popper-logic-scientific-discovery

probability 195
magnitude of ε changes. Now the physicist will attach little value to
more sharply defined boundaries of ∆p. And in the case of typical mass
phenomena, to which this investigation is restricted, ∆p can, we
remember, be taken to correspond to the interval of precision ± φ
which depends upon our technique of measurement; and this has
no sharp bounds but only what I called in section 37 ‘condensation
bounds’. We shall therefore call n large when the insensitivity of ∆p
in the neighbourhood of its characteristic value, which we can
determine, is at least so great that even changes in order of magnitude
of ε cause the value of ∆p to fluctuate only within the condensation
bounds of ± φ. (If n →∞, then ∆p becomes completely
insensitive.) But if this is so, then we need no longer concern ourselves
with the exact determination of ε: the decision to neglect a small ε
suffices, even if we have not exactly stated what has to be regarded
as ‘small’. It amounts to the decision to work with the characteristic
values of ∆p above mentioned, which are insensitive to changes
of ε.
The rule that extreme improbabilities have to be neglected (a rule
which becomes sufficiently explicit only in the light of the above)
agrees with the demand for scientific objectivity. For the obvious objection
to our rule is, clearly, that even the greatest improbability always
remains a probability, however small, and that consequently even the
most improbable processes—i.e. those which we propose to neglect—
will some day happen. But this objection can be disposed of by
recalling the idea of a reproducible physical effect—an idea which is closely
connected with that of objectivity (cf. section 8). I do not deny the
possibility that improbable events might occur. I do not, for example,
assert that the molecules in a small volume of gas may not, perhaps, for
a short time spontaneously withdraw into a part of the volume, or that
in a greater volume of gas spontaneous fluctuations of pressure will
never occur. What I do assert is that such occurrences would not be
physical effects, because, on account of their immense improbability,
they are not reproducible at will. Even if a physicist happened to observe such
a process, he would be quite unable to reproduce it, and therefore
would never be able to decide what had really happened in this case,
and whether he may not have made an observational mistake. If,
however, we find reproducible deviations from a macro effect which has