Hi Jim and Rachel,
I wouldn't say that Boromir deals only in the tangible. He has travelled for 110 days and 400 leagues seeking Imladris in response to a Dream!
Boromir is certainly willing to respect, and give credence to spiritual phenomena such as Divine Dreams. That is not very tangible.
As Jim says, I do guess that Boromir is thinking of how the Ring could help Gondor's war efforts. But I don't think that he is primarily thinking of that. I think he is primarily thinking about getting answers to his Dream. He has found the sword that was broken. He has identified Isildur's Bane, and the Halfling. They must all be important. But, what are the counsels that will be 'stronger than Morgul-spells'?
Boromir wonders if the Ring could be used, is meant to be used, as a weapon against Sauron. Why might it be useful as such? Because, Boromir has heard that it IS stronger than Morgul-spells. What he has heard at the Council, not least from the writing on the Ring itself, is that he who controls the Ring controls the Ring-wraiths. If the counsel of the Council were, "We should wield the Ring," then the wielder could (as far as Boromir can see) control the Nazgul, eliminate them as a threat to Gondor, and turn them against the forces of Sauron.
That would fit the Dream! As far as Boromir can see, Elrond's counsel, that the Ring should be destroyed, is not stronger than Morgul-spells. It will do nothing to counter the Nazgul. Thus, Boromir is still doubtful. He accepts (at the moment) Elrond's assessment, that it will not work long term to use the Ring against Sauron. But, he has still not heard counsels that are stronger than Morgul-spells. So, he is doubtful that the Council is on the right track.
As far as Boromir is concerned, the job of the Council is to answer the Dream! (Elrond and Gandalf might think that the job of the Council is to answer the question, "Here are we and here is the Ring....What shall we do with it?") Boromir is not, I think, quite as fixated on the Ring as Elrond and Gandalf. He is more fixated on his Dream. The Ring is an artifact (though a powerful and dangerous one), the Dream is a Divine Message! Divine Messages are more important than artifacts, especially to those who have received them (and, I suggest, Boromir is right. Gandalf and Elrond are too fixated on the Ring, and would be Wiser if they paid more attention to the Divine Dream which Boromir has brought).
JRRT has very cleverly constructed this chapter to make us almost forget Faramir and Boromirs' Dream, or to think that it has been dealt with. However, it has not. The Council has not yet come up with counsels stronger than Morgul-spells. Boromir will be doubtful until they do.