In Chapter 5, the narrator uses logos and ethos to argue against the idea that Black Americans are inferior to white Americans:
It is my opinion that the colored people of this country have done four things which refute the oft advanced theory that they are an absolutely inferior race, which demonstrate that they have originality and artistic conception; and, what is more, the power of creating that which can influence and appeal universally.
As promised, the narrator provides four examples of Black American's "originality and artistic conception:" the cake-walk, Uncle Remus stories, Jubilee songs, and ragtime. The examples themselves function as logos because the narrator is providing evidence readers may not have considered to make his point. All of these elements of Black culture have been, to varying degrees, appropriated into "mainstream" culture. That is to say, they have been consumed (especially by white people) without acknowledgment that they come from Black creators. In fact, they were all woven into minstrel performances, in which white performers caricatured Black people and their culture for a profit. The narrator reclaims these art forms as examples of Black ingenuity.
His defense of Black artistry also functions as ethos. Politicians and academics who opposed the extension of civil rights and voting rights to Black Americans often claimed that Black people were incapable of governing themselves. They should not be a protected or represented group, these white supremacists argued, because they were incapable of producing the artistic culture that anthropologists recognized as the hallmark of a civilization. The Harlem Renaissance of the early 20th century was in part a response to this argument: one reason Black Americans had for producing such a rich array of art—and specifically art that focused on their experience of being Black in the United States—was to prove that there was such a thing as African American art and culture. By citing not only examples of Black Americans' successes but specifically of their "originality and artistic conception," the narrator builds his people's collective ethos in the eyes of white readers who might have heard the argument that they are "uncivilized."
In Chapter 10, the narrator passes for white and listens to a conversation between a Texan and a former Union soldier. The Union soldier uses logos when he points out the situational irony of the anti-intermarriage laws in the South:
[“]As to the mulatto South, if you Southerners have one boast that is stronger than another, it is your women; you put them on a pinnacle of purity and virtue and bow down in a chivalric worship before them; yet you talk and act as though, should you treat the Negro fairly and take the anti-intermarriage laws off your statute books, these same women would rush into the arms of black lovers and husbands. It’s a wonder to me that they don’t rise up and resent the insult.”
Anti-intermarriage laws cropped up in the South in the late 19th and early 20th century, largely as a reaction to the gains made during Reconstruction. White southerners feared "miscegenation," or the birth of mixed-race children if people were allowed to marry across racial categories. This is what the Union soldier means by "the mulatto South." Mixed-race children born with all the rights conferred on American citizens threatened white supremacy because they made it more difficult to maintain strict racial categories (categories that were always blurry at best). The Union soldier takes apart the logic behind the anti-intermarriage laws by pointing out that they are at odds with the way Southerners like to portray white women. If white women are really "pure," "virtuous," and worthy of the kind of "chivalric worship" conferred on them in the South, the soldier argues, it doesn't follow that they would want to marry Black men if allowed. Either the laws are superfluous, or (as the soldier suggests) the women aren't as "pure" and "virtuous" as the Texan and other Southern men would like to believe.
This argument is itself both racist and misogynistic. The Union soldier's use of racism in his defense of marriage equality is just as ironic as the Texan's logic. The scene has another level of situational irony in the fact that the only reason the narrator is privy to the conversation at all is that he is passing for white—otherwise, he would not have been admitted to the smoking car on the train where the other two men are talking. The narrator is left with a deep sense of unease because he would like to challenge what the soldier is saying, but he can't do so without risking the revelation that he is "intruding." Instead, he must tacitly agree with the lesser of two bad stances on race.