But what we mean by the universe is the sum of our actual
and possible impressions.
So, again, whether our conception of number is derived from relations of
impressions in space or in time, the impressions must exist in nature,
that is, in experience, before their relations can be perceived. Form
and number are mere names for certain relations between matters of fact;
unless a man had seen or felt the difference between a straight line and
a crooked one, straight and crooked would have no more meaning to him,
than red and blue to the blind.
The axiom, that things which are equal to the same are equal to one
another, is only a particular case of the predication of similarity; if
there were no impressions, it is obvious that there could be no
predicates. But what is an existence in the universe but an impression?
If what are called necessary truths are rigidly analysed, they will be
found to be of two kinds. Either they depend on the convention which
underlies the possibility of intelligible speech, that terms shall
always have the same meaning; or they are propositions the negation of
which implies the dissolution of some association in memory or
expectation, which is in fact indissoluble; or the denial of some fact
of immediate consciousness.
The "necessary truth" A = A means that the perception which is called A
shall always be called A. The "necessary truth" that "two straight lines
cannot inclose a space," means that we have no memory, and can form no
expectation of their so doing.
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