Hume and, later, Kant argued that by the principle of association
when we think of one quality of a thing the others are naturally
brought before our minds, and thus that we get into the habit of
attributing to the notion of the thing a certain group of qualities.
And it is true that we do attend to a thing all at once, including
in the notion of it all the qualities which we know belong to it.
Now experience, according to Leibniz, gives us an example of a
unity which embraces a multiplicity of detail. Thus a thing is one
substance as embodying an individual experience, and its qualities
belong to it in the same sense as the constituents of experience
belong to the single experience. These qualities are in relation.
(The Pragmatist denies the existence of relations as part of a
higher unity.[23]) But they are not only relation, since relation
always implies something more than itself. Let us take the example
of number. Numbers could never have been counted if there had not
been things to count. Now suppose each quality could be analysed
into a new relation, we should still not get rid of the quality. At
each stage there remains a quality in relation, and this goes on
to Infinity. Such a constant subdivision perhaps results from our
finite experience seizing facts in a disjointed way. When we analyse
a law in its working, we always do seem to come to this Indefinite
Regress. Now it has been the reproach against metaphysics, as uttered
by the Pragmatist, that there is no correspondence in scientific fact
to this road into Infinity.
W. James asserts: “But in point of fact, nature doesn’t make eggs by
making first half an egg, then a quarter, then an eighth, &c., and
adding them together. She either makes a whole egg at once or none
at all, and so of all her other units. It is only in the sphere of
change, then, where one phase of a thing must needs come into being
before another phase can come, that Zeno’s paradox gives trouble.
And it gives trouble then only if the successive steps of change be
infinitely divisible.”[24]
The sphere of change, however, one would answer, includes all nature,
and science in its discoveries acts on the hypothesis that these
steps of change may be infinitely divisible. Royce held to it firmly
that any consistent attempt to make an orderly arrangement of the
terms of an infinite whole must lead to the Indefinite Regress. And
he further shows the connection with the fact that an infinite series
can be adequately represented by a part of itself.
In the Boyle Lecture, delivered in Oxford in 1908, on the properties
of radium, two facts emerged which show that the Indefinite Regress
is now recognised in science.
First, that in the region of experiment we become aware of groups of
elements allied to radium, which seem, in the number of individuals
in their groups, to follow a simple arithmetical progression.
Secondly, that radio-active elements lose in activity at a certain
rate, which always represents an exact proportion of the mass which
remains. The tremendous disintegrating force slackens in exact
relation to the time which passes, so that the smaller the morsel
the less the relative loss of mass. Here, then, is the Indefinite
Regress. In the world of fact as well as of ideas we are dealing with
aspects of Infinity.[25]