<ol>
<li><p>When somebody says "It is all but possible to do that", is he saying "to do that" is possible or impossible? I am confused about the usage of "all but".</p></li>
<li><p>Consider this sentence: I walk to the policeman, singing a song. Grammatically, who is singing the song? I or policeman? Why?</p></li>
</ol>
<ol>
<li><p>It means that it is possible. “But something” means that it can be done. “He is all but stupid”. That means he’s stupid.</p></li>
<li><p>Ambiguous reference. Those sentences are not grammatically correct. It should be changed to “I walked to the policeman, while I was singing a song”. Same goes for “The parents told the children that they would be going out that day”. Who would be going out? The parents or the children? Therefore, it is changed to “The children were told that they were going out that day by their parents.” Lots of corrections can be made.</p></li>
</ol>
<p>in spoken or written English. I do not believe it is idiomatic usage.</p>
<p>What you may have in mind is: “It is all but impossible to do that.” This is a tongue-in-cheek phrasing and the intent and meaning depends on the context and on the speaker.</p>
<p>First of all, like fogcity, I have never encountered the expression “all but possible” in standard English, written or spoken. </p>
<p>In addition, I’d venture to say that the expression all but [adjective] means “everything up to that point, but not including it.” If something is “all but impossible,” it is very, very difficult, but not impossible. If I am “all but certain” of something, I am not quite sure of it, but I suspect it very strongly.</p>