Chapter II: Propositions of Existence

A '=Proposition of Existence=', when in normal form, has, for its _Subject_, the Class "existing Things".

Its Sign of Quantity is "Some" or "No".

[Note that, though its Sign of Quantity tells us _how many_
existing Things are Members of its Predicate, it does _not_ tell
us the _exact_ number: in fact, it only deals with _two_
numbers, which are, in ascending order, "0" and "1 or more."]

It is called "a Proposition of Existence" because its effect is to assert the _Reality_ (i.e. the real _existence_), or else the _Imaginariness_, of its Predicate.

[Thus, the Proposition "Some existing Things are honest men"
asserts that the Class "honest men" is _Real_.

This is the _normal_ form; but it may also be expressed in any
one of the following forms:--

(1) "Honest men exist";
(2) "Some honest men exist";
(3) "The Class 'honest men' exists";
(4) "There are honest men";
(5) "There are some honest men".

Similarly, the Proposition "No existing Things are men fifty
feet high" asserts that the Class "men 50 feet high" is
_Imaginary_.

This is the _normal_ form; but it may also be expressed in any
one of the following forms:--

(1) "Men 50 feet high do not exist";
(2) "No men 50 feet high exist";
(3) "The Class 'men 50 feet high' does not exist";
(4) "There are not any men 50 feet high";
(5) "There are no men 50 feet high."]

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CHAPTER III.

_PROPOSITIONS OF RELATION._

§ 1.

_Introductory._

A =Proposition of Relation=, of the kind to be here discussed, has, for its Terms, two Specieses of the same Genus, such that each of the two Names conveys the idea of some Attribute _not_ conveyed by the other.

[Thus, the Proposition "Some merchants are misers" is of the
right kind, since "merchants" and "misers" are Specieses of the
same Genus "men"; and since the Name "merchants" conveys the
idea of the Attribute "mercantile", and the name "misers" the
idea of the Attribute "miserly", each of which ideas is _not_
conveyed by the other Name.

But the Proposition "Some dogs are setters" is _not_ of the
right kind, since, although it is true that "dogs" and "setters"
are Specieses of the same Genus "animals", it is _not_ true that
the Name "dogs" conveys the idea of any Attribute not conveyed
by the Name "setters". Such Propositions will be discussed in