Before Allah discusses ideas and theoretical matters. He gives tangible examples: one man cannot have two hearts in his body, and a man's wife does not become his mother if he says the words of Zihar to her: "You are to me like the back of my mother." By the same token, an adopted child does not become the son of the man who adopts him and calls him his son. Allah says:
}Allah has not made for any man two hearts inside his body. Neither has He made your wives whom you declare to be like your mothers' backs, your real mothers...}
This is like the Ayah:
}They cannot be their mothers. None can be their mothers except those who gave them birth} (58:2).
}nor has He made your adopted sons your real sons.}
This was revealed concerning Zayd bin Harithah, may Allah be pleased with him, the freed servant of the Prophet. The Prophet had adopted him before prophethood, and he was known as Zayd bin Muhammad. Allah wanted to put an end to this naming and attribution, as He said:
}nor has He made your adopted sons your real sons.}
This is similar to the Ayah later in this Surah:
}Muhammad is not the father of any of your men, but he is the Messenger of Allah and the last (end) of the Prophets. And Allah is Ever All-Aware of every thing .} (33:40).
And Allah says here:
}That is but your saying with your mouths.} meaning, 'your adoption of him is just words, and it does not mean that he is really your son,' for he was created from the loins of another man, and a child cannot have two fathers just as a man cannot have two hearts in one body.
}But Allah says the truth, and He guides to the way.}
Sa'id bin Jubayr said:
}But Allah says the truth,} means, justice. Qatadah said:
}and He guides to the way} means, the straight path.
Imam Ahmad said that Hasan told them that Zuhayr told them from Qabus, meaning Ibn Abi Zibyan, that his father told him: "I said to Ibn 'Abbas, 'Do you know the Ayah,
}Allah has not made for any man two hearts inside his body}
What does this mean?' He said that the Messenger of Allah stood up one day to pray, and he trembled. The hypocrites who were praying with him said, 'Do you not see that he has two hearts, one heart with you and another with them?' Then Allah revealed the words:
}Allah has not made for any man two hearts inside his body.}'"
This was also narrated by At-Tirmidhi, who said, "It is a Hasan Hadith". [2] It was also narrated by Ibn Jarir and Ibn Abi Hatim from the Hadith of Zuhayr. [3]

An Adopted Child should be named after His Real Father
}Call them (adopted sons) by their fathers, that is more just with Allah}
This is a command which abrogates the state of affairs that existed at the beginning of Islam, when it was permitted to call adopted sons after the man who adopted them. Then Allah commanded that they should be given back the names of their real fathers, and states that this was more fair and just. Al-Bukhari (may Allah have mercy on him) narrated that 'Abdullah bin 'Umar said: "Zayd bin Harithah, may Allah be pleased with him, the freed servant of the Messenger of Allah, was always called Zayd bin Muhammad, until (the words of the) Qur'an were revealed:
}Call them (adopted sons) by (the names of) their fathers, that is more just with Allah.}
[1] Ahmad 1:267.
[2] Tuhfat Al-Ahwadhi 9:58.
[3] Ahmad, no. 2410 and At-Tabari 20:204. Most of the scholars of Hadith consider the chain of narrators for this text to be defective.
[4] Fath Al-Bari 8:377.
As for calling a person "son" as an expression of honor and endearment, this is not what is forbidden in this Ayah, as is indicated by the report recorded by Imam Ahmad and the Sunan compilers - apart from At-Tirmidhi - from Ibn 'Abbas, may Allah be pleased with him, who said: "We young boys of Banu 'Abd Al-Muttalib came to the Messenger of Allah at the Jamarat, he slapped us on the thigh and said,
«O my sons, do not stone the Jamarah until the sun has risen.» [1]
This was during the Farewell Pilgrimage in 10 AH.
