Meaning of perfect aspect in infinite clauses

Question

Motivated by this question I've realised I have some difficulty in interpreting infinite clauses.

What is an infinite clause?

One of my grammar books says that an non-finite clause is a dependent clause that unlike finite clauses have no tense or modality. Infinite clauses are a particular case of non-finite clauses, and are constructed using a verb in infinitive form. Here are some examples:

To have thought this made him more cheerful

It's difficult to maintain a friendship

My goal now is to look into the future

My difficulty: Attaching a tense to an infinite clause

Probably because of the *-to-be expressions:

the bride-to-be

the groom-to-be

a failure-to-be

is-to-be

I have interpreted clauses like:

then to be seen only in Japan

as:

which are about to be seen only in Japan

In the question I linked above, @StoneyB points out that correct interpretation is:

which then could be seen only in Japan

My question: Do infinite clauses with perfect aspect imply a past tense?

I would like to get help to interpret the difference in meaning in these two clauses:

1. To think this makes him more cheerful

2. To have thought this makes him more cheerful

Amber already answered to this question in the comments:

1. You find it unthinkable that this makes him more cheerful.

2. You thought this would make him more cheerful, but in retrospect it seems unthinkable.

Additional question: Can an infinite clause carry meaning of future

I understand from Amber's comment that "to think" just describes the action of thinking without saying when, but "to have thought" describes a past event, a thinking I did in the past.

What I would like to see is whether there are cases where "to think" may carry meaning of a future action, as in the expression is-to-be.

Answer 1

A non-finite clause might better be defined as a clause headed by a non-finite verbform: an infinitive or a participle. Such a clause by definition¹ has no tense. It cannot be the main or matrix clause in a formal sentence, because a matrix clause must be headed by a finite verbform, which defines its Reference Time—the time you are talking about. (see the discussion of tense here.)

Consequently, non-finite clauses only appear in formal sentences as subordinate clauses. Their temporal reference is inferred from context. In most cases that temporal reference is to the Reference Time defined by the matrix clause:

To think this makes him more cheerful may be paraphrased as
That he thinks this makes him more cheerful or
When he thinks this it makes him more cheerful.

A non-finite perfect construction—one in which the HAVE component is cast as a non-finite verborm—works the same way. (Keep in mind that the tense of a perfect construction is expressed by the HAVE component which heads it: a present perfect signifies a present state, a past perfect signifies a past state. Those states, current at Reference Time, arise out of the prior eventuality mentioned by the past participle component.). The semantics of think make it sort of odd in this context, so let's look at do instead.

To have done this makes him more cheerful may be paraphrased as
That he has done this makes him more cheerful or
When he has done this it makes him more cheerful

In the right context, infinitive clauses (including infinitive perfects), readily bear a future reference. For instance:

To think this this will make him more cheerful tomorrow.
To have done this will make him more cheerful in his old age.

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¹ ‘by definition’ because an English non-finite verbform is defined as one which is not marked for tense. Note that tense here is used in the technical sense “morphologically marked temporal reference”; English has, in this sense, only two tenses, past and non-past.