So Sigwart's syllogism would be the following non-sequitur:- If anything is a professor, it is good.
Like Leibnitz, he proceeds from the fact that our perceptions are sometimes conscious, sometimes unconscious, to the inconsequent conclusion, that there are beings with nothing but unconscious perceptions; and by a similar non sequitur, because there is the idea of an end in will, he argues that there must be an unconscious idea of an end in instinctive, in reflex, in all action.
Thus, in order to infer that some wise men are good from the example of professors, Brentano's syllogism would be the following non-sequitur: There is not a not-good professor.
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.
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.
This illogical hypothesis, which consists of incautiously passing from the truth that the sensible object perceived is not external but within the organism to the non-sequitur that therefore it is within the mind, derived what little plausibility it ever possessed from three prejudices: the first, the scholastic dogma that the sensible object is a species sensibilis, or immaterial sensible form received from the external thing; the second, the Cartesian a priori argument that the soul as thinking thing can perceive nothing but its own ideas; the third, the common assumption of a sense of sensations.
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.