id, that a finger is short and longor short and not‑short, and long and not‑longdoes not contravene the formal logical principle of non‑contradiction.
Of very great interest are categories of propositions at what may be, termed different levels of abstraction, together with the connections between them. For example, to describe and distinguish things in terms of their sensible qualities (such as colour) is to operate at a certain level of abstraction. But information about what produces these sensible differences (for instance, what makes things look one colour rather than another) belongs to another level of abstraction and is formulated in propositions of different category. And the second category of information does not replace the first, but connects with it. Together these different categories of information constitute information about (in the case of colour) how bodies reflect light and how that affects our senses. This kind of connection of propositions at different levels of abstraction and of different category is of great importance in the management of information. For on it depends the proper assembly of relatively abstract items of information into something more concrete‑filling in and generalising our conceptions of the matters that concern us.
All information is abstract (how could it not be?). And what I have just called the management of information (which is the practical business of thinking, as distinct from what Engels called "idealist fancy") consists of assembling abstractions. Information is not only negative and positive (for example, "This rose is not white" and "This rose is red"), and more or less generalised ("All roses have thorns" and "All red roses have thorns"), and more or less abstract ("This rose is red" and "This rose is red and sweet‑smelling")all of which are differences of form and are treated in formal logic. It also exemplifies a host of what may be called different modes of abstraction, which are not distinguished in formal logic because they are not formal differences. For example, to talk about colour and to talk about shape, to talk about sensible appearance and to talk about physical‑chemical constitution, to talk about internal structure and to talk about interaction and interrelation with other things, and so on, all exemplify different modes of abstraction.
The sense in which the much‑abused word "category" is used in the context of a logical investigation of categories is the sense in which category of proposition corresponds to mode of abstraction. In general, different categories of proposition result from different modes of abstraction. To take a very simple example. "This is red" and "This became red in the process of being painted" are propositions of different category—the first exemplifying what one might (in semi‑Hegelian language) term a category of "being" or "quality", and the second of "becoming" or "causality". Their connection by way of abstraction is evident, since the first proposition is relatively more abstract than the second, and could be called an abstraction from the second. In both information is assembled, and the assembly of information in the second is such as to render a more concrete account of the same thing of which the first gives a more abstract account.
To investigate differences of category, therefore, is not simply to describe the ways words are permitted to be put together in various languages, as Ryle and other linguistic philosophers have supposed. It is to investigate modes of abstraction and their assembly, which are expressed in the permissibility and impermissibility of combinations of words.
In his paper on Categories Ryle said that "category propositions" describe and distinguish "the logical type" of different expressions used in statements, and so concern "only collocations of symbols". But he added that this does not equate them with "the propositions of philologists, grammarians or lexicographers . . . Nor does it imply that they can say nothing about the 'nature of things'. If a child's perplexity why the Equator can be