Why is he called the Tathagata (ITI 112)
This teaching is from the section The Planes of Realization of "In the Buddha's Words" by Bhikkhu Bodhi.
The Buddha explains why he is called the Tathāgata, the one who has fully comprehended the world, its arising, cessation, and the path leading to its cessation.
Thus it was said by the Blessed One, said by the Worthy One, as I heard:
"Bhikkhus, the world has been fully comprehended by the Tathāgata, the Tathāgata is detached from the world. Bhikkhus, the arising of the world has been fully comprehended by the Tathāgata, the arising of the world has been abandoned by the Tathāgata. Bhikkhus, the cessation of the world has been fully comprehended by the Tathāgata, the cessation of the world has been realized by the Tathāgata. Bhikkhus, the path leading to the cessation of the world has been fully comprehended by the Tathāgata, the path leading to the cessation of the world has been developed by the Tathāgata.
Bhikkhus, whatever is seen, heard, perceived, cognized, attained, sought for, or reflected on by the mind in the world with its deities, Māra, Brahmā, ascetics, and brahmins, including gods and humans, all that has been fully comprehended by the Tathāgata. Therefore, he is called the Tathāgata.
And bhikkhus, whatever the Tathāgata speaks, talks, or declares during the interval between the night he awakens to unsurpassed perfect enlightenment and the night he attains final Nibbāna in the element of Nibbāna without a remainder of clinging, all that is just so and not otherwise. Therefore, he is called the Tathāgata.
Bhikkhus, as he speaks, so he acts; as he acts, so he speaks. Therefore, one whose words match his actions and whose actions match his words is called the Tathāgata.
Bhikkhus, in the world with its deities, Māra, Brahmā, ascetics, and brahmins, including gods and humans, the Tathāgata is unsurpassed, unconquered, one who sees things as they are, and wielding power. Therefore, he is called the Tathāgata."
The Blessed One spoke thus, it is said:
"Having fully known the whole world, as it truly is; Disentangled from the whole world, and without engagement.
He is the unsurpassed of all, the wise one, liberated from all bonds; Having reached the supreme peace: Nibbāna, without fear from any quarter.
He is the Buddha, with defilements ended, untroubled and free from doubts; Having reached the exhaustion of all exertions, he is freed with the ending of all attachments.
This one, the Blessed One, the Buddha, the unsurpassed lion; In the world with its deities, sets in motion the wheel of Dhamma.
Thus, gods and humans, who have gone to the Buddha for refuge; Having come together, honor that great one free from fear.
Tamed, he is the best of those who tame; calm, he is the sage of those who calm; Freed, he is the foremost of those who free; crossed over, he is the best of those who cross over.
Thus they honor this great one free from fear; In the world with its deities, there is none your equal."
This matter too was spoken by the Blessed One, thus have I heard.
Related Teachings:
The Buddha and the Arahant (SN 22.58) - The Buddha shares the similarities and differences between him and another liberated by wisdom.
For the welfare of the many (ITI 84) - A mixed prose and verse teaching on three people who appear for the benefit of the world.