct, in comparison to others which are less correct or incorrect.

This is true not only of texts, but of any whole which is coherently divided into parts based on formal distinctions.

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