7

T̶h̶e̶r̶e̶ ̶c̶a̶n̶ ̶b̶e̶ ̶n̶o̶ ̶a̶p̶o̶d̶i̶c̶t̶i̶c̶ ̶c̶e̶r̶t̶a̶i̶n̶t̶y̶ ̶a̶b̶o̶u̶t̶ ̶t̶h̶e̶ ̶a̶c̶t̶u̶a̶l̶

Mathermatics is the study of what is true of hypotherical states of things.
That is its essence and definition. Everything in it, there-
fore, beyond the f̶i̶r̶s̶t̶ ̶d̶e̶s̶c̶r̶i̶p̶t̶i̶o̶n̶s̶ first precepts for the construc-
tion of the hypotheses, has to be of the nature of
doubt, apodictic c̶o̶n̶c̶l̶u̶s̶i̶o̶n̶ inference. No doubt we may reason
imperfectly and jump at a conclusion: still, the conclusion
so guessed at is, after all, that in a certain supposed state
of things something would necessarily be true. Conversely
too, every apodictic inference is, strictly speaking, mathe-
matics. But mathematics, as a serious science, has
over and above its essential character of being hy-
potherical, an accidental characteristic [peculiarity?]
a proprium, as the Aristotelians used today, -
which is of the greatest logical interest. Namely,
while as the "philosophers," follow Aris-
totle in holding [?] demonstration to be thoroughly satis-