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.”
I determine first the logical character of each proposition, finding the first to be an A, the second an E, the third an O and the fourth an I. Then I recall that in obversion the predicate must always be negated and an A must be changed to an E or an E to an A; also an I must be changed to an O or an O to an I. Hence, the obverse of each proposition is:
(1) “No earnest teacher is a not-diligent student.”
(2) “All self-respecting men can afford to be not-careless (careful) in their personal appearance.”
(3) “Some of the great teachers of the past did not-practice (failed to practice) what they preached.”
(4) “Some weeds are not not-beautiful.”
(4b) Infer by obversion from the following:
(1) “All roses are beautiful.”
(2) “None of the members of the stock exchange are dishonest.”
(3) “Some pupils are not industrious.”
(4) “Some teachers are tactful.”
(5a) Convert the following:
(1) “All that glitters is not gold.”
(2) “All good men are wise.”
(3) “Some books are to be chewed and digested.”
(4) “No man is perfectly happy.”
It is first necessary to determine the logical character of each proposition. Carelessness might lead one to call the first proposition an A because it is introduced by the quantity sign “all.” But on second thought we note that the meaning is to the effect that some glittering things are not gold; this is an O. It is clearthat the second is an A, the third an I and the fourth an E. It is now expedient to recall the rules regarding conversion. These are, (1) do not distribute an undistributed term; (2) do not change the quality. We may now attempt to interchange the subject and predicate of each proposition, with the following results:
(1) Conversion impossible.
(2) “Some wise men are good men.”
(3) “Some things to be chewed and digested are books.”
(4) “No perfectly happy being is a man.”
When attempting to convert proposition (1), I find that the subject which is undistributed becomes distributed, hence the rule pertaining to distribution is violated. This conclusion is verified by recalling the fact that an O proposition cannot be converted. The second proposition, being an A, is converted by limitation; while the third and fourth are converted simply, as is the natural procedure with all I’s and E’s.
(5b) Convert these propositions:
(1) “Blessed are the meek.” (All the meek are blessed.)
(2) “None but material bodies gravitate.” (All gravitating bodies are material.)
(3) “Gold is not a compound substance.”
(4) “Usually cruel men are cowards.”
NOTE.—The first proposition is poetical while the second is an exclusive.
(6a) Contravert the following propositions:
(1) “All virtue is praiseworthy.”
(2) “Some teachers are not tactful.”
(3) “A man who lies is not to be trusted.”
Contraversion consists in obverting first, and then converting; consequently, the contraverse of the three propositions is as follows:
(1) “No unpraiseworthy deed is virtue.”
(2) “Some not-tactful persons are teachers.”
(3) “Some untrustworthy men are those who lie.”
(6b) Write the contraverse of the following:
(1) “All honest men pay their debts.”
(2) “All men are rational.”
(3) “Nearly all the troops have left the town.”
(4) “Some teachers are not patient.”
(7a) The attending scheme indicates the logical process and rule involved in passing from one proposition to another:
A. “All men are imperfect.”
Process: Obversion.
Rule: Negate predicate and change to E.
E. “No men are perfect.”
Process: Simple Conversion.
Rule: Interchange subject and predicate.
E. “No perfect beings are men.”
Process: Contraversion.
Rule: Obvert and then convert.
I. “Some not-men are perfect beings.”
(7b) Treat in a manner similar to the above the proposition, “All horses are quadrupeds.”