Running things without the cats unravelling everything
Tradition must give way to logic! I was pleased to discover that a popular and logical use of the word sen is winning, despite it being a usage that Zamenhof himself warned people away from.
sen
without
vi ne povas vivi sen kato
you can't live without a cat
But before we see this logical and once forbidden usage, it'll really pay to understand the construction: sen tio ke. Notice above that it was a noun (kato) that followed sen. It could also have been a noun phrase, e.g. "a shy grey cat". But it couldn't have been a whole clause with its own verb and subject. For that, you'd need to introduce a subphrase using tio ke.
You can think of tio as a placeholder - it acts like the replacement for whatever we are "without" in this phrase. It means "that" or "that thing" by itself. You could in fact say:
vi ne povas vivi sen tio
you can't live without that (thing)
What we can then do - a thing that happens all over Esperanto - is to elaborate on what tio "that thing" is, with a whole phase, by means of the little marker ke (which also often translates as "that"):
vi ne povas vivi sen tio ke kato dormas sur la lito nokte
you can't live without (that thing, that...) a cat sleeping on the bed at night
So the phrase that tio is placeholder-ing is: a cat sleeping on the bed at night!
Now on to the main. The following is an example of an error in Zamenhof's eyes:
vi ne povas vivi sen zorgi pri kato
you can't live without taking care of a cat
It is that sen + i-verb (infinitive) combo that was once hissed at. But in a way, this is just the same kind of structure as the sen tio ke example.
But here, the subject of the "living" and the "caring" is now the same: "you" - and just as in English, we don't need to repeat the vi "you" in the second part of the phrase. We do a similar thing with more simple usage:
meloj amas trompi sciurojn
badgers love tricking squirrels
versus:
meloj amas ke vulpoj trompas sciurojn
badgers love that foxes trick squirrels
See how in the first case the subject is the same (badgers are both loving and tricking), so we only need the infinitive (i-verb). But in the second example the subject is different (badgers are loving, foxes are tricking), so we need a subphrase with its own subject and verb in a tense (you wouldn't say "badgers love that foxes tricking squirrels" in English, any more than you'd say "meloj amas ke vulpoj trompi sciurojn" in Esperanto).
And that's before we consider that sen zorgi has obvious intent here - I see no real chance for misunderstanding, so it makes sense as a construction to me!
Here's the PMEG discussion on this usage becoming more accepted in this modern age. The page also has suggestions about rephrasing to avoid the issue in the first place. One technique being the use of the noun form of the verb instead of the infinitive, either with the base -o or with the helping suffix -ado.
Note that there's plenty other uses of i-verbs, i.e. not only contexts where we have implicit references to a subject already mentioned.
There's even mention of other prepositions that are commonly in use in front of i-verbs, but I'll save those for another day. The main objection to their use in this way appears to be that prepositions should stick to complementing nouns, not spreading their wings to infinitives. But who are we to limit their dreams?
