Mysticism and Logic and Other EssaysRussell, Bertrand
Philosophy
Mysticism and Logic and Other Essays
Russell, Bertrand
Mathematics; Philosophy; Science
In all science we have to distinguish two sorts of laws: first, those
that are empirically verifiable but probably only approximate;
secondly, those that are not verifiable, but may be exact. The law of
gravitation, for example, in its applications to the solar system, is
only empirically verifiable when it is assumed that matter outside the
solar system may be ignored for such purposes; we believe this to be
only approximately true, but we cannot empirically verify the law of
universal gravitation which we believe to be exact. This point is very
important in connection with what we may call "relatively isolated
systems." These may be defined as follows:--
A system relatively isolated during a given period is one which,
within some assignable margin of error, will behave in the same way
throughout that period, however the rest of the universe may be
constituted.
A system may be called "practically isolated" during a given period
if, although there _might_ be states of the rest of the universe which
would produce more than the assigned margin of error, there is reason
to believe that such states do not in fact occur.
Strictly speaking, we ought to specify the respect in which the system
is relatively isolated. For example, the earth is relatively isolated
as regards falling bodies, but not as regards tides; it is
_practically_ isolated as regards economic phenomena, although, if
Jevons' sunspot theory of commercial crises had been true, it would
not have been even practically isolated in this respect.
It will be observed that we cannot prove in advance that a system is
isolated. This will be inferred from the observed fact that
approximate uniformities can be stated for this system alone. If the
complete laws for the whole universe were known, the isolation of a
system could be deduced from them; assuming, for example, the law of
universal gravitation, the practical isolation of the solar system in
this respect can be deduced by the help of the fact that there is very
little matter in its neighbourhood. But it should be observed that
isolated systems are only important as providing a possibility of
_discovering_ scientific laws; they have no theoretical importance in
the finished structure of a science.
The case where one event A is said to "cause" another event B, which
philosophers take as fundamental, is really only the most simplified
instance of a practically isolated system. It may happen that, as a
result of general scientific laws, whenever A occurs throughout a
certain period, it is followed by B; in that case, A and B form a
system which is practically isolated throughout that period. It is,
however, to be regarded as a piece of good fortune if this occurs; it
will always be due to special circumstances, and would not have been
true if the rest of the universe had been different though subject to
the same laws.
Public-domain text, read in full here on John Shaqi.
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