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What is "Disquisition" in this context? I would like to know its most similiar word ...

Is Candid has the right meaning for the word bluntness in y text?
He was quite candid about his past.

"As Obama listened to the senior senator from Nevada, he wasn’t sure where the old man was going. But then
Reid’s disquisition took an unexpected turn, surprising Obama in both its bluntness and adamancy."

Some lines later they discover more details ...

“So,” asked Gibbs from behind his desk, “what did we *** up?”
“Nothing,” Obama replied. “Harry wants me to run for president.”
“That whole meeting was about you running for president?”
“Yeah,” Obama said, then grinned. “He really wants me to
run for president.”
Comments 
The most appropriate synonyms for the word "Disquisition" as it is used in the example you have provided are: discussion, lecture, address, presentation, speech, talk.

To be "blunt" is to be very candid, frank, direct, and to the point.

Flash quiz question: How would you use the word "candid" in your example sentence?

Answer:
I'm not certain that the term "conversation" is the best choice to replace "disquisition." Were Senators Reid and Obama speaking to each other, or were other people present? A conversation is, generally, between two people, right?
Why would the author have chosen such a precise word instead of saying, simply, "conversation?" I wouldn't use "conversation" for fear of changing the author's perception of how Senator Reid was speaking.

Yes, please write me a sentence using "candid" in the context of your example. Just for fun Emotion: smile !
Thanks John Emotion: smile