In chapter three of F. Scott Fitzgerald's novel The Great Gatsby, Nick discovers that Jordan Baker is "incurably dishonest." This is his conclusion based on evidence from her past as well as his own observations, but he is not remarkably concerned about it. He enjoys her company, and thinks at times he may love her.
When he first meets Jordan Baker, Nick learns of her cool detachment and impersonal nature. He also learns that she is a gossip, as she shushes him in order to hear a conversation between Tom and his mistress. She also lets Nick in on the story of Tom's affair.
Jordan is a typical example of the flapper culture. Flappers rejected the strict dress and behavioral codes of the Victorian era. They were coming of age during wartime, and they had a live-for-today philosophy of life. Many flappers smoked, drank, and embraced their sexuality.
In chapter three, Nick's relationship with Jordan progresses. They spend an evening together at Gatsby's party. It is hard to tell at that point if the relationship progresses because of their mutual affection or because of the influence of alcohol and their shared interest in the mysterious Gatsby. Later in the chapter, Nick explains that he loses sight of Jordan for a while, but then their relationship is rekindled. He explains that he isn't exactly in love with her, but feels a "tender curiosity" toward her. Shortly after that, he reveals what he discovers about her, which is her dishonesty. The textual evidence is cited below.
"Jordan Baker instinctively avoided clever shrewd men and now I saw that this was because she felt safer on a plane where any divergence from a code would be thought impossible. She was incurably dishonest. She wasn’t able to endure being at a disadvantage, and given this unwillingness I suppose she had begun dealing in subterfuges when she was very young in order to keep that cool, insolent smile turned to the world and yet satisfy the demands of her hard jaunty body. It made no difference to me. Dishonesty in a woman is a thing you never blame deeply—I was casually sorry, and then I forgot. It was on that same house party that we had a curious conversation about driving a car. It started because she passed so close to some workmen that our fender flicked a button on one man’s coat."