Math Error

1. Math Error

Infographic with Quran Verses
Inheritance math error source verses, Quran 4:11-12Inheritance math error calculation cases and conclusionEnlargeEnlarge

Quran gives rules for inheritance with specific mathematical fractions "of the estate" for specific heirs Quran 4:11-12, Quran 4:176.

Case 127/24 (112.5%)

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 away more than 100% of your estate. The Quran provides no resolution for this.

Analogy

If I tell you to give 1/2 of your cake to your brother and 2/3 of your cake to your sister, without telling you how:

  • Would you think there is a flaw in my instructions?
  • Would you think I am an all-knowing being?

Quran (Case 2): Give 1/2 of the estate to the husband and 2/3 of the estate to two sisters, without telling you how.

Allah, after internally stating the conditions (heirs) and assigning them mathematically impossible fractions, says in these same verses:

  • "This is an obligation from Allah. Surely Allah is All-Knowing, All-Wise." Quran 4:11
  • "This is a commandment from Allah. And Allah is All-Knowing, Most Forbearing." Quran 4:12
  • "Allah makes this clear to you so you do not go astray. And Allah has perfect knowledge of all things." Quran 4:176
Fixing Allah’s Fractions: Sunni vs Ibn Abbas vs Shia
Sunni Fix

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

Umar said: "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."Fatwa No. 222526, IslamWeb

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

Case 1
Quran
Sunni
Case 2
Quran
Sunni

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

Case 1
Two Daughters2/3 (Quran) ≠ 16/27 (Sunni) ▼ −7.4%
Two Parents2/6 (Quran) ≠ 8/27 (Sunni) ▼ −3.7%
Wife1/8 (Quran) ≠ 3/27 (Sunni) ▼ −1.4%
Case 2
Husband1/2 (Quran) ≠ 3/7 (Sunni) ▼ −7.1%
Two Sisters2/3 (Quran) ≠ 4/7 (Sunni) ▼ −9.5%
Ibn Abbas' Disagreement

Ibn Abbas, whom Muhammad prayed would understand the Quran correctly, disagreed with Umar on how to fix Allah's fractions but was intimidated by him.

Sunan Ibn Majah 166 screenshot: it was narrated that Ibn Abbas said the Messenger of Allah embraced him and said, O Allah, teach him wisdom and the (correct) interpretation of the Book. Graded Sahih (Darussalam).
Sunan Ibn Majah 166
Enlarge

Ibn Abbas: "I was intimidated by [Umar], by God."

Az-Zuhri said to me: "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

Muhammad's son-in-law and 4th Caliph Ali also disagreed, leading to a Shia/Sunni split on how to fix Allah's fractions.

Wasa'il al-Shia Vol. 26 (pp. 82-83)

Ali suggested reducing Allah's fractions of the estate for the daughters/sisters:

Case 1
Quran
Shia
Case 2
Quran
Shia

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

Case 1
Two Daughters2/3 (Quran) ≠ 13/24 (Shia) ▼ −12.5%
Case 2
Two Sisters2/3 (Quran) ≠ 3/6 (Shia) ▼ −16.7%

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

One-Liners
  • The Fixed Fraction: 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."
  • The Semantic Trap: 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 16/27 of the estate.
  • The Useless Fraction: If 2/3 of the estate can silently become 16/27 of the estate, the fraction communicates nothing.
  • The Internal Condition: The Quran internally states the conditions (heirs) and assigns them mathematically impossible fractions.
  • The Impossible Command: When the command assigns 7/6 of the estate, reducing it to 6/6 doesn't solve the instruction. It corrects it.
  • The Missing Rule: One verse would have solved it: "if it overflows, reduce proportionally." But there is no solution in the Quran for this.
  • The Caliph's Dilemma: 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?
  • The Omniscience Check: Why would an omniscient being give a mathematically impossible inheritance law and wait for Umar to fix it when He could have put the principle of awl in the text?