McCall R.J. Basic logic (2ed., 1952)(T)(263s).djvu: eKnigu

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McCall R.J. Basic logic (2ed., 1952)(T)(263s).djvu

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In these cases only, we contradict "is" by
"may not be," "need not be" by "may have to b*" or "may neces-
necessarily be," and "can be" by "may not be able to be." In all other
cases, we contradict "is" by "is not," "need not be" by "must be,"
and "can be" by "cannot be." The disjunctive proposition and the
consequent of the conditional proposition are thus special cases,
where the ordinary rules of contradiction are complicated by the
presence of the implicitly necessary mode...
The exponible proposition will be contradicted like any
other copulative proposition, but we must first make clear its copula-
copulative nature...
Upon it hinges the very important operation
of conversion, and much of the theory of the categorical syllogism...
The formal reason why the predicate of an affirmative proposition
is always taken particularly is derived from the rule that every
affirmative proposition places its P in the comprehension of its S,
and its S in the extension of its P...
It is incorrect to
say "Some men are all carpenters," since, when this proposition is
stated in acceptable form, "Some man is every carpenter," it implies
that each man who is a carpenter is every carpenter...
Euler's circles
customarily illustrate this type of proposition as follows:
with the shaded portion of the outer circle denoting the "men who
are not carpenters" and who are, therefore, excluded from the exten-
extension of "carpenter" taken universally...
As though it were," we say, for in truth a singular is not a universal
Judgment and Proposition 113
term, but happens to function more or less like one in this and many
other instances...
If occasionally the reciprocal of a true A proposition is
itself true—as when the P of the original is the definition or a spe-
specific property of the S—this is only by reason of the matter, or con-
content, of the proposition...
In converting, we should note that
the S of the convertend becomes the P of the converse, so that if
our original S is, as above, "dog," "dog" must be our new P...
To obvert a proposition we
Judgment and Proposition 121
simply negative its copula and its predicate...
To obtain the partial contra-
positive of a given proposition:
Obvert the original and then convert the obverse...
From our square of opposition, this last proposition is seen as: "true,
subaltern of full contrapositive of original," so our first proposition
would be classified as "true: obverse of simple converse of subaltern
of full contrapositive of original." Notice that it is not necessary to
remember the operations performed to render the given proposition
comparable with the original...
The
student who can successfully complete the exercises in this section
by applying what he has learned concerning opposition, conversion,
ob version, and the like, has a good grasp of the logic of categorical
propositions, and is ready to begin the analysis of categorical deduc-
deductive inference, which is our next topic...
It is this connection which the mind, in affirming the antecedent,
sees, and which compels the movement whereby it affirms the conse-
consequent also...
It should be written first, but it is not the fact that it is written
first that earns for it the title of "major premise." It is called the
major premise because it unites the middle term with the '"greater"
term, i.e., the term which is to be the predicate of the conclusion...
(Thus, if "risible" is affirmed universally of "man," it
can be affirmed of everything that comes under "man":
Peter, John, Michael, et al.)
4...