ugh 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.

Neither of these arguments is formally good; nor, of course, is either
of them materially valid, if it be possible for trade to prosper in
spite of protective tariffs.

An important example of this fallacy is the prevalent notion, that if
the conclusion of an argument is true the premises must be trustworthy;
or, that if the premises are false the conclusion must be erroneous.
For, plainly, that--

If the premises are true, the conclusion is true, is a hypothetical
proposition; and we argue justly--

The premises are true;
.'. The conclusion is true;
or, The conclusion is false;
.'. The premises are false (or one of them is).

This is valid for every argument that is formally correct; but that we
cannot trust the premise