THE LOGIC NOTES

Name Glossary


Definition

A name is a referring expression with no internal structure.

Comments

In natural language, proper nouns behave approximately like names in the sense of logic. However, logically proper names are guaranteed to pick out exactly one object on any given interpretation, whereas natural language names may fail to denote anything or may denote ambiguously if several individuals have the same name.

In the formal language of first order logic, a name (also known as a constant) is a 0-ary function symbol. In writing proofs, we use the letters 'a', 'b', etc as names.

In Logic for Fun, a name is a vocabulary item standing for a function returning an object of a specified sort without needing to be supplied with any argument.

In free logic, unlike ordinary logic, a name may have no value (denote nothing) on an interpretation. Logic for Fun implements a free logic in this sense, as names may be declared to be "partial".

Examples

  1. In English, 'Aristotle', 'Canberra' and 'Tuesday' are names.
  2. In ordinary mathematics, numerals like '15' and '3.14159' are names.
  3. in a formula like

    ALLx(Fx IMP (Ga OR Gb))

    the 'a' and 'b are names. The 'x' is not a name; it is a variable.

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