Chapter 30

_PROPOSITIONS GENERALLY._

§ 1.

_Introductory._

Note that the word "some" is to be regarded, henceforward, as meaning "one or more."

The word 'Proposition,' as used in ordinary conversation, may be applied to _any_ word, or phrase, which conveys any information whatever.

[Thus the words "yes" and "no" are Propositions in the ordinary sense of the word; and so are the phrases "you owe me five farthings" and "I don't!"

Such words as "oh!" or "never!", and such phrases as "fetch me that book!" "which book do you mean?" do not seem, at first sight, to convey any _information_; but they can easily be turned into equivalent forms which do so, viz. "I am surprised," "I will never consent to it," "I order you to fetch me that book," "I want to know which book you mean."]

But a '=Proposition=,' as used in this First Part of "Symbolic Logic," has a peculiar form, which may be called its '=Normal form='; and if any Proposition, which we wish to use in an argument, is not in normal form, we must reduce it to such a form, before we can use it. pg009 A '=Proposition=,' when in normal form, asserts, as to certain two Classes, which are called its '=Subject=' and '=Predicate=,' either

(1) that _some_ Members of its Subject are Members of its Predicate;

or (2) that _no_ Members of its Subject are Members of its Predicate;

or (3) that _all_ Members of its Subject are Members of its Predicate.

The Subject and the Predicate of a Proposition are called its '=Terms=.'

Two Propositions, which convey the _same_ information, are said to be '=equivalent='.

[Thus, the two Propositions, "I see John" and "John is seen by me," are equivalent.]

§ 2.

_Normal form of a Proposition._

A Proposition, in normal form, consists of four parts, viz.--

(1) The word "some," or "no," or "all." (This word, which tells us _how many_ Members of the Subject are also Members of the Predicate, is called the '=Sign of Quantity=.')

(2) Name of Subject.

(3) The verb "are" (or "is"). (This is called the '=Copula=.')

(4) Name of Predicate.

pg010 § 3.

_Various kinds of Propositions._

A Proposition, that begins with "Some", is said to be '=Particular=.' It is also called 'a Proposition =in I=.'

[Note, that it is called 'Particular,' because it refers to a _part_ only of the Subject.]

A Proposition, that begins with "No", is said to be '=Universal Negative=.' It is also called 'a Proposition =in E=.'

A Proposition, that begins with "All", is said to be '=Universal Affirmative=.' It is also called 'a Proposition =in A=.'

[Note, that they are called 'Universal', because they refer to the _whole_ of the Subject.]

A Proposition, whose Subject is an _Individual_, is to be regarded as _Universal_.

[Let us take, as an example, the Proposition "John is not well". This of course implies that there is an _Individual_, to whom the speaker refers when he mentions "John", and whom the listener _knows_ to be referred to. Hence the Class "men referred to by the speaker when he mentions 'John'" is a one-Member Class, and the Proposition is equivalent to "_All_ the men, who are referred to by the speaker when he mentions 'John', are not well."]

Propositions are of two kinds, 'Propositions of Existence' and 'Propositions of Relation.'

These shall be discussed separately.

pg011