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An Introduction To Non-aristotelian Systems And General Semantics.

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and Smith very large numbers as their orders of abstractions. But this is unnecessary, as we shall presently see.
We note that Fido dpes abstract from events, at any rate, in lower orders, 'has objects' (Oa) which he can recognize. The question is, does he abstract in higher orders ? We might answer that he does within certain limits. Or, we might prefer to take the limits of his abstracting capacities for granted and to include them all as lower order abstractions. For the sake of convenience and simplicity, we select the last method and say that he does not abstract in higher orders. In our schematic representation, we shall discover some very important differences between the abstracting capacities of humans and animals, and so we introduce here only as much complexity as we need. As animals have no speech, in the human sense, and as we have called the verbal labelling* of the object 'second order abstraction' we say that animals do not abstract in higher orders.
If we compare our diagram and what it represents with the well-known facts of daily life, we see that Smith's abstracting capacities are not limited to two orders, or to any 'n' orders of abstractions.
In our diagrams, the label (L) stands for the name which we assigned to the object. But we can also consider the level of the first label (L) as a descriptive level or statement. We know very well that Smith can always say something about a statement (L), on record. Neurologically considered, this next statement (Lx) about a statement (L) would be the nervous response to the former statement (L) which he has seen or heard or even produced by himself inside his skin. So his statement (La), about the former statement (L), is a new abstraction from the former abstraction. In my language, I call it an abstraction of a higher order. In this case, we shall be helped by the use of numbers. If we call the level (L) an abstraction of second order, we must call an abstraction from this abstraction an abstraction of third order, (Lj). Once an abstraction of third order has been produced, it becomes, in turn, a fact on record, potentially a stimulus, and can be abstracted further and a statement made about it, which becomes an abstraction of the fourth order (L2). This process has no definite limits, for, whenever statements of any order are made, we can always make a statement about them, and so produce an abstraction of still higher order. This capacity is practically universal among organisms which we call 'humans'. Here we reach a fundamental difference between 'Smith'
♦In the present system the_ terms 'label', 'labelling'., are always connected with their meanings, and so, for simplicity, from now on the reference to meanings will be omitted.