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## The End Is Near

‘The’ can be a quantifier, e.g. ‘the square is broken’. How to formalise it?
The square is broken \\ ⫤⊨ There is exactly one square and it is broken
Recall that we can translate There is exactly one square' as:
\hspace{5mm} ∃x ( Square(x) ∧ ∀y ( Square(y) → x=y ) )
So There is exactly one square and it's broken':
\hspace{5mm} ∃x ( Sqr(x) ∧ ∀y ( Sqr(y) → x=y ) ∧ Broken(x) )

There is an end, and all ends are this end, and it is near.

∃x ( End(x) ∧ ∀y ( End(y) → x=y ) ∧ Near(x) )

14.26, 14.28
14.2
14.4, 14.5
14.10, 14.11
14.26, 14.28