be able to vs could

[tom3m]

In Michael Lewis's book The English Verb: An Exploration of Structure and Meaning I found this:

My doctor can say I can see you tomorrow or I ’m able to see you tomorrow.
Both are possible, and they are different. Difference of form implies difference
of meaning, and that difference can be understood.

How do the sentences in bold differ in meaning.?

[Barb_D]

I see no difference in intended meaning between "I'm able to see you tomorrow" and "I can see you tomorrow."

What does Mr. Lewis say is different about them?

[tom3m]

I do not know. Here is the full paragraph:

8. Paradigms do not need to be complete


My doctor can say I can see you tomorrow or I ’m able to see you tomorrow.
Both are possible, and they are different. Difference of form implies difference
of meaning, and that difference can be understood. In those
circumstances it is nonsense to pretend that “the infinitive of can is to be
able to.

But I would let it go if it conveys the same meaning.

[bhaisahab]

I don't find "I'm able to see you tomorrow" to be a very natural sentence.

[Tdol]

I don't find "I'm able to see you tomorrow" to be a very natural sentence.

Nether do I, but if I heard it, I would assume a greater degree of concession from the doctor- squeezing me in to a busy schedule.