7

10

number of conclusions could be drawn.
In the alpha-part of logic to which the ordinary textbooks
of logic are virtually confined, because although if the
problem they consider were stated in graphical form,
there would be ligatures, yet they are only such as
can all be joined throughout the graph, so that the
rules of operation become the same as if there were no
ligature at all,— this is not a minutely accurate statement
because the books are so unsystematic that no brief statement
of what they contain could be quite accurate, but it is substantially so—
in this alpha-part of logic a premiss can only be
efficient once. But in the beta part of logic premisses
can be applied efficient over and over and
over again endlessly. A moment's reflexion on
any simple branch of mathematics will show that
it must be so. For instance, the whole theory of numbers