Monday, September 13, 2010

Difference, Relations, and Properties

What is true in the relation of difference is true about other relations. The nature of any term, unless that term is itself a relation, is attributes or properties in the non-technical sense. The nature of an apple means its roundness, redness, juiciness, and so on. So a change in any properties would be a change in the apple's nature.

Now a relation is not a property. But when a term has a relation to anything else, it also has a property because of that relation, a relational property, and that property belongs to its nature just as much as any other property.

If Ann is the mother of Beth, then you are asserting the relational property of being the mother of Beth. And this property is not itself a relation in the sense in which the relation of motherhood is. Hence, even though a relation is not a property, it gives rise to a property. And these properties are a part of the nature of what has those properties. The properties of being 'above the beast of the field', 'a little lower than the angels', and 'the mother of Beth', belong to Ann as part of her nature.

But the relations could not be diffferent without the properties being different. And the properties could not be different without their terms being different. For the properties are part of the terms. Therefore, if all relations were different, their terms would also be different. Consequently, all relations are internal.

32.03

The Difference Difference Makes

The internal relation of each object to each other object is a condition implicit in the being of anything. For something to exist, it must be this rather than that, and the 'rather than that' belongs to its essence just as much as the 'this'.

Something is in this relation to other things from its own nature and because otherness is stated in it, as is its own movement. Its being comprehends negation, through which alone it now has its affirmative existence. . . . It is something by not being other things. (Hegel, Science of Logic)

Everything is related to everything else at least by the relation of difference. Otherwise, a thing would not be the thing it is, since it would then be no different from anything other than itself.

But a relation that cannot be theoretically changed without changing the thing itself is what is meant by an internal relation. Consequently, everything is related internally to everything else.

Common sense is not used to moving among such abstract considerations. It might say that difference is not a relation. The reply would be a definition of relation that includes difference but answered to people's common notion of relation. But we are cut off from this reply, since 'relation' is indefinable.

But the indefinability of a term does not mean that there is anything either arbitrary or indefinite in our thought of it. And difference does fall within the common meaning of relation. Likeness and difference go together in our thought as having the same sort of existence. But likeness is a relation. If difference were not a relation, what else could it be? To call it a substance, or a quality, or an event, or a way of behaving, or anything except a relation is forced and unnatural. Consequently, difference is either a relation or some unique form of being, which it is not.

It might be replied that it's arbitrary to take it's not being something else as part of what a thing is.

It may be objected that it is paradoxical and wilful to treat it as part of the nature of a table that it is not a phoenix or not a prime number, and to place such characteristics on a level with its characteristic of being a table, or even with its negative characteristic of not being a chair. And from any practical point of view it is more important to believe about any substance which is in fact a table, that it has the characteristics of being a table, or of not being a chair, than that it possesses the characteristics of not being a phoenix or a prime number.

And even apart from all practical considerations, we shall gain more knowledge about the nature of the substance by realizing that it possesses the first two characteristics than we shall by realizing that it has the other two characteristics. But the last two characteristics are characteristics of the substance as the first two characteristics are.

For any person who asserts that the table is not a prime number would be saying something that is true. The assertion may be unimportant, foolish, a waste of time. But it is not fales, and it must be true. And it cannot be true unless it is made true by the nature of that thing about which the assertion is made. (G. E. Moore, Philosophical Studies)

Consequently, if something is as characterized by not being x as it is characterized by being y, then a change in its relations of difference would mean a change in itself. Therefore, it is internally related to everything else in the universe.


32.02. . . 4b77