That which is capable of proof
but assumed by the teacher without proof is, if the pupil believes and
accepts it, hypothesis, though only in a limited sense hypothesis-that
is, relatively to the pupil; if the pupil has no opinion or a contrary
opinion on the matter, the same assumption is an illegitimate
postulate. Therein lies the distinction between hypothesis and
illegitimate postulate: the latter is the contrary of the pupil's
opinion, demonstrable, but assumed and used without demonstration.
The definition-viz. those which are not expressed as statements that
anything is or is not-are not hypotheses: but it is in the premisses
of a science that its hypotheses are contained. Definitions require
only to be understood, and this is not hypothesis-unless it be
contended that the pupil's hearing is also an hypothesis required by
the teacher. Hypotheses, on the contrary, postulate facts on the being
of which depends the being of the fact inferred. Nor are the
geometer's hypotheses false, as some have held, urging that one must
not employ falsehood and that the geometer is uttering falsehood in
stating that the line which he draws is a foot long or straight,
when it is actually neither.
Pages:
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46