Explanation

Because, actually, the last part of the sentence indeed says:

suggests that this supposed reticence was perhaps more artistic (iii) __________ than historical fact.

This reticence was more formal than substantial. I.E. it was more an attitude, a posture rather than a fact, a concrete thing.

hope now is clear.
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The recent publication of the painter Robert Motherwell's substantial body of writing, as well as writings by fellow Expressionist Barnett Newman, (i) ___________ Ann Gibson's assertion that the Abstract Expressionists were reluctant to (ii) ___________ issues of artistic meaning in their work and suggests that this supposed reticence was perhaps more artistic (iii) __________ than historical fact.

The recent publications by the painters did something to Ann Gibson's assertion that the Abstract Expressionists were reluctant to __________ issues of artistic meaning in their work and suggests that this supposed reticence was perhaps more artistic......

the phrase "this supposed reticence" points to the second blank. Hence the proper way to complete the blank would be "were reluctant to articulate issues" and in fact we find the word articulate in the choices and it is the correct choice.

Now if Ann Gibson's assertion was that they were reluctant to articulate issues, then what does the publication of the writings of these artists prove? It proves that her assertion was wrong. It undermines her assertion.

Now, if this reticence did not exist as a historical fact then , what can it be? It can only be artistic posturing.
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why posturing for last blank? why not focus

What is the clue which leads to the first blank being 'undermines'?

Hope this helps.

Regards
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Since you say that reticence is more formal / habitual , then Doesn't CONSCIENCE also plays the same role where Artists in their Clear Conscience had refrained from Articulating the .....

No.

Actually, his posture was an appearance.

In this case, he shows himself alike a rock star shows as a drug-addicted because is cool, is a role, the mainstream wants this...but indeed he is not that way.

It is like a mask.

Regards
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The recent publication of the painter Rober Motherwell`s substantial body of writing, as well as writings by fellow Expressionist Barnett Newman, (i) _____Ann Gibson`s assertion that the Abstract Expressionists were reluctant to (ii) ______ issues of artistic meaning in their Work and suggests that this supposed reticence was perhaps more artistic (iii) _____than historical fact.
Blank(i)
Substantiates
Undermines
Overlook

Blank(ii)
Forgo
Articulate
Conceal

Blank(iii)
Conscience
Focus
Posturing

Merged similar topic.

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Regards
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All this you are imagining or reading into the phrase. There is nothing in the sentence itself to suggest all this.
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I thought the word "posturing" generally has a negative connotation to it, in which case "focus" should be apt. I'd be hardpressed to go with "posturing", but again English is a nuanced language, and such questions will always prove complicated.

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