Being, subsistence, existence etc.

Vallicella is still going on about the Intentionality problem. Here is his ‘aporetic triad’ again.

1. We sometimes think about the nonexistent.
2. Intentionality is a relation that ties a thinker to an object of thought.
3. Every relation is such that, if it holds, then all its relata exist.

He wonders (albeit hesitantly) if we can resolve the problem by distinguishing between different ‘modes of being’. He says

Some will be tempted at this point to distinguish between two modes of being,
a strong mode and a weak mode if you will, call them existence and
subsistence. The relations principle could then be reformulated to say
that if a relation R holds, then all of R's relata have being (either exist or
subsist). This seems to allow a solution of our problem. When Tom
thinks about a nonexistent item such as a mermaid, he does indeed stand in a
relation to something, it's just that the item in question subsists rather than
exists. The object of thought has being but does not exist.

But of course we already addressed that problem in a few places, e.g. here. Consider

Tom is thinking about a mermaid, but nothing is a mermaid.

The range of ‘thing’ in ‘nothing’ covers absolutely everything whatsoever – existing objects, objects with being, subsisting objects. ‘Thinking of the nonexistent’ covers even ‘thinking of a non-thing’. A mermaid is not a thing, not any kind of thing, not even a subsisting Meinongian thing, and still Tom can think of a mermaid. Different kinds of existence or being is no good.