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
{ (1) A to E
Negate the predicate { (2) E to A
and change { (3) I to O
{ (4) O to I
(3) _IMMEDIATE INFERENCE BY CONVERSION._
_Conversion is the process of inferring from a given proposition
another which has, as its subject, the predicate of the given
proposition, and, as its predicate, the subject of the given
proposition._ It is simply a matter of transposing subject and
predicate. The original proposition is called the _convertend_ while
the derived proposition is named the _converse_.
The process of conversion is limited by two rules. First rule. No term
must be distributed in the converse which is not distributed in the
convertend. Second rule. The quality of the converse must be the same
as that of the convertend. More briefly: (1) _Do not distribute an
undistributed term._ (2) _Do not change the quality._
We recall that a term is distributed when it is referred to as a
_definite whole_. An undistributed term is referred to only _in part_.
The principle underlying rule “1,” therefore, is the one which forms
the basis of inference by opposition; namely, “_Whatever may be said of
the entire class may be said of a part of that class_.” The converse of
this is _not true_, that is, “What is said of part of a class cannot be
said of the whole of that class.” When we distribute an undistributed
term we are saying of the _whole_ class what was said only of a _part_
of that class. This is fallacious. On the other hand, we may say of a
part what was said of the whole, or “undistribute” a distributed term.
We recall that the conclusion of the whole matter of inference by
opposition was, that only an I could be inferred from an A and only an
O from an E, or to put it in another way: Only an affirmative from an
affirmative and only a negative from a negative. This establishes the
truth of the second rule in conversion: “Do not change the quality.”
Let us apply the two rules to the four logical propositions.
_Converting an A proposition._
Take as a type, “All horses are quadrupeds.” Here the subject
“_horses_” is distributed, but the predicate “_quadrupeds_” is
undistributed. In transposing subject and predicate we cannot
distribute the term “quadrupeds,” according to the rule which says, “Do
not distribute an undistributed term.” Hence in interchanging subject
and predicate we cannot say, “All quadrupeds are horses,” but must
limit the assertion to, “_Some_ quadrupeds are horses.” Logicians call
this process _Conversion_ by _Limitation_.
_Conversion by Limitation Exemplified Further._
_Convertend._ _Converse._
All metals are elements. Some elements are metals.
All bees buzz. Some buzzing insects are bees.
All men are fallible. Some fallible beings are men.
All good teachers are Some sympathetic persons are good
sympathetic. teachers.
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