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The following quotation is from Anthony Trollope's The Small House at Allington:

Lily did not analyse her own feelings, or closely make inquiry as to those of her mother, but she perceived that it was not all as she would have wished it to have been.

I understand what perfect infinitive can refer to and its use.

I would like to know if in the cited context the perfect infinitive can be grammatically replaced by present infinitive. There's that past time reference it was not all which makes me doubt.

So, can we phrase it like this:

Lily did not analyse her own feelings, or closely make inquiry as to those of her mother, but she perceived that it was not all as she would have wished it to be.

I know they are different and mean different things but I don't know if the second is grammatical too.

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As you stated, they mean different things. The important thing, I think, is to remove some context.

...it was not as she would have wished it to be.

The situation, at some point in the past (relative to when the story is being read), was not in accordance with her wishes.

...it was not as she would have wished it to have been

The situation, at that point in the past, was not in accordance with her wishes for some time prior to that.

Consider this. The conditional, "would have," makes it clear that her wishing is dependent on some nonexistent condition, likely her power to actually make her wishes come true. Now, let us assume that this condition is true (so we can dispense with the conditional). Now, when one says, with regard to some event, "I wish it to be tomorrow," this clearly references a near future instance, whereas when one says "I wish it to have been yesterday," this implies the desire to change the past. This is the principle at work here. In the case in the original sentence, the present perfect situates the situation wished for in the past relative to the time at which the wish was made.

Now, here's the trick! The first sentence makes a comparison between two different time frames. It was not (at the time of the wish) the way she would have (if she had the power) wished it to have been (at some time before the wish). This is not terribly confusing, because the present perfect implies that the effects of wishing something to "have been" a certain way carry over to the present, making it plausible that such a situation is now real. One should properly say, though, "..it had not been as she would have wished it to have been."

This is all very confusing, but perhaps it will be made more clear if we replace "wish" with another verb, say, "forced."

...it was not as she would have forced it to be.

So if she had the power, she would have forced the situation to be a certain way.

...it had not been as she would have forced it to have been.

If she'd had the power, back before she was musing on her situation, the situation would have played out very differently.

And finally the mismatch

...it was not as she would have forced it to have been.

If she had had the power, her previous situation would have been very different, carrying over into the present time.

Note that there is a small ambiguity. When she "would have forced it to have been" a certain way, does the "would have" refer to the current time, conditionally? That is to say, time manipulation? Or does it refer to the past? That is, is the implied phrase "if she had had the power," or 'if she had the power"?

The point though, is that they are all grammatically correct, but one is much easier to parse than others: the one with "to be."

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