A Class Room Logic: Deductive and Inductive, with Special Application to the Science and Art of TeachingMcNair, George Hastings
Philosophy
A Class Room Logic: Deductive and Inductive, with Special Application to the Science and Art of Teaching
McNair, George Hastings
Logic
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.”
ILLUSTRATIONS:
(1) “_All_ men are not honest.”
(2) “_Few_ men live to be a hundred.”
(3) “_Some_ men are consistent.”
The first proposition with the emphasis placed upon _all_ suggesting
that _some men are not honest_, is the intended proposition while _some
men are honest_ is the implied. In reducing it to the logical form the
intended proposition is the one which should be used.
With the emphasis upon _few_ and _some_, the second and third
propositions may be interpreted as follows: (2) Intended proposition,
_Some men do not live to be a hundred_. Implied proposition, _Some
men do live to be a hundred_. (3) Intended proposition, _Some men are
consistent_. Implied proposition, _Some men are not consistent_.
(6) Exceptive Propositions.
These are introduced by such signs as _all except_, _all but_,
_all save_. To wit: (1) “_All except_ James and John may be excused”;
(2) “_All but_ a few of the culprits have been arrested”; (3) “_All_
birds _save_ the English sparrow are serviceable to man” are exceptive
propositions.
Public-domain text, read in full here on John Shaqi.
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