popper-logic-scientific-discovery

appendix *viii 393
smaller the number of atomic statements needed to compose a potential
falsifier, the greater the content of the theory.)
But I do not want to operate either with the fiction of atomic statements,
or with an artificial language system in which atomic statements
are available to us. For it seems to me quite clear that there are no
‘natural’ atomic predicates available in science. To some older logicians,
the predicates ‘man’ and ‘mortal’ seem to have presented themselves as
examples of something like atomic predicates. Carnap uses ‘blue’ or
‘warm’ as examples—presumably because ‘man’ and ‘mortal’ are
highly complex ideas which (some may think) can be defined in terms
of simpler ideas such as ‘blue’ or ‘warm’. Yet it is characteristic of
scientific discussions that neither these nor any other predicates are
treated as (absolutely) atomic. Depending upon the problem under
consideration, not only ‘man’ and ‘mortal’ but also ‘blue’ or ‘warm’
may be treated as highly complex; ‘blue’, say, as the colour of the sky,
explicable in terms of atomic theory. Even the phenomenal term ‘blue’
may be treated, in certain contexts, as definable—as a character of
visual images correlated with certain physiological stimuli. It is characteristic
of scientific discussion that it proceeds freely; and the attempt
to take away its freedom, by tying it down upon the Procrustean bed of
a pre-established language system would, if successful, be the end of
science.
For these reasons I rejected in advance the idea of using atomic
statements for the purpose of measuring the degree of content or simplicity
of a theory; and I suggested that we might use, instead, the idea of
relative-atomic statements; and further, the idea of a field of statements which
are relative-atomic with respect to a theory or a set of theories to the
testing of which they are relevant; a field F which could be interpreted
as a field of application of the theory, or of the set of theories.
If we take as our example again, as in the preceding appendix, the
two theories a 1 = ‘All planets move in circles’ and a 2 = ‘All planets move
in ellipses’, then we can take as our field all the statements of the form
‘At the time x the planet y was in the position z’, which will be our
relative atomic statements. And if we assume that we already know that
the track of the planet is a plane curve, then we can take a graphpaper
that represents the field and enter on it the various positions, marking
in each case the time, and the name of the planet in question, so that