On The Qur'an, Logic And The FTMecca

Mohd Elfie Nieshaem Juferi

Recently “Freethought Mecca”, an anti-Islamic website of atheist persuasion, came forth with an article that claimed to have found at least one error in the Qur’an. The article (and its supporters) took pleasure in pointing out the irony of the alleged error’s location: in Sura 4:82, the very verse Muslims have invoked for centuries when challenging detractors to find a discrepancy in the Book.

The article first claims that the logical structure of the verse has it putting forth a proposition that is “demonstrably false”. To add insult to injury, it is further claimed that yet more irony can be derived from the discovery that the challenge put forth in Sura 4:82 is not really a challenge at all. The argument of the article is actually quite subtle, and rather potent. We would like to offer this short analysis-cum-rebuttal at this time.

Have They Considered The Qur’an?

The article paraphrases the relevant portion of Sura 4:82 as “if the Qur’an is not from Allah, it would have errors.” It is pointed out that this sentence has the logical structure of a conditional proposition (an “if-then” sentence), and thus implies that a text not from Allah has errors, and contrapositively that a text that is free of errors is from Allah. This is where it is claimed that the sentence is demonstrably false, as a single instance of a text that is both free of error and not of a divine origin would falsify it, and such texts do indeed exist.

First we need to explain the logic behind this argument. To use the variables used in the article, let ‘A’ stand for “the Qur’an is from Allah,” and let ‘E’ stand for “the Qur’an has errors.” The tilde ‘~’ then serves as a diacritical mark representing the negation of the variables being employed to represent sentences, so if ‘A’ stands for “the Qur’an is from Allah,” then ‘~A’ stands for “the Qur’an is not from Allah.” The article employed an arrow ‘–>’ to represent the logical connective in a conditional proposition, but we will instead use the symbol more familiar to logicians, the so-called “horseshoe” ‘É’ which has the same value. The proposition is then translated into logical form as:

~A É E

With this sort of sentence, it is also noted that if you negate the right side (referred to as the consequent), you must also negate the left side (referred to as the antecedent), and then the reverse of the above is logically equivalent. This is referred to as contraposition (or, when employed in a syllogism, it is referred to as modus tollens):

~E É A

This is the part that the article has a problem with. Here it is asked why anyone should assume this is the case. On what grounds should be believe that if a text is not from Allah, it will have errors, or that a text that does not have errors will be from Allah? Surely there are objections that can be raised. Surely there are counter-examples that can be called to witness to serve as a defeater for this claim.

The responses offered by Muslims to date have failed to tackle the essential argument being put forth here. The reality is that there are texts written by men that are free of error, i.e. a college textbook or restaurant menus. While indeed most texts written by human beings are prone to error, there have been bodies of writing that managed to be free of any discrepancies. Some have tried to object that we are discussing the Qur’an, not a bus map or a model-plane instruction manual, but then fell short of defending their special pleading on behalf of the Qur’an

We would like to now offer a response, and it is through an appeal to justified special pleading. So, like the previous criticisms, we too would like to say that the verse reserves this rule for not just any text, but the text of the Qur’an specifically. We agree that it is, at least in principle, possible for a human being to create a text that is free of error. So now we must defend our plea on behalf of this rule being only with regard to the Qur’an.

Why do we feel that if we hold up the Qur’an and say “if this text were not from God, it would have errors”, we are uttering a true proposition, yet if we do the same for a phone book it is false? In the case of the phone book it is possible that it could be both free of error and not from God, yet this is not possible for the Qur’an. We are justified in making this distinction when it is pointed out that the Qur’an can be defined as a set of propositions, a number of which state that the set itself originates with a Divine source, while the same cannot be said of a phone book.

In other words, on a number of occasions the Qur’an states that it is from God. Once this is understood, it is impossible for it to both not be from God and free of error. If the Qur’an was not from God, every verse that states that it is from God would be false, thus there would be numerous errors present. The contrapositive is also true in light of the fact that if the Qur’an was free of error, that would mean every sentence in it would be true, including those sentences that claim it is from God. Now, we are not saying that the Qur’an is from God simply because it says so. However, what we are saying is that its numerous claims to Divinity justify its being a special case distinct from a phone directory, and thus make it immune to the claim that the proposition is “demonstrably false”.

