Language evidently is not a system. It is more than finite options.
None of the President quotes here has error.
More than that, and breaking precedent once more, I do not intend to commence any sentence with these words ― “If George Washington had been alive today”, or “If Thomas Jefferson”, or “If Alexander Hamilton”, or “If Abraham Lincoln had been alive today…”
― Theodore Roosevelt
If Lincoln were alive today, he’d be turning over in his grave.
― Gerald Ford
If men were angels, no government would be necessary.
― James Madison
“If I had permitted my failures, or what seemed to me at the time a lack of success, to discourage me, I cannot see any way in which I would ever have made progress.”
― Calvin Coolidge
We may return to our symbolic line for time. Our PRESENT today is not going to be our PRESENT tomorrow. All days in the PAST were once our PRESENT.

We may first compare real-time and the figurative premise.
REAL TIME
Lincoln was alive today…?
Lincoln is alive…?
Men are angels…?
I have permitted…?
FIGURATIVE TALK
If Lincoln had been alive…
If Lincoln were…
If men were…
If I had permitted…
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Let us now compare real-time and the figurative consequent.
REAL TIME SENSE
Lincoln is not turning over…
Government is necessary.
I have made progress.
FIGURATIVE TALK
Lincoln would be turning over…
No government would be…
How I would have made…
Figurative talk is in a way relative, but it is not merely parallel to real time. Let us think about guessing the premise for language as in example 92.
92. She would have made progress.
If we decide not to depend on clairvoyance, and to perceive the structure for a closed Modal frame, we do not have to ponder, if —
she has made / has not made; she had made / had not made; she does make / does not make; did make / did not make progress, or will make / will not make; will have made; or even will not have made progress.

Telling the premise could be cumbersome most of the time, so the closed Modal frame does not make us simplistic. We are realistic, about talk and time. We may only expand into more of a notional frame, further in the journey.
The frame with Modal verbs closes on the object of thought rather than any particular time extent. This is why forms many as above could be real-time premise to the closed frame in 92,
She would have made progress.

The real-time frame closes on any particular time extent, and opens only for the Perfect, where the time reference is not singular:
92b. Calvin Coolidge had made progress, and spoke about it.

In conversation, we mostly seek a cognitive ground in common (as in ■→CHAPTER 6). It can help think about Modal structures as,
92a. She MAY have made progress.
How likely would we be to say:
92b. Calvin Coolidge MAY have made progress?
He made his progress in the past — and MAY is a PRESENT form.
The thing is not about probability or certainty. Progress is a development and we humans usually think we may have made progress before we say we have made it. Let us imagine we are writing a biography. These often use embedded discourse — it is talk as if at the time things happened — but our intent is to report.
Our President wrote:
92c. I MAY have made progress.
He perceived he was making progress, but there were things he held for the time ahead still. To refer to such a stage from our present day, we may feel like stating, he wrote he MIGHT have made progress, rather than he MAY have, the time to be PAST to us and past probability for MIGHT being the same as for MAY in the PRESENT.
Observations here are for us not to get stuck on a preliminary conclusion; part 4 of the journey has Reported Speech. Let us note that it is natural to relate own talk to the real time we live. We yet do not need “unreal time” for language about theories or hypotheses: for these, we close the frame on the object of thought rather than time; we do not need “non-existent time”.

For grammar as well, we may have another quote:
No group and no Government can properly prescribe precisely what should constitute the body of knowledge with which true education is concerned.
— President Franklin Delano Roosevelt
Let us consider the Relative Progressive, feel welcome.
■→10.2. FORM RELATIVITY AND THE PROGRESSIVE
■→This text is also available in Polish.
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The world may never have seen her original handwriting, if her skill was taken for supernatural. Feel welcome to Poems by Emily Dickinson prepared for print by Teresa Pelka: thematic stanzas, notes on the Greek and Latin inspiration, the correlative with Webster 1828, and the Aristotelian motif, Things perpetual — these are not in time, but in eternity.
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