gives only part of the proposition concerned. An instance will make this clearer. Consider "the present King of France is bald." Here "the present King of France" has a primary occurrence, and the proposition is false. Every proposition in which a description which describes nothing has a primary occurrence is false. But now consider "the present King of France is not bald." This is ambiguous. If we are first to take "
is bald," then substitute "the present King of France" for "
" and then deny the result, the occurrence of "the present King of France" is secondary and our proposition is true; but if we are to take "
is not bald" and substitute "the present King of France" for "
" then "the present King of France" has a primary occurrence and the proposition is false. Confusion of primary and secondary occurrences is a ready source of fallacies where descriptions are concerned.
Descriptions occur in mathematics chiefly in the form of descriptive functions, i.e. "the term having the relation