This is usually put into English thus--'Whatever is affirmed or denied
of a class, may be affirmed or denied of any part of that class,'
and such an affirmation or denial is supposed to be an act of reason.
Archbishop Whately expounds the Dictum in analysing the following
theorem--Whatever exhibits marks of design had an intelligent author;
the world exhibits marks of design; therefore the world had an
intelligent author.
'In the first of these premises,' he says, 'we find it assumed
universally of the _class_ of "things which exhibit marks of
design," that they had an intelligent author; and in the other
premise, "the world" is referred to that class as comprehended
in it: now it is evident that whatever is said of the whole of
a class, may be said of anything comprehended in that class:
so that we are thus authorised to say of the world, that "it
had an intelligent author." Again, if we examine a syllogism
with a negative conclusion, as, _e.g._ "nothing which exhibits
marks of design could have been produced by chance; the
world exhibits, &c.; therefore the world could not have been
produced by chance:" the process of Reasoning will be found
to be the same; since it is evident, that whatever is _denied_
universally of any class may be denied of anything that is
comprehended in that class. On further examination it will be
found, that all valid arguments whatever may be easily reduced
to such a form as that of the foregoing syllogisms; and that
consequently the principle on which they are constructed is
the UNIVERSAL PRINCIPLE of Reasoning.'[20]
The examples given by Whately are perfectly valid; the first is a
constructive argument in the Sixth Category, the second a stigmatic
in the Fifth. I have in several places admitted that the arguments
adduced by syllogists are sometimes correct, the fault complained of
being in the mode in which such correct arguments are interpreted.
They are interpreted wrongly, and then other theorems are found or
made agreeing with the _interpretation_, and the admitted soundness
of the first theorems is used to procure acceptance for the second.
Things brought under the same definition ought to be essentially
alike, but they are not so when the utmost latitude is taken to
'assume' that predicates have properties which they obviously have
not.
The objections we make to the Dictum as above interpreted are--(1)
that in reasoning the precedent (major premise) need not be a class;
(2) if it is a class, it consists of all _known_ things of a similar
kind, not of all _possible_ things of a similar kind. When interpreted
in the latter sense the Dictum becomes dialectically tautological, as
has been often observed.