In Chapter 7, what is ironic about Tom saying that he has second sight?
Even as Tom says “I have a—almost a second sight, sometimes that tells me what to do. Maybe you don’t believe that, but science---,” Nick, and we with him, smile at (or ridicule) Tom’s ridiculous posturing. Even the long dash in the text has meaning, for it indicates the man is unable to see sufficiently into the future to finish his sentence. The dash represents that absence in knowledge that corresponds to Daisy asking what they will do with themselves for the rest of that day, the next, and the next thirty years (125). As if to emphasize this, when Tom pauses (with the dash), Nick says “the immediate contingency overtook him.” “Contingency” means “possibility,” indicating Tom’s limitations are such that the slightest chance in events will leave him speechless, unable to complete a thought.
Having second sight means having the ability to see into the future. If Tom had this ability, he would have seen that Daisy and Gatsby would have an affair. Furthermore, he would have anticipated Myrtle's death and could perhaps have prevented it by staying at home that day. As it is, Tom is clueless about the future; he lives entirely in the present with little thought about the effects of his actions.
It is ironic that Tom says he has a second sight because he would have instantly sensed Daisy having an affair with Gatsby. Tom likes to say he is very educated and higher up than most of society because of the books he reads and because he is wealthy. He is just talk and he is too busy with his own affair to have his "sixth sense" kick in.