structure of our world has, within its own limits,
validity.[1]
VI
But what are the limits of this way of viewing things? What is the precise nature and range of its validity?
We have followed the logical genesis of the categories of what we may now call The World of Description, from their simplest forms to the point where we must abandon the attempt to develope here more fully their detail.[2]
The most fundamental of these categories is that of Likeness and Difference. Upon the basis of a consideration of the nature of this primal conception, we come to view the Objective World as, in one aspect of its Being, a realm of Objects of Possible Attention. The Categories of Relation, which have to do with the connections existing amongst these Objects, we could not
- ↑ The first systematic attempt to classify the laws present in a system by regarding these laws as the “invariants” of “systems of transformations” was, so far as I know, stated in Klein’s Erlanger Programm of 1872: Vergleichende Betrachtungen über Neuere Geometrische Forschungen. Klein regarded the types of laws demonstrable in the various different sorts of geometry (Projective Geometry, Analysis Situs, etc.) as so many species, each definable in terms of the invariants of a Group of Transformations. The conception has since been extended to other fields of science. Owing to the irreversible character of many of the serial processes present in our experience, the “Group” character, in the narrower sense of that term, will be absent from many of the systems of transformations with which science has to deal. But a law will still be the expression of the “invariants” of a system of transformations.
- ↑ We shall return, in our Fourth Lecture, to the consideration of these categories as they appear when applied to our actual study of nature.
