Part Ii.]

The Genus, of which the two Terms are Specieses, is called the '=Universe of Discourse=,' or (more briefly) the '=Univ.='

The Sign of Quantity is "Some" or "No" or "All".

It is called "a Proposition of Relation" because its effect is to assert that a certain relationship exists between its Terms.

pg013 § 2.

Reduction of a Proposition of Relation to Normal form.

The Rules, for doing this, are as follows:--

(1) Ascertain what is the Subject (i.e., ascertain what Class we are talking about);

(2) If the verb, governed by the Subject, is not the verb "are" (or "is"), substitute for it a phrase beginning with "are" (or "is");

(3) Ascertain what is the Predicate (i.e., ascertain what Class it is, which is asserted to contain some, or none, or all, of the Members of the Subject);

(4) If the Name of each Term is completely expressed (i.e. if it contains a Substantive), there is no need to determine the 'Univ.'; but, if either Name is incompletely expressed, and contains Attributes only, it is then necessary to determine a 'Univ.', in order to insert its Name as the Substantive.

(5) Ascertain the Sign of Quantity;

(6) Arrange in the following order:--

Sign of Quantity, Subject, Copula, Predicate.

(1)

"Some apples are not ripe."

(1) The Subject is "apples."

(2) The Verb is "are."

(3) The Predicate is "not-ripe * * *." (As no Substantive is expressed, and we have not yet settled what the Univ. is to be, we are forced to leave a blank.)

(4) Let Univ. be "fruit."

(5) The Sign of Quantity is "some."

(6) The Proposition now becomes

"Some | apples | are | not-ripe fruit."

pg014 (2)

"None of my speculations have brought me as much as 5 per cent."

(1) The Subject is "my speculations."

(2) The Verb is "have brought," for which we substitute the phrase "are * * * that have brought".

(3) The Predicate is "* * * that have brought &c."

(4) Let Univ. be "transactions."

(5) The Sign of Quantity is "none of."

(6) The Proposition now becomes

"None of | my speculations | are | transactions that have brought me as much as 5 per cent."

(3)

"None but the brave deserve the fair."

To begin with, we note that the phrase "none but the brave" is equivalent to "no not-brave."

(1) The Subject has for its Attribute "not-brave." But no Substantive is supplied. So we express the Subject as "not-brave * * *."

(2) The Verb is "deserve," for which we substitute the phrase "are deserving of".

(3) The Predicate is "* * * deserving of the fair."

(4) Let Univ. be "persons."

(5) The Sign of Quantity is "no."

(6) The Proposition now becomes

"No | not-brave persons | are | persons deserving of the fair."

(4)

"A lame puppy would not say "thank you" if you offered to lend it a skipping-rope."

(1) The Subject is evidently "lame puppies," and all the rest of the sentence must somehow be packed into the Predicate.

(2) The Verb is "would not say," &c., for which we may substitute the phrase "are not grateful for."

(3) The Predicate may be expressed as "* * * not grateful for the loan of a skipping-rope."

(4) Let Univ. be "puppies."

(5) The Sign of Quantity is "all."

(6) The Proposition now becomes

"All | lame puppies | are | puppies not grateful for the loan of a skipping-rope."

pg015 (5)

"No one takes in the Times, unless he is well-educated."

(1) The Subject is evidently persons who are not well-educated ("no one" evidently means "no person").

(2) The Verb is "takes in," for which we may substitute the phrase "are persons taking in."

(3) The Predicate is "persons taking in the Times."

(4) Let Univ. be "persons."

(5) The Sign of Quantity is "no."

(6) The Proposition now becomes

"No | persons who are not well-educated | are | persons taking in the Times."

(6)

"My carriage will meet you at the station."

(1) The Subject is "my carriage." This, being an 'Individual,' is equivalent to the Class "my carriages." (Note that this Class contains only one Member.)

(2) The Verb is "will meet", for which we may substitute the phrase "are * * * that will meet."

