In both these cases, Wealth, though undistributed in the convertend, is
distributed in the converse.
(3) To attempt to syllogise with two premises containing four terms, as
The Papuans are savages;
The Javanese are neighbours of the Papuans:
∴ The Javanese are savages.
Such an argument is excluded by the definition of a Syllogism, and
presents no formal evidence whatever. We should naturally assume that
any man who advanced it merely meant to raise some probability that
'neighbourhood is a sign of community of ideas and customs.' But, if so,
he should have been more explicit. There would, of course, be the same
failure of connection, if a fourth term were introduced into the
conclusion, instead of into the premises.
(4) To distribute in the conclusion a term that was undistributed in the
premises (an error essentially the same as (2) above), i.e., Illicit
process of the major or minor term, as--
Every rational agent is accountable;
Brutes are not rational agents:
∴ Brutes are not accountable.
In this example (from Whately), an illegitimate mood of Fig. I., the
major term, 'accountable,' has suffered the illicit process; since, in
the premise, it is predicate of an affirmative proposition and,
therefore, undistributed; but, in the conclusion, it is predicate of a
negative proposition and, therefore, distributed. The fact that nearly
everybody would accept the conclusion as true, might lead one to
overlook the formal inconclusiveness of the proof.
Again,
All men are two-handed;
All two-handed animals are cooking animals:
∴ All cooking animals are men.
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.
Public-domain text, read in full here on John Shaqi.
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