An interesting net

Bill Vallicella mentions another argument for non-existent objects here. He writes

Imagination of a mermaid is not consciousness of a mental image or other content
of consciousness but precisely consciousness of a mermaid. Consciousness of a
mermaid is just as outer-directed and revelatory of a material item as
consciousness of a dolphin. But mermaids do not exist. Therefore, some objects
do not exist.

Here is the argument expressed in numbered statements. I have added some additional premisses and logical steps

1. (A) Tom is conscious of a mermaid
2. (A) Consciousness of a mermaid is just as outer-directed and revelatory of a material item as consciousness of a dolphin.
3. (interpreting 2) If Tom is conscious of a mermaid then Tom is conscious of some object which is a mermaid.
4. (from 1, 3) Tom is conscious of some object which is a mermaid.
5. (A) 'Is conscious of' is a logically transitive verb.
6. (from 4, 5) some object is a mermaid.
7. (A) Mermaids do not exist.
8. (from 6, 7) Therefore, some objects do not exist.

The questionable assumption is (5). I argued earlier that a 'logically transitive verb' Ø is such that the truth of 'a Ø's an F' is inconsistent with the truth of 'nothing is an F', and so implies 'something is an F'. Bill needs to justify the assumption that 'is conscious of' is logically transitive. This is questionable. 'Bill is conscious of a mermaid' is clearly consistent with 'nothing is a mermaid'.

"A clever man got caught in this net of language! So it must be an interesting net. "