{ { Affirmative-A All S is P Categorical { Universal { Negative-E No S is P Propositions { { { Affirmative-I Some S is P { Particular { Negative-O Some S is not P Henceforth the symbols A, E, I, O will be used to designate the four kinds of categorical propositions. The propositions have other quantity signs aside from the ones used above. These may be summarized: { A――all, every, each, any, whole. { E――no, none, all-not. Quantity signs of { I――some, certain, most, a few, many, the { greatest part, any number. { O――some - - not, few. =6. PROPOSITIONS WHICH DO NOT CONFORM TO THE LOGICAL TYPE.= It has been observed that all expressed judgments must be reduced to one of the four logical types A, E, I or O, before they can be used argumentatively. Logic insists upon definiteness and clearness――there must be no ambiguity, no opportunity for a wrong interpretation. From this viewpoint the four types fulfill every requirement. Their meaning cannot be misunderstood. To any one with normal intelligence their significance may be made perfectly clear. Any argument when once put in terms of the four types may be spelled out with mathematical precision. In consequence it is of prime importance that the four types not only be well understood, but that a certain facility be gained in reducing ordinary conversation to some _one_ of these types. (1) Indefinite and Elliptical Propositions. It is known that every logical proposition must be expressed in terms of the four elements――_quantity sign_, _logical subject_, _copula_ and _logical predicate_, consequently the four types A, E, I and O which epitomize every form of logical proposition, are expressed in terms of these four elements. But in common conversation often the quantity sign, as well as the copula, is omitted. See section 3. Propositions without the quantity sign are called _indefinite_, while those with the suppressed copula may be termed _elliptical_ propositions. Both may be made logical as the attending illustrations will indicate: _Illogical_ _Logical_ _Indefinite_ Men are fighting animals. _All_ men are fighting animals. (A) Lilies are not roses. _No_ lilies are roses. (E) Good is the object of moral _All_ good is the object of moral approbation. approbation. (A) Perfect happiness is _In all cases_ perfect happiness impossible. is impossible. (A) _Elliptical_ Fashion rules the world. _All_ fashions _are_ ruling the world. (A) Trees grow. _All_ trees _are plants which_ grow. (A)