In Act I, Scene IV, of William Shakespeare's King Lear, what reference is made to Cordelia?

If her failure to match her two older sisters, Goneril and Regan, to see who among the king’s daughters could be most obsequious would result in Cordelia’s disgrace and banishment, it was a price she was willing to pay to retain her dignity and to spare her father the lies and deceit that the aging monarch seemed to be inviting. In Act I, Scene I, of King Lear, the titular character is contemplating the division of his kingdom among his offspring, with the older, already married daughters doing the utmost to curry favor with their father. Goneril and Regan are only too happy to comply, dousing their father with the most flattering homilies and commitments to enduring love imaginable. To King Lear’s discredit, he is very receptive to these false declarations of love, and turns his wrath instead on Cordelia, angrily declaring to the King of France, who has just prevailed in the competition for Cordelia’s hand in marriage,

“Thou hast her, France: let her be thine; for we
Have no such daughter, nor shall ever see
That face of hers again. Therefore be gone
Without our grace, our love, our benison.”

If King Lear has allowed himself to be deceived by virtue of Cordelia’s refusal to add to her sisters’ obsequiousness into believing that Cordelia’s love for him is less than that suggested in Goneril and Regan’s homilies, than this will prove a fatal weakness that he will come to realize in Act I, Scene IV. Early in this scene, the king, while visiting the castle of Goneril, encounters a stranger who is Kent in disguise. Kent, of course, is, like Cordelia (and the Fool) among the more loyal of the king’s subjects, and sincerely wishes to help the falling monarch contend with the maliciousness of Lear’s oldest daughter. The unseen presence of Cordelia is now felt, with the incognito Kent suggesting the very attributes the king most requires:

KING LEAR

What services canst thou do?

KENT

I can keep honest counsel, ride, run, mar a curious
tale in telling it, and deliver a plain message
bluntly: that which ordinary men are fit for, I am
qualified in; and the best of me is diligence.

This comment by Kent—“I can keep honests counsel”—is reminiscent of the integrity missing from the king’s castle since the departure of Cordelia. The king’s visit to Goneril’s castle is a disaster, with tension hanging in the air and Lear developing a greater appreciation for the extent to which he has fallen subsequent to his decision to divide his kingdom. When a king is shunned by a mere servant—“Why came not the slave back to me when I called him,” to which a knight replies, “Sir, he answered me in the roundest manner, he would not”—it becomes all too apparent that his glory days are over. The king’s entourage is being poorly treated, and the king disrespected (although, the entourage was not exactly behaving in the manner to which Goneril and her staff have no doubt become accustomed), and, it is in this context that King Lear acknowledges his grave error in judgement with respect to his youngest and most loyal daughter, Cordelia:

[To GONERIL] Detested kite! thou liest.
My train are men of choice and rarest parts,
That all particulars of duty know,
And in the most exact regard support
The worships of their name. O most small fault,
How ugly didst thou in Cordelia show!
That, like an engine, wrench'd my frame of nature
From the fix'd place; drew from heart all love,
And added to the gall. O Lear, Lear, Lear!

Beat at this gate, that let thy folly in,

King Lear recognizes that Cordelia’s refusal to abide her father’s expectations, including her declaration that, when she does marry, her love will be shared with a husband as well as with her father, was actually a more honest and endearing display of love for the king than either of the other daughters was able to muster. Cordelia’s frankness, in other words, is now being appreciated by King Lear, his dignity having been insulted by the malevolent Goneril. This, then, is the context and the meaning of the reference to Cordelia in Act I, Scene IV, of Shakespeare’s play.