Chapter 34

A Proposition of Relation, beginning with "Some", is henceforward to be understood as asserting that there are _some existing Things_, which, being Members of the Subject, are also Members of the Predicate; i.e. that _some existing Things_ are Members of _both_ Terms at once. Hence it is to be understood as implying that _each_ Term, taken by itself, is _Real_.

[Thus, the Proposition "Some rich men are invalids" is to be understood as asserting that _some existing Things_ are "rich invalids". Hence it implies that _each_ of the two Classes, "rich men" and "invalids", taken by itself, is _Real_.]

A Proposition of Relation, beginning with "No", is henceforward to be understood as asserting that there are _no existing Things_ which, being Members of the Subject, are also Members of the Predicate; i.e. that _no existing Things_ are Members of _both_ Terms at once. But this implies nothing as to the _Reality_ of either Term taken by itself.

[Thus, the Proposition "No mermaids are milliners" is to be understood as asserting that _no existing Things_ are "mermaid-milliners". But this implies nothing as to the _Reality_, or the _Unreality_, of either of the two Classes, "mermaids" and "milliners", taken by itself. In this case as it happens, the Subject is _Imaginary_, and the Predicate _Real_.]

A Proposition of Relation, beginning with "All", contains (see § 3) a similar Proposition beginning with "Some". Hence it is to be understood as implying that _each_ Term, taken by itself, is _Real_.

[Thus, the Proposition "All hyænas are savage animals" contains the Proposition "Some hyænas are savage animals". Hence it implies that _each_ of the two Classes, "hyænas" and "savage animals", taken by itself, is _Real_.]

pg020 § 5.

_Translation of a Proposition of Relation into one or more Propositions of Existence._

We have seen that a Proposition of Relation, beginning with "Some," asserts that _some existing Things_, being Members of its Subject, are _also_ Members of its Predicate. Hence, it asserts that some existing Things are Members of _both_; i.e. it asserts that some existing Things are Members of the Class of Things which have _all_ the Attributes of the Subject and the Predicate.

Hence, to translate it into a Proposition of Existence, we take "existing Things" as the new _Subject_, and Things, which have _all_ the Attributes of the Subject and the Predicate, as the new Predicate.

Similarly for a Proposition of Relation beginning with "No".

A Proposition of Relation, beginning with "All", is (as shown in § 3) equivalent to _two_ Propositions, one beginning with "Some" and the other with "No", each of which we now know how to translate.

[Let us work a few Examples, to illustrate these Rules.

(1)

"Some apples are not ripe."

Here we arrange thus:--

"Some" _Sign of Quantity_. "existing Things" _Subject_. "are" _Copula_. "not-ripe apples" _Predicate_.

or thus:--

"Some | existing Things | are | not-ripe apples." pg021 (2)

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

Here we arrange thus:--

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

(3)

"No lambs are accustomed to smoke cigars."

Here we arrange thus:--

"No | existing Things |are | lambs accustomed to smoke cigars."

(4)

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

Here we arrange thus:--

"No | existing Things | are | speculations of mine, which have brought me as much as 5 per cent."

(5)

"None but the brave deserve the fair."

Here we note, to begin with, that the phrase "none but the brave" is equivalent to "no not-brave men." We then arrange thus:--

"No | existing Things | are | not-brave men deserving of the fair."

(6)

"All bankers are rich men."

This is equivalent to the two Propositions "Some bankers are rich men" and "No bankers are poor men."

Here we arrange thus:--

"Some | existing Things | are | rich bankers"; and "No | existing Things | are | poor bankers."]

[Work Examples § =1=, 1-4 (p. 97).]

pg022