84

90

The reason is that a reasoning about graphs
will necessarily consist in showing that something is true of every
possible graph of a certain general description.
But we cannot scribe every possible graph of
any general description, and therefore if we
are to reason in graphs we must have a
graph which is a general description of the
kind of graph to which the reasoning is to
relate.

For the alpha graphs, it is easy to see
what is wanted. Let [*], the old Greek form
of the letter A, denote the sheet of assertion.
Let —γ is a graph. Let Y[diagram]X mean
that X is scribed or placed on Y. Let W–k–Z
mean that Z is the area of the cut W. Let

90

The reason is that a reasoning about graphs
will necessarily consist in showing that something is true of every
possible graph of a certain general description.
But we cannot scribe every possible graph of
any general description, and therefore if we
are to reason in graphs we must have a
graph which is a general description of the
kind of graph to which the reasoning is to
relate.

For the alpha graphs, it is easy to see
what is wanted. Let [*], the old Greek form
of the letter A, denote the sheet of assertion.
Let —γ is a graph. Let Y[diagram]X mean
that X is scribed or placed on Y. Let W–k–Z
mean that Z is the area of the cut W. Let