Part I of My "symbolic Logic."

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.

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.

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.

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.

(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."]

pg022