Here we have Bramantip concluding in A.; and there is, formally, an illicit process of the minor; though the conclusion is true; and the evidence, such as it is, is materially adequate. ('Two-handed,' being a peculiar differentia, is nugatory as a middle term, and may be cut out of both premises; whilst 'cooking' is a proprium peculiar to the species Man; so that these terms might be related in U., All men are all cookers; whence, by conversion, All cookers are men.)
(5) To omit to distribute the middle term in one or the other premise, as—
All verbal propositions are self-evident;
All axioms are self-evident:
∴ All axioms are verbal propositions.
This is an illegitimate mood in Fig. II.; in which, to give any conclusion, one premise must be negative. It may serve as a formal illustration of Undistributed Middle; though, as both premises are verbal propositions, it is (materially) not syllogistic at all, but an error of classification; a confounding of co-ordinate species by assuming their identity because they have the generic attribute in common.
(6) To simply convert an hypothetical proposition, as—
If trade is free, it prospers;
∴ If trade prospers, it is free.
This is similar to the simple conversion of the categorical A.; since it takes for granted that the antecedent is co-extensive with the consequent, or (in other words) that the freedom of trade is the sole condition of, or (at least) inseparable from, its prosperity.
The same assumption is made if, in an hypothetical syllogism, we try to ground an inference on the affirmation of the consequent or denial of the antecedent, as—
If trade is free it prospers:
It does prosper;
∴ It is free.
It is not free;
∴ It does not prosper.