It's a different approach and I think it is going to make interesting reading. Perhaps this is more brainwashing that there should always be a purpose behind our actions which is indicated by what you say here:.Here's a thought. Is it worth trying to pin down the wide variety of situations when the ing form is used? We've all been so brainwashed into thinking that European infinitives are "To ............." in English that students are prone to ask "When should I use ing instead of the infinitive?" Well, the answer is "Pretty much all the time".
The question should be "When shouldn't I use the ing form?". It's more straightforward to treat ing as the default answer and highlight when " to" is used. I'll have a go:
"to" is used between resolute purposeful verbs and verbs describing actions or states that are subsequent in time to the first verb. If the first verb is not resolute or purposeful enough even though the action is subsequent (eg fancy/wouldn't mind) then -ing is still used. ing is always used if the second verb is temporally previous to the first verb. (more or less)
Here I disagree with you. "tolerate" is not purposeful, it is introspective and indicates that one is not going to do anything about something that is against one's own sensibilities. The depressing part is that purpose related to to+inf seems to have to relate to getting sth done (ie deontic) and not to ones own feelings on sth. "decisiveness , then is a criterion that may have to go from my table. "Risk" actually doesn't contain the idea of purpose. You may risk sth with a purpose in mind, but risk itself is not purposeful. Extreme risk is reckless and there is certainly no purpose there. BTW, I ask my students to work both ways and also think about what the fact of being followed by one or other form tells you about the meaning of the preceding verb.It's depressing though, because you look at some of the dreaded lists and notice say " tolerate" or "risk" . Tolerate is quite purposeful enough but is that ing that comes after really "previous" enough to shoe horn this into such a rule? Risk seems sometimes decisive, sometimes fatalistic.
This one's easy:Or "allow" "permit" etc. What's the difference between "We don't allow smoking" and "We don't allow visitors to smoke"? I think there is something to choose between the default blanket
ing (1 smoking 2 not allow) and a specific imposition in a particular case ( 1 visitor 2 not smoke)
We don't allow smoking=the activity itself.
We don't allow visitors to smoke=highly deontic we impose our will on people in the real world. We have a strong intention and folllow through to impliment that. Yes, this gets even more complicated because the existance of an object affects all this too. The existance of an object usually indicates an agent of some sort when followed by to+inf and often indicates restraint followed by V-ing. Prevent sb from, stop sb from. Congratulate sb on doesn't fit this idea, however.
Going back to "allow" note that this can be paraphrased as:
3. We don't let visitors smoke.
"Let" implies passivity of the person who lets sth happen (purpose is not even addressed). Whereas "allow" is a clear purpose.
I don't think this is just a coursebook thing: "I like arriving at the airport in plenty of time" is only likely to be said by sb who has in fact arrived at the airport with plenty of time to spare.And "like" won't go away, although there is said to be something more decided about the "like to": "I like to arrive at the airport in plenty of time (because I'm a meticulous person)" vs "I like arriving at the airport in plenty of time (because I can go round the shops ha ha )"
Though I'm not sure this isn't a BrE nicety that anyway exists more in coursebooks than in reality. Swap the sentences around a bit and see if you suddenly get a purposeful shopper. Probably not.
What won't go away is the fact that purpose is addressed in V-ing but is lacking. Whereas it isn't even addressed in modals and transitive modals.