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
(3) 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_.
Conversion is limited by the two rules, (1) do not distribute an
undistributed term; (2) do not change the quality.
To convert an A interchange subject and predicate, limiting the latter
by _some_, or a word of like significance. This is called conversion by
limitation.
The co-extensive A may be converted without limiting the predicate.
This is called simple conversion.
An E proposition may be converted either simply or by limitation. When
converted by limitation the inference is a _weakened_ one.
An I proposition is converted simply only.
The O proposition does not admit of conversion.
(4) Immediate inference by contraversion is a process involving first
_obversion_ and then _conversion_.
“A,” “E” and “O” may be contraverted; “I” cannot be contraverted.
=7. ILLUSTRATIVE EXERCISES.=
(1a) From the antecedent judgment, “All weeds are plants,” I am able
to derive by immediate inference these judgments: (1) “All weeds are
not not-plants,” or “No weeds are not plants.” (2) “No not-plants are
weeds.” (3) “Some plants are weeds.” (4) “Some weeds are plants.”
(1b) “All vertebrates have a backbone.” From the foregoing judgment
derive immediately five different conclusions.
(2a) “All good citizens try to vote,”
“Albert White is a _good citizen_,”
Hence, “Albert White will try to vote.”
I know that the above is an example of mediate inference because the
two antecedent judgments make use of the middle term, “_good citizen_.”
(2b) Why is the following illustrative of mediate inference?
“All wise men are close observers,”
“All wise men are thoughtful,”
Hence, “Some thoughtful men are close observers.”
(3a) Derive immediate inferences by opposition from the following:
(1) “Good men are wise.”
(2) “No teacher can afford to be unjust.”
(3) “All birds fly.”
(4) “None of the inner planets are as large as the earth.”
I first determine that “1” and “3” are A propositions, while “2” and
“4” are E’s. Then I recall that by opposition an I may be derived from
an A and an O from an E. Hence, the inferences are:
(1) “Some good men are wise.”
(2) “Some teachers cannot afford to be unjust.”
(3) “Some birds fly.”
(4) “Some of the inner planets are not so large as the earth.”
(3b) Derive by opposition inferences from the following:
(1) “No true woman will neglect her home for society.”
(2) “All patriotic men love the flag.”
(3) “Fools rush in where angels fear to tread.”
(4a) Obvert the following:
(1) “All earnest teachers are diligent students.”
(2) “No self-respecting man can afford to be careless in his personal
appearance.”
(3) “Some of the great teachers of the past did not practice what
they preached.”
(4) “Some weeds are beautiful.”
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