Grammaticality – Examples of Verbs That Can Be Negated with ‘Not’ Instead of ‘Don’t’

Yes. So is an alternative to as in this construction in negative contexts, but not otherwise. I don't use it in my idiolect, but many people do.

The Original Poster was given the following rule:

To be possible/impossible can be followed by an infinitive verb only when the subject of the finite verb is the introductory "it". With any other subject, the infinitive would be wrong.

However, these examples which are wrong according to the rule, are in fact perfectly grammatical:

• Oranges are impossible to grow here.
• The lecturer was impossible to hear.

So this clearly shows the rule is wrong.

However! Hang on one second! Part of the rule seems to be correct. The Original Poster's examples all used impossible and not possible. The following are indeed ungrammatical, or at least a bit wonky:

• *Oranges are possible to grow here.
• *The lecturer was possible to hear.

Now this is properly, bona fide crazy. Who designed this language? Shame on them whoever they are. We have one rule for possible and a different one for impossible. It is, of course, completely natural, and indeed commonsensical, and intelligent, to extrapolate that if there's a rule for possible, that impossible will work the same way. But it doesn't.

There are a couple of other unusual and interesting things hidden in the OP's post. First their example:

• *The lecturer was impossible to be heard.

This is clearly wrong in the passive like this, but it's difficult to see why. The active version above is, of course fine. Secondly, it's not immediately clear why the first example here is wrong - although it is:

• *a situation possible to arise
• *a situation impossible to arise
• a situation likely to arise.

Here we see that both possible and impossible seem to be problematic. On the other hand likely seem to be entirely acceptable.

Now if you want to know why possible and impossible behave so differently, the answer is: I don't know. I can however explain how they behave, which will get us half-way there.

Infinitives as clauses

We might think of infinitives as kind of free-standing verbs. Most of the time when we see them, they have no subject, and they often have no visible object either:

• I want to travel.

However, these verbs always have some kind of unexpressed subject. The example above means:

• I want myself to travel.

Note that if the subject of the infinitive is different from the subject of want, it must be overtly expressed:

• I want them to travel.

The fact that we can omit subject of the infinitive here is a property of the verb want. If the subject position of the infinitive is not expressed, the subject of want controls its interpretation:

• The hephalumps_(i) want [ ______(i) to be rolled in marmalade].

So the subject of to be rolled in marmalade here is controlled here by the hephalumps, the subject of want. The hephalumps want the hephalumps to be rolled in marmalade. Because it behaves in this way want is known as a control verb.

Adjectives 1: Control

Adjectives work this way too. Adjectives often occur as complements of verbs. These adjectives often take infinitive clauses as their own complements. These clauses may also have positions that are controlled. Take the adjective keen:

• The hephalumps are keen for the hippos to impress the giraffes.
• The hephalumps_(i) are keen _______(i) to impress the giraffes.

Here the adjective keen is the complement of the verb BE. In turn keen is taking an infinitival clause as complement. When the subject of the infinitive isn't expressed, it's identity is controlled by the subject of the verb - in the case the hephalumps. The second example above means:

• The hephalumps are keen for the hephalumps to impress the giraffes.

Again this is a property of the adjective keen. Some other adjectives that have this pattern are anxious, delighted and eager. However, neither possible nor impossible pattern this way. For this reason the following are unacceptable and the grammar prevents accidents from being the subject of happen:

• *Accidents are possible __ to happen.
• *Accidents are impossible __ to happen.

Adjectives 2: Hollow clauses

• The book was difficult ____ to read _____ .

With the adjective difficult, the subject of the infinitive is freely interpretable. We can extrapolate who was trying to read the book from the surrounding discourse. The subject of to read is not being stipulated by the subject of the main verb, the book. The book was not reading the book!

However, if you look carefully at the other side of read you'll realise that the book is being interpreted as the Object of read. The sentence means something like:

• The book_(i) was difficult for (someone) to read (it)_(i).

In some grammars they stipulate that the object has been moved from that gap at the end there to the subject position of the main verb. Tough is one of the adjectives that behaves in this way, and for this reason this is often called tough-movement. In the CaGEL these clauses are known as hollow clauses, because they have that gap at the end.

One of the adjectives that takes hollow clauses is impossible. For this reason the OP's examples were correct:

• Oranges are impossible to grow here.
• The lecturer was impossible to hear.

These work like this:

• Oranges_(i) are impossible (for people) to grow (them)_(i) here.
• The lecturer_(i) was impossible (for people) to hear (him)_(i).

Possible

Possible does not occur in control constructions. It's also said that possible doesn't take hollow clauses. It cannot control the interpretation of the subject in an infinitival clause, and does not allow for the gap at the end of a hollow clause to be interpreted through a subject higher up in the sentence structure.

• *A situation possible to arise.

The reason the example above fails is that the speaker wants to use possible in a control construction meaning something like this:

• A situation_(i) possible (for it)_(i) to arise.

Unfortunately, this won't work. Similarly the problem with:

• The lecturer was impossible to be heard.

..is that again, the speaker here is trying to use impossible like a control adjective, whereas as we have have seen, it actually takes hollow clauses. They expect the sentence to be heard like this:

• The lecturer_(i) was impossible (for him)_(i) to be heard.

Because the adjective is impossible, the item lecturer here cannot be interpreted as the subject of to be heard. In fact lecturer cannot be processed properly as an actor in the infinitival clause at all, because there is no object position in the clause - it's passive!