An I proposition is one in which the predicate affirms something of a part of the logical subject. An O proposition is one in which the predicate denies something of a part of the logical subject. Every proposition must be reduced to one of the four types before it can be used as a basis of argumentation. It is incumbent on the student to recognize these four types with precision and accuracy. (6) There are a few proposition types which are recognized as being illogical in form. These may be defined as follows: (1) An indefinite proposition is one without the quantity sign. It usually may be classed as universal. (2) An elliptical proposition is one in which the copula is suppressed. (3) An individual proposition is one which has a singular subject. It is universal in content. (4) Plurative propositions are those introduced by “most,” “a few” or some equivalent quantity sign. These are particular in meaning. (5) Partitive propositions are particulars which imply a complementary opposite. These arise through the ambiguous use of “all-not,” “some” and “few.” “All-not” sometimes means “_no_,” while at other times it may mean “_not-all_.” If the quantity sign means the latter, then it introduces a partitive proposition. “_Some_” may mean “_some only_,” or “_some at least_.” The latter is the logical meaning. The former interpretation makes the proposition partitive. When “few” means “few only,” it is partitive in nature. (6) Exceptive propositions are those introduced by such signs as “all except,” “all but,” “all save,” etc. They are universal only when the exceptions are mentioned. (7) Exclusive propositions are those introduced by such words as “only,” “alone,” “none but” and “except.” In an exclusive the predicate and not the subject is distributed. Consequently the easiest way to make an exclusive logical is to interchange subject and predicate and call it an A. (8) An inverted proposition is one where the predicate precedes the subject. Interchanging them gives the logical form. Of the grammatical sentences only the declarative is logical. The relative clause, though out of place, must be used with the word it modifies. (7) There are other propositions, though not illogical, to which the logician usually gives some attention. These may be defined as follows: (1) An analytical proposition is one in which the predicate gives information already implied in the subject. (2) A synthetic proposition is one in which the predicate gives information not implied in the subject. (3) A modal proposition is one which states the manner in which the predicate belongs to the subject. The adverbs of time, place, degree and manner are the signs of the modal proposition. (4) A pure proposition simply states that the predicate belongs or does not belong to the subject.