Monotonicity and intensional adjectives
Suppose we have a sequence of properties N1 … Nn such that: N1 ⊆ … ⊆ Nn. If A is the property expressed by an extensional, i.e., subsective or intersective, adjective, it holds that (A ∩ N1) ⊆ … ⊆ (A ∩ Nn). Contrariwise, for some intensional adjectives this breaks down in an interesting way: we can have A(N1) ⊆ … ⊆ A(Ni) while we do not have: A(Ni+1) ⊆ … ⊆ A(Nn). 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 Nn 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.
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