The meaning of the I proposition may be represented by two circles intersecting each other:
The significant feature of the diagram is the shaded part which represents a part of the “men” circle as belonging to a part of the “wise” circle. The unshaded part of each circle is the unknown field.
(4) _The Particular Negative or O Proposition._
_The common symbolization of the O is “Some S is not P.”_ Put in statement form: Some of the subject is excluded from the whole of the predicate. Here, as in the I, the same logical import must be given to _some_; e. g., in the proposition, “Some men are not wise,” our knowledge is confined to the group who are not wise. Whether or not the others are wise or not-wise is unknown.
The significance of the O proposition may be shown by two intersecting circles as in Fig. 4:
A similar diagram represents the I proposition, the only difference being in the _part shaded_. In the O proposition the investigated field is all of the “men” circle _outside_ of the “wise” circle, while in the I proposition the known field is that part of the “men” circle _inside_ the “wise” circle.
In comparing the four diagrams the student will note that the affirmative propositions are _inclusive_, while the negative propositions are _exclusive_.
(5) _The Distribution of Subject and Predicate._
_A term is said to be distributed when it is referred to as a definite whole._
In the proposition, “All men are mortal,” the subject _all men_ is considered as a whole. “_All_ men” stands for every specimen of the human race; not a single one has been left out. Again, _the whole_ is definite; any one, if he were given the time and opportunity, could ascertain by actual count just how many “all men” represented.
It should be observed that if the word _definite_ is not incorporated in the definition of a distributed term, there is afforded an opportunity for error. The attending illustrations will make this clear:
1. “All the students except John and James are dismissed.”
2. “All the students except John, James, etc., are dismissed.”
The subject of the first proposition is distributed, while the subject of the second is undistributed. Reasons: The first subject, “All the students except John and James,” is referred to as a whole and that whole is definite, therefore, it is distributed; the second subject, “All the students except John, James, etc.,” is referred to as a whole, but as the whole is not definite, the term is not distributed. Because _all_ is the quantity sign of the second subject the casual observer might easily be misled in designating it as a distributed term.