The only difference between these and the previous examples (2) and (3) is that, while those break the rule against two negative premises, these break that against undistributed middle.
S is partially identical with P. In the first the fallacy is the indifferent contingency of the conclusion caused by the non-sequitur from a negative premise to an affirmative conclusion; while the second is either a mere repetition of the premises if the conclusion means " S is like P in being M," or, if it means " S is P," a non-sequitur on account of the undistributed middle.
The last supposed syllogism, namely, that having two affirmative premises and entailing an undistributed middle in the second figure, is accepted by Wundt under the title "Inference by Comparison" (Vergleichungsschluss), and is supposed by him to be useful for abstraction and subsidiary to induction, and by Bosanquet to be useful for analogy.
But to say from these premises, " God and metal are similar in what is signified by the middle term," is a mere repetition of the premises; to say, further, that " Gold may be a metal " is a non-sequitur, because, the middle being undistributed, the logical conclusion is the contingent "Gold may or may not be a metal," which leaves the question quite open, and therefore there is no syllogism.
Thus, we must think in (r) All P is M " to avoid illicit process of the major, in (2) "All y is z " to avoid undistributed middle, in (3) "All x is y" to avoid illicit process of the minor.
To give the name of syllogism to inferences which infringe the general rules against undistributed middle, illicit process, two negative premises, non-sequitur from negative to affirmative, and the introduction of what is not in the premises into the conclusion, and which consequently infringe the special rules against affirmative conclusions in the second figure, and against universal conclusions in the third figure, is to open the door to fallacy, and at best to confuse the syllogism with other kinds of inference, without enabling us to understand any one kind.
Violation of this is the fallacy of " undistributed middle."