In the first scene of Shakespeare's Othello, Iago and Roderigo go to Desdemona's father, Brabantio, to tell him that Desdemona has eloped with Othello.
In act 1, scene 3, Brabantio goes before the Duke of Venice and the Venetian senators to tell them that Desdemona has been tricked by Othello into marrying him.
BRABANTIO. She is abused, stol'n from me and corrupted
By spells and medicines bought of mountebanks;
For nature so preposterously to err,
Being not deficient, blind, or lame of sense,
Sans witchcraft could not. (1.3.69-73)
Othello is asked to explain his side of the story, and he denies that he used any drugs or magic to win Desdemona's love. The Duke sends for Desdemona, and while she's being brought to the Duke's council, Othello tells the story of how Desdemona came to love him. Desdemona enters and tells the Duke that she chose Othello of her own free will. Brabantio relents, and the Duke rules in Othello's favor.
The words "eyes to see" occur only once in Othello, in this scene. In his parting words to Othello, it is Brabantio, Desdemona's own father, who plants the seed that Iago will nurture and help to grow into Othello's murderous rage against Desdemona.
BRABANTIO. Look to her, Moor, if thou hast eyes to see;
She has deceived her father, and may thee. (1.3.313)
The word "seems" is just as important in Othello as the words "eyes" and "seeing." What Othello sees with his eyes leads him to believe what seems to be the truth but what isn't, in fact, the truth.
By the end of this scene, Iago has firmly established this theme, and he's decided to deceive Othello and destroy him with what seems to be true.
IAGO. ... The Moor is of a free and open nature,
That thinks men honest that but seem to be so;
And will as tenderly be led by the nose
As asses are.
I have't. It is engender'd. Hell and night
Must bring this monstrous birth to the world's light. (1.3.409-413)
In act 3, scene 3, Iago casts doubts in Othello's mind about Desdemona's relationship with Michael Cassio. At the beginning the scene, Desdemona is speaking with Cassio, who is asking her to intercede on his behalf with Othello. Othello sees Cassio talking with Desdemona, and he sees Cassio quickly leave the scene when Othello enters.
IAGO. Ha! I like not that.
OTHELLO. What dost thou say?
IAGO. Nothing, my lord; or if I know not what.
OTHELLO. Was not that Cassio parted from my wife?
IAGO: Cassio, my lord! No, sure, I cannot think it,
That he would steal away so guiltylike,
Seeing you coming. (3.3.37-43)
A little later in the scene, Iago casts doubt on Cassio's honesty.
IAGO. For Michael Cassio,
I dare be sworn I think that he is honest.
OTHELLO. I think so too.
IAGO. Men should be what they seem;
Or those that be not, would they might seem none!
OTHELLO. Certain, men should be what they seem. (1.3.141-146)
Iago cautions Othello about jealousy with one of Shakespeare's most famous lines.
IAGO. O, beware, my lord, of jealousy!
It is the green-eyed monster, which doth mock
The meat it feeds on. (1.3.187-189)
Othello vacillates between jealousy and his love for Desdemona, and between what he sees and what he feels. For the moment, Othello gives Desdemona the benefit of the doubt, and of his love, and decides that he needs more proof before he decides that Desdemona is unfaithful to him.
OTHELLO. ... ' 'Tis not to make me jealous
To say my wife is fair, feeds well, loves company,
Is free of speech, sings, plays, and dances well;
Where virtue is, these are more virtuous.
Nor from mine own weak merits will I draw
The smallest fear or doubt of her revolt;
For she had eyes and chose me.
No, Iago, I'll see before I doubt; when I doubt, prove;
And on the proof, there is no more but this,
Away at once with love or jealousy! (1.3.206-215)
Iago takes this opportunity to cast even more doubt on Desdemona's faithfulness by reiterating what Brabantio said to Othello in act 1, scene 3.
IAGO. She did deceive her father, marrying you;
And when she seem'd to shake and fear your looks,
She loved them most. (1.3.229-231)
Othello trusts his eyes to see the truth, but he's constantly deceived by Iago into believing that seems to be the truth.