}Call them by their fathers .} This is concerning Zayd bin Harithah, may Allah be pleased with him. He was killed in 8 AH at the battle of Mu'tah. In Sahih Muslim it is reported that Anas bin Malik, may Allah be pleased with him, said: "The Messenger of Allah said:
«O my son.»" [2] It was also reported by Abu Dawud and At-Tirmidhi. [3]
}But if you know not their father's then they are your brothers in the religion and Mawalikum (your freed servants).}
Here Allah commands that adopted sons should be given back their fathers' names, if they are known; if they are not known, then they should be called brothers in faith or freed servants, to compensate for not knowing what their real lineage is.
When the Messenger of Allah left Makkah after performing his 'Umrat Al-Qada', [4] the daughter of Hamzah, may Allah be pleased with her, followed them calling, "O uncle, O uncle!" 'Ali took her and said to Fatimah, "Take care of your uncle's daughter." So she took care of her. 'Ali, Zayd and Ja'far disputed over her, and the Messenger of Allah said:
«As for you, O 'Ali, you are from me and I am from you. As for you, O Ja'far, you resemble me in both your looks and your character. As for you, O Zayd, you are our brother and our freed servant.»
}your brothers in faith and your freed servants.}
Then Allah says:
}And there is no sin on you concerning that in which you made a mistake,}
meaning, if you call one of them after someone who is not in fact his father, by mistake, after trying your best to find out his parentage, then Allah will not attach any sin to this mistake. This is like the Ayah in which Allah commands His servants to say:
}Our Lord! Punish us not if we forget or fall into error} (2:286).
It was reported in Sahih Muslim that the Messenger of Allah said:
«Allah says, "Certainly I did (so)."» [1]
In Sahih Al-Bukhari, it was recorded that 'Amr bin Al-'As, may Allah be pleased with him, said: "The Messenger of Allah said:
«If the judge makes Ijtihad and reaches the right decision, he will have two rewards; if he makes Ijtihad and reaches the wrong decision, he will have one reward.» [2]
In another Hadith:
«Allah will forgive my Ummah for mistakes, forgetfulness and what they are forced to do.» [3]
And Allah says here:
}And there is no sin on you concerning that in which you made a mistake, except in regard to what your hearts deliberately intend. And Allah is Ever Oft-Forgiving, Most Merciful.}
meaning, the sin is on the person who deliberately does something wrong, as Allah says elsewhere:
}Allah will not call you to account for that which is unintentional in your oaths} (2:225).
Imam Ahmad narrated from Ibn 'Abbas that 'Umar said: "Allah sent Muhammad with the Truth and revealed to him the Book. One of the things that was revealed in it was the Ayah of stoning, so the Messenger of Allah stoned [adulterers] and we stoned [them] after he died." Then he said, "We also used to recite, 'Do not attribute yourselves to anyone other than your fathers, for this is disbelief, to attribute yourselves to anyone other than your fathers.'" The Messenger of Allah said:
«Do not exaggerate in praising me as 'Isa bin Maryam was praised upon him be peace and blessings. I am just a servant of Allah. Say, "He is His servant and Messenger."»
Or Ma'mar may have said:
«As the Christians praised the son of Maryam.» [1]
This was also narrated in another Hadith:
«Three things that people do are parts of disbelief: slandering a person's lineage, wailing over the dead and seeking rain by the stars.» [2]
[1] Ahmad 1:234, Abu Dawud 2:480, An-Nasa'i 5:271, Ibn Majah 2:1007
[2] Muslim 3:1693.
[3] Abu Dawud 5:247, Tuhfat Al-Ahwadhi 8:120.
[4] This was the 'Umrah performed by the Prophet in the year following Al-Hudaybiyah (6 H) when he had been prevented from performing 'Umrah as he had intended.
[1] Muslim 1:116.
[2] Fath Al-Bari 13:330. Ijtihad means "struggles."
[3] Tuhfat Al-Ahwadhi 1:659.
[1] Ahmad 1:47.
[2] Muslim No. 934, Ahmad 5:342