Schopenhauer already defined "intentionality". It's called Representation.
He separates representation into subject and object and says that neither can exist without the other.
No object without a subject. "The World as Will and Representation", Vol. 1, App. Critique of the Kantian philosophy.
To be Object for the Subject and to be our representation, are the same thing. - Delphi Collected Works of Arthur Schopenhauer (Delphi Series Eight Book 12) (p. 63). "On the Fourfold Root of the Principle of Sufficient Reason", §16.
All knowledge presupposes Subject and Object ... Proposition “I know” is identical with “Objects exist for me,” and this again is identical with “I am Subject,” - Delphi Collected Works of Arthur Schopenhauer (Delphi Series Eight Book 12) (p. 191).
Then he nailed it here:
A consciousness without an object is no consciousness. - Delphi Collected Works of Arthur Schopenhauer (Delphi Series Eight Book 12) (p. 969). "The World as Will and Representation", Vol. 2, Chap. 1.
Which is a thing known as "intentionality" in philosophy.
I am not familiar with modern philosophy but I had to ask was it necessary to create term "intentionality" and spend various lifetimes on writing PHDs about it?
Why philosophers did not use this simple definition of Schopenhauer but instead had to create weird conceptions?