Singular terms and identity

We begin with the addition of singular terms to predicate logic. Consider again the following two sentences:

Kermit is a frog.

Kermit is green.

“Kermit” is a proper name. Proper names are singular terms, not general terms. They are terms that, in everyday discourse, refer to one and only one individual, one and only one entity in the domain. Proper names like “Emma”, “Socrates”, “Pickwick”, “Pegasus” and “Excalibur” are singular terms. If I say “Emma is a student,” then I am not taken to be talking about all the people who are named “Emma”, but only about one individual named “Emma”. This is so even though we know that there are many individuals called “Emma”. Similarly when I say, “Excalibur was cast into the lake,” I am taken to be talking about just one sword: the sword named “Excalibur”.

There are other words and phrases that we normally take to be singular terms as well. Some of these are singular pronouns like “I” and “she”. Some are descriptive singular terms like “the King of France”, “the Lord Mayor of Brisbane” and “the fountain of youth”. The definite article, “the”, in English usually gives indication of a descriptive singular term.

Individual constants and proper names

It is not unusual to translate all singular terms in English to individual constants in predicate logic. If this is done then the descriptive content of some singular terms is lost.