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 approbation. | All good is the object of moral approbation. (A) |
| Perfect happiness is impossible. | In all cases perfect happiness 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 theiruniversality is so apparent that they may be unhesitatingly classed as universals.
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