I'd like to know if the phrase "he might think he saw" in the chapter Seven of The Great Gatsbyis an idiomatic expression and what is the meaning of "saw" in this context:
A new point of view occurred to me. Suppose Tom found out that Daisy had been driving. He might think he saw a connection in it—he might think anything. I looked at the house: there were two or three bright windows downstairs and the pink glow from Daisy’s room on the second floor.
"He might think he saw a connection" is idiomatic because the verb saw is used in a non-literal sense. After all, saw does not mean to have recorded a visual image in one's mind, to have perceived with one's eyes. Instead, in these sentences--
"He might think he saw a connection- He might think anything"--
the second sentence underscores the idea of Tom's thinking and believing that he has deduced something. What he has actually seen is nothing because he was not present when Gatsby's car struck Myrtle.
In Chapter Seven, what Tom Buchanan has probably learned as he talks to his wife over a plate of cold fried chicken is that Daisy has driven Gatsby's car has struck Myrtle Wilson with it. Everything after this fact is mere conjecture on his part. He may think Daisy has struck Myrtle because she wishes to kill Tom's mistress; he may think that Gatsby identified her somehow; he may think Mrytle wanted to commit suicide. But, he has physically seen nothing. Any perception that occurs is not physical, but mental conjecture as Tom tries to understand what has happened. Therefore, what he "saw" is not literal, but figurative and idiomatic.
This is not an idiomatic verb construction, but a combination of a modal verb and a simple past tense. Modal verbs contemplate possibility, what could happen in the future or could have happened in the past. Nick is speculating about what Tom might think, and the speculation is that he could see a connection. Here are some other examples for you:
She might think that she saw the accident clearly and accurately, but in the excitement of the moment, that is not likely to be the case.
He might think he acted reasonably under the circumstances.
They might think they will be on time, but if they only allow ten minutes to get there, it's not going to work.
One of the greatest things about English is how we can combine all these different verb forms to show hypothetical and speculative ideas, along with a precise pinpointing of past, present, or future. The complexity of verb construction in English is fascinating.