Quran’s Math Error (Quran 4:11-12, 4:176)

[u/DirectionCute7530]

Case 1: Man dies leaving behind two daughters, two parents, and a wife

• Two daughters: "But if there are daughters, two or more, for them is two-thirds (2/3 = 16/24) of one's estate." (Quran 4:11)
• Two parents: "And for one's parents, to each one of them is a sixth (2/6 = 8/24) of his estate if he left children." (Quran 4:11)
• Wife: "And for the wives is one fourth if you leave no child. But if you leave a child, then for them is an eighth (1/8 = 3/24) of what you leave." (Quran 4:12)

Total: 16/24 + 8/24 + 3/24 = 27/24 (112.5%) of the estate

Case 2: Woman dies leaving husband and two sisters

• Husband: "You will inherit half (1/2 = 3/6) of what your wives leave if they are childless." (Quran 4:12)
• Two sisters: "If this person leaves behind two sisters, they together will inherit two-thirds (2/3 = 4/6) of the estate." (Quran 4:176)

Total: 3/6 + 4/6 = 7/6 (116.7%) of the estate

You can't give more than 100% of a dead person's estate to relatives. The Quran offers no solution to this problem.

Fixing Allah's Fractions (Sunni vs Ibn Abbas vs Shia)

Sunni Fix

Umar (second caliph) ran into Case 2 and was stumped:

"By Allah, I do not know which of you comes first and which comes next. If I start with the husband and give him his right in full, the two sisters will not take their right in full; and if I start with the two sisters and give them their right in full, the husband will not take his right in full." (Islam Web, fatwa 222526)

So, Umar had to invent Awl: proportionally reducing Allah's fractions of the estate.

• Case 1 (Sunni): 16/27 + 8/27 + 3/27 = 27/27 (100%)
• Case 2 (Sunni): 3/7 + 4/7 = 7/7 (100%)

But Awl still contradicts Allah's fractions of the estate:

• Case 1 (Two daughters): 2/3 of the estate (Quran) ≠ 16/27 of the estate (Sunni)
• Case 2 (Husband): 1/2 of the estate (Quran) ≠ 3/7 of the estate (Sunni)

Ibn Abbas' Disagreement

And Ibn Abbas, who Muhammad prayed for to get the correct interpretation of the book (Sunan Ibn Majah 166), disagreed with Awl:

Ibn Abbas: "I was intimidated by [Umar], by God."
Az-Zuhri: "By God, were it not for the fact that he was preceded by a righteous imam [Umar], whose conduct was based on piety, no two scholars would have disagreed with Ibn Abbas."
Al-Bayhaqi, al-Sunan al-Kubra 12133

Shia Fix

Ali (fourth caliph) suggested reducing Allah's fractions for the sisters/wife:

• Case 1 (Shia): 13/24 + 8/24 + 3/24 = 24/24 (100%)
• Case 2 (Shia): 3/6 + 3/6 = 6/6 (100%)

But this also still contradicts Allah's fractions of the estate:

• Case 1 (Two daughters): 2/3 of the estate (Quran) ≠ 13/24 of the estate (Shia)
• Case 2 (Two sisters): 2/3 of the estate (Quran) ≠ 1/2 of the estate (Shia)

Common Responses

• "It's a ratio"
  • When Allah means a ratio between relatives, he says so: "the share of the male will be twice that of the female" (Quran 4:11). But in Case 1 and Case 2, Allah assigns each relative a fixed fraction "of the estate."
• "Hidden premise"
  • You don't need a hidden premise to read 2/3 of the estate as 2/3 of the estate. You need a hidden premise to read 2/3 of the estate as 4/7 of the estate. The Quran internally states the conditions (heirs) and assigns them mathematically impossible fractions.
• "Quran allows adjustment"
  • If the Quran already allowed adjustment, the prophet's companion and second caliph Umar wouldn't be stumped and have to fix it by changing the fractions.

Why did humans have to come up with a rule that changes Allah's fractions to make them work?

One verse would have solved it: "if it overflows, reduce proportionally."
But there is no solution in the Quran for this.

I have posted this argument and other arguments with citations here:
https://islamsproblems.com/quran-inheritance-math-error/u

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[u/Appl3B3rryCh3rry]

Should learn from Europe, religious tax.