Principia mathematica, vol. 1 (of 3)

A description is a phrase of the form "the term which etc.," or, more explicitly, "the term which satisfies ," where , is some function satisfied by one and only one argument. For reasons explained in the Introduction (Chapter III), we do not define "the which satisfies ," but we define any proposition in which this phrase occurs. Thus when we say: "The term which satisfies satisfies ," we shall mean: "There is a term such that is true when, and only when, is , and is true." That is, writing "" for "the term which satisfies ," is to mean This, however, is not yet quite adequate as a definition, for when ( occurs in a proposition which is part of a larger proposition, there is doubt whether the smaller or the larger proposition is to be taken as the "." Take, for example, . This may be either If "(" is false, the first of these must be true, while the second must be false. Thus it is very necessary to distinguish them.

The proposition which is to be treated as the "" will be called the scope of (. Thus in the first of the above two propositions, the scope of ( is , while in the second it is . In order to avoid ambiguities as to scope, we shall indicate the scope by writing "" at the beginning of the scope, followed by enough dots to extend to the end of the scope. Thus of the above two propositions the first is while the second is Thus we arrive at the following definition:

It will be found in practice that the scope usually required is the smallest proposition enclosed in dots or brackets in which "(" occurs. Hence when this scope is to be given to (, we shall usually omit explicit mention of the scope. Thus e.g. we shall have Of these the first necessarily implies (, while the second does not. We put

It will be shown *14·113 that the truth-value of a proposition containing two descriptions is unaffected by the question which has the larger scope. Hence we shall in general adopt the convention that the description occurring first typographically is to have the larger scope, unless the contrary is expressly indicated. Thus e.g. will mean i.e. By this convention we are able almost always to avoid explicit indication of the order of elimination of two or more descriptions. If, however, we require a larger scope for the later description, we put

This proposition is obvious, since "E" is, by the definitions, part of "." When, in ordinary language or in philosophy, something is said to "exist," it is always something described, i.e. it is not something immediately presented, like a taste or a patch of colour, but something like "matter" or "mind" or "Homer" (meaning "the author of the Homeric poems"), which is known by description as "the so-and-so," and is thus of the form (. Thus in all such cases, the existence of the (grammatical) subject ( can be analytically inferred from any true proposition having this grammatical subject. It would seem that the word "existence" cannot be significantly applied to subjects immediately given; i.e. not only does our definition give no meaning to "," but there is no reason, in philosophy, to suppose that a meaning of existence could be found which would be applicable to immediately given subjects.