Some domestic animals (e.g., pugs) are useful.
The derivation of negative syllogisms from the Law of Contradiction (he might add) may be shown in a similar manner.
But the force of this ingenious argument depends on the participial clause--'having once identified pugs with domestic animals.' If this is a distinct step of the reasoning, the above syllogism cannot be reduced to one step, cannot be exhibited as mere subalternation, nor be brought directly under the law of Identity.

If 'pug,' 'domestic,' and 'useful' are distinct terms; and if 'pug' and 'useful' are only known to be connected because of their relations to 'domestic': this is something more than the Laws of Thought provide for: it is not Immediate Inference, but Mediate; and to justify it, scientific method requires that its conditions be generalised.

The _Dictum_, then, as we have seen, does generalise these conditions, and declares that when such conditions are satisfied a Mediate Inference is valid.
But, after all (to go back a little), consider again that proposition _All pugs are domestic animals_: is it a distinct step of the reasoning; that is to say, is it a Real Proposition?
If, indeed, 'domestic' is no part of the definition of 'pug,' the proposition is real, and is a distinct part of the argument.

But take such a case as this: All dogs are useful; All pugs are dogs.
Here we clearly have, in the minor premise, only a verbal proposition; to be a dog is certainly part of the definition of 'pug.' But, if so, the inference 'All pugs are useful' involves no real mediation, and the argument is no more than this: All dogs are useful; .'.

Some dogs (e.g., pugs) are useful.
Similarly, if the major premise be verbal, thus: All men are rational; Socrates is a man-- to conclude that 'Socrates is rational' is no Mediate Inference; for so much was implied in the minor premise, 'Socrates is a man,' and the major premise adds nothing to this.
Hence we may conclude (as anticipated in chap.vii.Sec.