The root of the confusion lies in quoting sentences from common speech as examples of the logical forms, forgetting that those forms are purely artificial. "Omnis homo est mortalis," "All men are mortal," is not an example formally of All S is P. P is a symbol for a substantive word or combination of words, and mortal is an adjective. Strictly speaking, there is no formal equivalent in common speech, that is, in the forms of ordinary use—no strict grammatical formal equivalent—for the syllogistic propositional symbols. We can make an equivalent, but it is not a form that men would use in ordinary intercourse. "All man is in mortal being" would be a strict equivalent, but it is not English grammar.
Instead of disputing confusedly whether All S is P should be interpreted in extension or in comprehension, it would be better to recognise the original and traditional use of the symbols S and P as class names, and employ other symbols for the expression in comprehension or connotation. Thus, let s and p stand for the connotation. Then the equivalent for All S is P would be All S has p, or p always accompanies s, or p belongs to all S.
It may be said that if predication is treated in this way, Logic is simplified to the extent of childishness. And indeed, the manipulation of the bare forms with the help of diagrams and mnemonics is a very humble exercise. The real discipline of Syllogistic Logic lies in the reduction of common speech to these forms.
This exercise is valuable because it promotes clear ideas about the use of general names in predication, their ground in thought and reality, and the liabilities to error that lurk in this fundamental instrument of speech.
[Footnote 1:] For perfect symmetry, the form of E should be All S is not P. "No S is P" is adopted for E to avoid conflict with a form of common speech, in which All S is not P conveys the meaning of the Particular Negative. "All advices are not safe" does not mean that safeness is denied of all advices, but that safeness cannot be affirmed of all, i.e., Not all advices are safe, i.e., some are not.
[Footnote 2:] His most precise form, I should say, for in "P is predicated of every S" he virtually follows common speech.
II.—The Practice of Syllogistic Analysis.
The basis of the analysis is the use of general names in predication. To say that in predication a subject is referred to a class, is only another way of saying that in every categorical sentence the predicate is a general name express or implied: that it is by means of general names that we convey our thoughts about things to others.
"Milton is a great poet." "Quoth Hudibras, I smell a rat." Great poet is a general name: it means certain qualities, and applies to anybody possessing them. Quoth implies a general name, a name for persons speaking, connoting or meaning a certain act and applicable to anybody in the performance of it. Quoth expresses also past time: thus it implies another general name, a name for persons in past time, connoting a quality which differentiates a species in the genus persons speaking, and making the predicate term "persons speaking in past time". Thus the proposition Quoth Hudibras, analysed into the syllogistic form S is in P, becomes S (Hudibras) is in P (persons speaking in past time). The Predicate term P is a class constituted on those properties. Smell a rat also implies a general name, meaning an act or state predicable of many individuals.