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 conclusions from the foregoing are these: First, the usual mode of
converting an A is to interchange subject and predicate, limiting the
latter by the word “_some_” or a word of similar significance. Second,
this mode is called _conversion by limitation_. Third, the converse of
an _A_ is an _I._
_The Co-extensive A._
In the conversion of A propositions there is the one exception of
“co-extensive A’s,” such as truisms and definitions. It will be
remembered that with these both subject and predicate are distributed;
hence, they may be interchanged without limiting the predicate by
“some.” To illustrate: The converse of the truism, “A man is a _man_.”
is “A _man_ is a man,” while the converse of the definition, “A man
is a rational animal,” is “A rational animal is a man.” This mode
of interchanging subject and predicate without limiting the latter
is called _Simple Conversion_. The ordinary A proposition is thus
_converted_ by _limitation_, while the co-extensive A is _converted
simply_.
_Converting an E proposition._
As both terms of the E proposition are distributed it is not possible
to violate the rule of distribution. It is to be remembered that no
fallacy is committed by “undistributing” a term which is already
distributed.
_Illustrations._
_Convertend._ _Converse._
No men are immortal. No immortals are men. Simply.
No birds are quadrupeds. No quadrupeds are birds. Simply.
No metals are compounds. No compounds are metals. Simply.
No men are immortal. Some immortals (at least) are not
men. Limitation.
No birds are quadrupeds. Some quadrupeds are not birds.
Limitation.
No metals are compounds. Some compounds are not metals.
Limitation.
Three facts are evident relative to the converting of an E. First: An E
proposition may be converted either _simply_ or by _limitation_. Second:
E may be converted into either _E_ or _O_. Third: If the converse is
an O then is the inference a _weakened_ one, being _particular_ when it
could just as well be _universal_.
_Converting an I proposition._
With an I proposition neither term is distributed. Thus care must be
used lest an undistributed term in the convertend be distributed in the
converse. _Illustrations_:
_Convertend._ _Converse._
Some men are wise. Some wise beings are men.
Some teachers scold. Some who scold are teachers.
Some high school graduates Some who enter college are high
enter college. school graduates.
Some Americans live simply. Some who live simply are Americans.
From the foregoing we conclude first, that I is _converted simply_;
second, that I is converted _into I_.
_The O Proposition._
Public-domain text, read in full here on John Shaqi.
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