It's common to say “I see” when we understand something. And indeed, “seeing” in the Bible represents grasping and understanding spiritual things. So it makes sense that the eyes, which allow us to see, represent the intellect, which allows us to understand spiritual things. This can also be used in the negative, of course; the Bible speaks of people having eyes and refusing to see, and the Lord when He was in the world advised plucking out an offending eye. These represent a refusal to acknowledge truth, or being misled by falsity.

9051. 'Eye for eye' means if anything is injured by them in the inner part of the understanding. This is clear from the meaning of 'the eye' as the understanding, in this instance the inner part of it, the life of which is the life of faith. A person's understanding has an outer part and an inner part The outer part of his understanding is where thought that enters his awareness is, whereas the inner part is where thought that does not enter his awareness is, though it enters that of the angels. This part of the understanding is what the Lord enlightens when a person receives faith, for it exists in the light of heaven and holds within it a person's spiritual life. This is not made plainly evident to the person while in the world, but it is made so to that person in the next life when he becomes an angel among angels in heaven. In the meanwhile that life lies hidden within the thought belonging to the outer part of the understanding, producing there the holiness and reverence for the Lord, for love and faith in Him, for the Word, and for everything else that is the Church's. The reason why 'the eye' means the understanding is that the eye corresponds to the understanding; for the understanding sees in the light of heaven, but the eye sees in the light of the world. The things that the former eye, that is, the understanding, sees are spiritual, and its field of vision is the factual knowledge contained in the person's memory. But the things which the physical eye sees are earthly, and its field of vision consists in every object that appears in the world. Regarding 'the eye', that in the spiritual sense it means the understanding, and also faith since faith composes the life of the inner part of the understanding, see 2701, 4403-4421, 4523-4534.

[2] Anyone who does not know that 'the eye' is used in the Word to mean the understanding cannot know what the meaning is of the things which the Lord spoke concerning the eye in the Gospels, first of all these,

If your right eye causes you to stumble, pluck it out. It is better for you to enter the kingdom of God with one eye, than having two eyes, to be cast into the Gehenna of fire. Matthew 5:29; Mark 9:47.

Everyone recognizes that the eye should not be plucked out even if it does cause a person to stumble, and that no one enters the kingdom of God with only one eye. But 'the right eye' means falsity in a person's belief about the Lord; this is what must be plucked out. Then there are these things spoken by the Lord,

The lamp of the body is the eye. If therefore your eye is sound, your whole body will be full of light. If your eye is evil your whole body will be full of darkness. If therefore the light that is in you is darkness, how great is the darkness! Matthew 6:22-23; Luke 11:34.

Nor is 'the eye' used here to mean the eye, but an understanding composed of the truth of faith. This is why the eye is called 'the lamp of the body' and why the Lord says, 'If the light that is in you is darkness, how great is the darkness!' For 'darkness' in the spiritual sense is falsities constituting faith, 1839, 1860, 4418, 4531, 7688, 7711.

[3] There are these words too spoken by Him,

Why do you notice the speck which is in your brother's eye, but do not consider the plank that is in your own eye? Matthew 7:3-5.

'Noticing a speck in a brother's eye' means seeing something erroneous in a person's understanding of truth; 'the plank in one's own eye' is huge evil of falsity, since 'wood' in the internal sense means good and in the contrary sense evil, 643, 2784, 2812, 3720, 8354. Good is also represented in the next life by a plank, which is why those who pretend to have good within themselves are seen carrying a plank, walking in safety as they do so. If 'eye' and 'plank' did not have these meanings, would 'seeing a plank in an eye' have any meaning at all? If it is not known that 'eye' in the Word means the understanding of truth, which is faith, neither can it be known what is implied by the Lord's action when He healed the blind man,

He spat on the ground and made clay with His saliva, and said to him, Go, wash in the pool of Siloam. John 9:6-7.

Since all the Lord's miracles, like all Divine miracles, had to do with those things that belong to the Lord's kingdom and the Church, 7337, 8364, so did this miracle too.