8 Identity and Definite Descriptions

Atomic formulae of L=:

All atomic formulae of L2 are atomic formulae of L=. Furthermore, if s and t are variables or constants then s = t is an atomic formula of L=.

Formulae of L=

(i) All atomic formulae of L= are formulae of L=.
(ii) If φ and ψ are formulae of L= then ¬φ, (φ ∧ ψ), (φ ∨ ψ), (φ → ψ) and (φ ↔ ψ) are formulae

of L=.
(iii) If v is a variable and φ is a formula then ∀vφ and ∃vφ are formulae of L=.
(iv) Nothing else is a formula of L=

|s = t|α A = T iff

|s| α A = |t| α A

Numerical identity is when

There is only one thing, the same thing. This is what is being formalised