Definite desceription Glossary
In English, phrases of the form 'the F' are typically definite descriptions. Other natural languages may not have definite articles such as 'the', so in those languages definite descriptions have to be indicated by context or in other ways.
Following the account first suggested by Bertrand Russell in 1905, we can parse definite descriptions in first order logic not as singular terms, but rather as quantifiers, so 'The F is G' is rendered as 'For the thing, x, such that Fx, Gx'. This gives a smooth account of cases in which there is no such thing as "the F". With identity in the language, the definite description quantifier can be expressed in terms of the usual existential and universal ones.
- 'The president of Australia in 2020 does not exist' could be written in Russell's form as NOTSOMExALLy(Py IFF x=y).
- 'The president of Australia in 2020 was born in Sydney' could be written using the definite description as a term something like B(x Px, s). The truth value of this is unclear, as there is no such president. If we take the definite description operator to form a quantifier, we can write (x: Px) Bxs. Following Russell, this can be expressed as SOMEx(ALLy(Py IFF x=y) AND Bxs).