(3) The Predicate is "* * * that will meet you at the station."

(4) Let Univ. be "things."

(5) The Sign of Quantity is "all."

(6) The Proposition now becomes

"All | my carriages | are | things that will meet you at the station."

(7)

"Happy is the man who does not know what 'toothache' means!"

(1) The Subject is evidently "the man &c." (Note that in this sentence, the Predicate comes first.) At first sight, the Subject seems to be an 'Individual'; but on further consideration, we see that the article "the" does not imply that there is only one such man. Hence the phrase "the man who" is equivalent to "all men who".

(2) The Verb is "are."

(3) The Predicate is "happy * * *."

(4) Let Univ. be "men."

(5) The Sign of Quantity is "all."

(6) The Proposition now becomes

"All | men who do not know what 'toothache' means | are | happy men."

pg016 (8)

"Some farmers always grumble at the weather, whatever it may be."

(1) The Subject is "farmers."

(2) The Verb is "grumble," for which we substitute the phrase "are * * * who grumble."

(3) The Predicate is "* * * who always grumble &c."

(4) Let Univ. be "persons."

(5) The Sign of Quantity is "some."

(6) The Proposition now becomes

"Some | farmers | are | persons who always grumble at the weather, whatever it may be."

(9)

"No lambs are accustomed to smoke cigars."

(1) The Subject is "lambs."

(2) The Verb is "are."

(3) The Predicate is "* * * accustomed &c."

(4) Let Univ. be "animals."

(5) The Sign of Quantity is "no."

(6) The Proposition now becomes

"No | lambs | are | animals accustomed to smoke cigars."

(10)

"I ca'n't understand examples that are not arranged in regular order, like those I am used to."

(1) The Subject is "examples that," &c.

(2) The Verb is "I ca'n't understand," which we must alter, so as to have "examples," instead of "I," as the nominative case. It may be expressed as "are not understood by me."

(3) The Predicate is "* * * not understood by me."

(4) Let Univ. be "examples."

(5) The Sign of Quantity is "all."

(6) The Proposition now becomes

"All | examples that are not arranged in regular order like those I am used to | are | examples not understood by me."]

pg017 § 3.

A Proposition of Relation, beginning with "All", is a Double Proposition.

A Proposition of Relation, beginning with "All", asserts (as we already know) that "All Members of the Subject are Members of the Predicate". This evidently contains, as a part of what it tells us, the smaller Proposition "Some Members of the Subject are Members of the Predicate".

The question now arises "What is the rest of the information which this Proposition gives us?"

In order to answer this question, let us begin with the smaller Proposition, "Some Members of the Subject are Members of the Predicate," and suppose that this is all we have been told; and let us proceed to inquire what else we need to be told, in order to know that "All Members of the Subject are Members of the Predicate".

Let us also suppose that the 'Univ.' (i.e. the Genus, of which both the Subject and the Predicate are Specieses) has been divided (by the Process of Dichotomy) into two smaller Classes, viz.

(1) the Predicate;

(2) the Class whose Differentia is contradictory to that of the Predicate.

Also we have been told that, in the case we are discussing, some Members of the Subject are in Class (1). What else do we need to be told, in order to know that all of them are there? Evidently we need to be told that none of them are in Class (2); i.e. that none of them are Members of the Class whose Differentia is contradictory to that of the Predicate.

Hence a Proposition of Relation, beginning with "All", is a Double Proposition, and is '=equivalent=' to (i.e. gives the same information as) the two Propositions

(1) "Some Members of the Subject are Members of the Predicate";

(2) "No Members of the Subject are Members of the Class whose Differentia is contradictory to that of the Predicate".

(1) "Some bankers are rich men";

(2) "No bankers are poor men".]

pg019 § 4.

What is implied, in a Proposition of Relation, as to the Reality of its Terms?

Note that the rules, here laid down, are arbitrary, and only apply to