#### Monotonicity and intensional adjectives

Suppose we have a sequence of properties *N*_{1} … *N*_{n} such that: *N*_{1} ⊆ … ⊆ *N*_{n}. If *A* is the property expressed by an extensional, i.e., subsective or intersective, adjective, it holds that (*A* ∩ *N*_{1}) ⊆ … ⊆ (*A* ∩ *N*_{n}). Contrariwise, for some intensional adjectives this breaks down in an interesting way: we can have *A*(*N*_{1}) ⊆ … ⊆ *A*(*N*_{i}) while we do *not* have: *A*(*N*_{i+1}) ⊆ … ⊆ *A*(*N*_{n}). Example: a one-guilder piece is a coin, is a piece of currency, is a material object. A blackened one-guilder piece is a blackened coin, is a blackened piece of currency, is a blackened material object. But although a false one-guilder piece is a false coin and a false piece of currency, it is not a false material object. This shows that somewhere along the line of *N*_{1} to *N*_{n} there is a break, between different kinds of properties, say characteristic and non-characteristic ones, and that intensional qualifications such as *false* are a means to determine where the break occurs.

*Martin Stokhof[from: Aantekeningen/Notesdate: 30/06/1998]*