An introduction to mathematics, by A. N. Whitehead.

METHODS OF APPLICATION 27
false. In fact, the very meanings assigned
to x and y, as being a number of cubic feet
and a number of pounds sterling, are indifferent. During the mathematical investigation we are, in fact, merely considering the
properties of this correlation between a pair
of variable numbers x and y. Our results
will apply equally well, if we interpret y to
mean a number of fishermen and x the number of fish caught, so that the assumed law
is that on the average each fisherman catches
twenty fish. The mathematical certainty of
the investigation only attaches to the results
considered as giving properties of the correlation 20y=x between the variable pair of
numbers x and y. There is no mathematical
certainty whatever about the cost of the
actual building of any house. The law is not
quite true and the result it gives will not be
quite accurate. In fact, it may well be hopelessly wrong.
Now all this no doubt seems very obvious.
But in truth with more complicated instances
there is no more common error than to assume
that, because prolonged and accurate mathematical calculations have been made, the
application of the result to some fact of
nature is absolutely certain. The conclusion
of no argument can be more certain than the
assumptions from which it starts. All mathematical calculations about the course of