Monotonicity and intensional adjectives

Suppose we have a sequence of properties N₁ … N_n such that: N₁ ⊆ … ⊆ N_n. If A is the property expressed by an extensional, i.e., subsective or intersective, adjective, it holds that (A ∩ N₁) ⊆ … ⊆ (A ∩ N_n). Contrariwise, for some intensional adjectives this breaks down in an interesting way: we can have A(N₁) ⊆ … ⊆ 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 N₁ 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/Notes
date: 30/06/1998