(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:
_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)
Children play. _All_ children _are_ playful. (A)
Some men cheat. Some men _are persons who_ cheat. (I)
Here it is noted that the logical form of some propositions is not always the most forceful. Often the logical form gives an awkward construction and should be resorted to only for purposes of logical argument.
The reduction of either kind to the logical form must be determined by the meaning of the proposition. As a usual thing the indefinite is _universal_ (either an A or an E) in meaning, while the problem of the elliptical is to give it in terms of the _copula_, expressed with as little awkwardness as possible.
General truths, because attended with no quantity sign, might be classed as indefinite propositions, though their universality is so apparent that they may be unhesitatingly classed as universals.
“Things equal to the same thing are equal to each other.”
“Trees grow in direct opposition to gravity.”
Because the indefinite proposition is so frequently of a general nature, it is sometimes classed as _general_ rather than _indefinite_.
Sir William Hamilton would class the indefinite as an _indesignate proposition_.