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.”]
| “Some” | Sign of Quantity. | |
| “existing Things” | Subject. | |
| “are” | Copula. | |
| “not-ripe apples” | Predicate. |
[Work Examples § 1, 1–4 ([p. 97]).]
[pg022]BOOK III.
THE BILITERAL DIAGRAM.
CHAPTER I.
SYMBOLS AND CELLS.
First, let us suppose that the above Diagram is an enclosure assigned to a certain Class of Things, which we have selected as our ‘Universe of Discourse.’ or, more briefly, as our ‘Univ’.