What does "be true of" mean?

Question

What does "be true of" mean in the following context?

There is a debate in the literature on properties between the abundant conception of properties (, according to which there is a property corresponding to every natural language predicate and, more generally, every class of individuals,) and the sparse conception of properties ( , according to which a predicate expresses a property only if the objects that predicate is true of resemble one another in an intrinsic way ) .

p.s. The above sentence is quite long, so I get the structure across with brackets. Please feel free to point out if I make any errors.

Answer 1

Abundance is not a property of the clarity property of that sentence.

We know that the verb resemble is plural and so its subject must be "the objects".

According to the "sparse" conception of properties, a predicate expresses a property only if the objects which can be said to have that property resemble one another in an intrinsic way.

"the objects that predicate is true of" = the objects that can (truly) be said to be characterized by that predicate, i.e. truly have the predicated property.

Skyscrapers are tall. Is tallness true of skyscrapers? Yes, tallness is a characteristic of skyscrapers.

P.S. When we say that "a property or characteristic is true of something" we mean that the something does have that characteristic. The characteristic can be expressed adjectivally (a predicate adjective) or by a verb. Consider:

Birds can fly.

While that capability is true of most birds, it is not true of all birds. The emu and the ostrich cannot fly.

The emu is flightless.

The emu is a flightless bird.

The emu cannot fly.

Flightlessness is a property or characteristic of the emu.