Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

LECTURE VIII
Postulate Properties
SCIENTIFIC PLATFORMS-THEIR FERTILITY, COMPENDENCE
AND COMPATIBILITY-DIFFERENCES OF EQUIVALENT
PLATFORMS-VARIETIES OF PLATFORMS AND FUNCTIONS-MEANINGS OF INDEPENDENCE AND CATEGORICALNESS-THEORETICAL AND PRACTICAL DOUBT.
UNLESS I am mistaken, you, as students of philosophy,
should find no little interest in certain questions connected with the properties I have mentioned as essential
to a genuine postulate system and as therefore common
to all such systems. I desire to draw your attention to
some of the questions without thereby promising or pretending to answer all of them, for I can not do so
satisfactorily.
If a collection of propositional functions be fertile or
infertile, how may we ascertain the fact? Of course, if
we actually deduce one or more consequences from them,
we then know that the collection is fertile. But the question I desire to ask and to commit to you for future consideration is this: Is there a criterion for deciding a priori
whether a given collection of propositional functions is
fertile or not, and if there is, what is the criterion?
Another question-which I believe to be important
and difficult-is this: What is the essential nature of the
rôle of variables in propositional functions by virtue of
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