“All-not,” then, is negative in any case, but universal when it means _no_ and particular when it means _not all_. Any proposition is partitive in nature when the quantity sign is _not all_, or _all-not_ interpreted as the equivalent of _not all_.
It may be observed here that _all_ has two distinct uses. First, it may be used in a collective sense; second, in a distributive sense. For example: _All_ is used in the _collective_ sense in such propositions as, “All the members of the football team weighed exactly one ton,” or “All the angles of the triangle are equal to two right angles.” Using _all_ in the distributive sense would make true these: “All the members of the football team weigh more than 140 pounds”; “All the angles of a triangle are less than two right angles.” _All_ is used collectively when reference is made to an aggregate, but distributively when reference is made to each.
The quantity sign _some_ is likewise ambiguous, as it may mean (1) some only――some, but not all, or (2) some at least――some, it may be all or not all. When “some” is used as the quantity sign of any particular proposition which has been accepted as logical, the second meaning, “some at least,” is always implied. This interpretation of “_some_” will be explained more in detail in a succeeding section.
When _some_ is used in the sense of _some only_, the partitive nature of the proposition is apparent, as both I and O are implied. For example, with reference to the human family, to say that “some only are wise” necessitates an investigation, which leads to the discovery that some are wise, while others are not wise. If the proposition be an I, then its complementary O is implied, or if it be an O, the I is implied.
_Few_ given as a sign of a plurative proposition also serves as a sign of the partitive. The plurative aspect is prominent when it is said that “Few men can be millionaires” and emphasis is placed upon the meaning that “Most men cannot be millionaires.” But when emphasis is given to “few,” as meaning _few only_ rather than the _most are not_, then the I and the O are both implied; e. g., _Some men become millionaires, but the most do not_.
To put it in a word, “all-not,” “some” and “few” introduce partitive propositions when the meaning implies both an I and an O. When treating such in logic the meaning which seems to be given the greater prominence must be accepted. Surely in the statement, “All that glitters is not gold,” the O-interpretation is the one intended; namely, “Some things which glitter are not gold.”