In his Principles of Psychology, William James asserts that the physical body is at the center of a person's concept of himself or herself and at the center of his idea of the "social" self—how others perceive one. Madame Merle articulates this concept of self when she says to Isabella, before Isabella has any money:
When you’ve lived as long as I you’ll see that every human being has his shell and that you must take the shell into account. By the shell I mean the whole envelope of circumstances. There’s no such thing as an isolated man or woman; we’re each of us made up of some cluster of appurtenances. What shall we call our "self"? Where does it begin? where does it end? It overflows into everything that belongs to us—and then it flows back again. I know a large part of myself is in the clothes I choose to wear. I’ve a great respect for things! One’s self—for other people—is one’s expression of one’s self; and one’s house, one’s furniture, one’s garments, the books one reads, the company one keeps—these things are all expressive.
For Madame Merle, the self is purely social: it is how a person fits into the social order and how a person is perceived by others. For her, the self consists of one's clothing, house, and furniture: it is the image one projects. As stated above, this fits well with William James's notion of the social self.
Isabel disagrees strongly with what Madame Merle says above, stating that her self-concept is not based on the clothes she wears and that they do not express who she is. Isabel says her clothes are "imposed" on her by her dressmaker. She calls these outward appearances a "barrier" to who she really is.
Madame Merle is an evil character who takes advantage of Isabel's naivete to manipulate her into marrying her lover Osmond, who is the father of her daughter Pansy. It would be easy, therefore, to argue that since Madame Merle is evil and Madame Merle's philosophy of self is similar to William James's, Henry James is using her to critique his brother's psychology of selfhood. However, I do not believe this is the case. What is going on is that Henry James is critiquing Isabel for not fully enough understanding William James's psychology of self and for being blind to the extent she herself lives by it. I would say Henry James creates Isabel as overly idealistic, and therefore, self-deluded: this is the tragic flaw in her character that leads to her undoing.
First, James establishes that Isabel might want to reject the notion of evaluating people based on their outward appearance, but that is how people evaluate her. Ralph Touchett does love Isabel's soul, but he also loves her beauty and grace—these are part of what make her a fascinating study or portrait to him. "Portrait" is a key term in this novel: James writes a "portrait" rather than an "analysis" of Isabel. The title points to the integral importance of the outer shell as a part of who a person is.
Second, Isabel herself judges people by their outer shells. This is the tragic mistake she makes with both Madame Merle and Osmond. She can't see Madame Merle's evil until it's too late, even after Merle tries to warn her of it, and she can't see that Osborne's artistic pose is nothing more than an empty, egotistical shell until after she makes the mistake of marrying him.
I would state that Henry James is arguing that Isabel badly needs to develop the awareness to read the meaning of the outer shell of people's demeanor. It is a sign of her development into a wiser, if much sadder and more disillusioned person, when, for example, she can read the intimate meaning in how Madame Merle and Osborne's bodies relate to each other when they believe nobody is looking:
She perceived that they had arrived at a desultory pause in their exchange of ideas and were musing, face to face, with the freedom of old friends who sometimes exchange ideas without uttering them. There was nothing to shock in this; they were old friends in fact. But the thing made an image, lasting only a moment, like a sudden flicker of light. Their relative positions, their absorbed mutual gaze, struck her as something detected.
This ability to read the social self—and to understand its value—is an important part of Isabel's growth. The flaw is in Isabel, not William James.