§ 7. (1) The first of these may be called the _Fixity of Terms_. Syllogistic reasoning manifestly depends on the assumption that the terms occurring in it have meanings sufficiently stable to stand transplantation from one context to another; for only so can they establish connexions between one context and another. Thus a syllogism in _Barbara_ argues that because _all M is P_ and _all S is M, all S must be P_. But it can do this ‘validly’ only if _M_, its middle term, remains immutably itself, and is the same in both premisses. Doubt, dispute, or confute this assumption, and the cogency of the syllogism as a form of ‘proof’ is overthrown at once. If the sense in which _M is P_ is not the same as that in which _S is M_, the syllogism breaks in two, and its conclusion becomes precarious. Raise the question of how far reality conforms to this assumption, and you get at once a subtle problem of the applicability of the syllogistic form to the case in hand, which is precisely analogous to the question whether a theorem of pure mathematics is applicable to the behaviour of a real thing. In either case the cogency of the ‘proof’ which establishes the conclusion is impaired and ceases to be unconditional. The conclusion of a ‘valid’ syllogism will only follow _if_ the middle term can be known to be unambiguous, and if the objects designated by the terms do not change rapidly enough to defeat the inference. And that this is the case can usually be ascertained only by actual experience. The conclusion, therefore, cannot be simply deduced; it has actually to _come true_, before we can be sure that the reasoning _was_ sound. Absolutely _a priori_ proof thus becomes impossible, if the assumption of the fixity of terms is contested: all proof becomes, in a sense, empirical. Nevertheless, experience shows that the fixity of terms, though not a ‘fact’, is _a valid ‘fiction’_: in ordinary discussion the terms may usually be taken as fixed enough to render valid syllogisms common. An ordinary debate proceeds upon the assumption that the meaning of the terms involved is fixed, and cannot be varied arbitrarily. To science, however, this assumption does not apply without restriction. In a progressive science the meaning of terms often develops so rapidly that such verbal reasoning does _not_ suffice. Hence the mere occurrence of verbal contradictions in a scientific reasoning is no proof that the argument is unsound. It may show merely that its terms are _growing_.