Challenging The Formal Translation

Now that we have defended the Qur’an against this attack, all that is left is the claim that no challenge is present. To understand this attack, one again must be familiar with the tenets of basic logic. The article claims that the logical structure of the verse negates there being any challenge of the sort that so many Muslims claim is put forth. Let us consider again the logical structure of the verse:

~A É E

This translates to “if the Qur’an is not from Allah, then the Qur’an has errors”. While it is a common belief that the existence of errors negates a text being from God, this is not implied in the logical structure of the proposition above. To argue that because the consequent (‘E’) is true, the antecedent (‘~A’) is also true is to abuse logic. The logical fallacy being committed here is known as “affirming the consequent.”

The article actually explained this fallacy quite well via an example using Santa Claus; we would like to use this as well since the Christian holiday passed so recently. Here we will let ‘H’ stand for “Santa came to my house,” and let ‘P’ stand for “presents will be under my tree.” Now, if we suspend our common sense and concede that maybe it is possible that Santa Claus exists, then the sentence “if Santa came to my house, presents will be under my tree” can be translated as:


One can imagine a small American child in his room saying precisely that on Christmas morning, and then going down stairs to see if anything is under the tree. However, if the child does find presents under his tree (if ‘P’ is true), does this mean that Santa came the night before? Does it mean that ‘H’ must be true also? The answer is of course not. The logical structure of the conditional proposition does not allow one to conclude that the antecedent is true just because it has been realized that the consequent is true.

So then, the article notes that ‘~A É is not really a challenge to disprove ‘A’ by finding ‘E’. It is argued that even if an error could be found, while common sense may lead us to reject the claim that the Qur’an is from God the logical structure of the verse does not permit such a conclusion. If one actually found an error in the Qur’an and then claimed to have met the challenge, the argument would be as follows:

  • If the Qur’an is not from Allah, it would have errors.
  • The Qur’an has errors.
  • Therefore, the Qur’an is not from Allah.

Such an argument is logically invalid, as the person putting forth this argument has affirmed the consequent. The argument is equivalent to arguing:

  • If I am in Kuala Lumpur, then I am in Malaysia.
  • I am in Malaysia.
  • Therefore, I am in Kuala Lumpur.

Imagine a person who is lost (maybe he is suffering from amnesia), trying to figure out where he is. Then imagine him figuring out that he is in Malaysia, and using the above sort of logic to conclude that he is in Kuala Lumpur. Just because he is in Malaysia does not mean he is in Kuala Lumpur, and one can imagine how foolish he would look if he was in a different Malaysian city and uttering the above before the locals. Once again, the fallacy committed is affirming the consequent.

In short, the verse is saying that if the Qur’an is not from God, it has errors (‘~A ? E’), which is different from stating that if the Qur’an has errors, it is not from God (‘E ? ~A’).1 That these two statements are logically inequivalent can be demonstrated via the following equation, which is beyond dispute (it is an analytic truth, a priori):

(~A É E) ¹ (E É ~A)

So, the Muslim is faced with a problem, as on one hand the logic fits, while on the other admitting such would mean that for centuries no Muslim could see the fallacious nature of the challenge. Is there a way out? Indeed there is. Rather than treat the verse as a conditional proposition, we can treat it as a biconditional proposition.

Up until now we went along with the verse being rendered into logical form as a conditional proposition. Due to the fact that one would read aloud the logical formulas in English, it is assumed that they are in fact English. The reality is that it is not the same language that this article is written in; the formulas are in a different language. Writing a sentence in logical form is referred to as translating it into a formal language (the formal language in this case being sentential logic). In light of this fact, we should note here what the linguists Gentzler and Tymoczko have said about the art of translation:

Translations are inevitably partial; meaning in a text is always over-determined, and the information in a source text is therefore always more extensive than a translation can convey. Conversely, the receptor language and culture entail obligatory features that shape the possible interpretations of the translation, as well as extending the meanings of the translation in directions other than those inherent in the source text. As a result, translators must make choices, selecting aspects or parts of a text to transpose and emphasize. Such choices in turn serve to create representations of their source texts, representations that are also partial.2

So, just as a translation from Arabic to English involves choices that will dictate how one understands a sentence, so too is the case for a translation from a natural language to a formal one. Of course, translation into sentential logic is a special case, since it is rarely ever vague and is used to analyze the structure of language. Nonetheless, there are instances where the translator has to make a decision, and which path he or she chooses plays directly on the progress of further analysis.

The article capitalized on the fact that ‘~A ? E’ is different from ‘E ? ~A’, and then argued that the former is what the Qur’an is stating, while the latter is what the Muslims seem to think it is stating (or at least what it would have to state in order for a challenge to be present). We, however, would like to argue that the verse in the Qur’an can be interpreted as stating both.

The clues as to how one would go about doing such were provided in the article itself. As was stated above, the article conceded that one could also translate the verse as a biconditional (rather than a conditional) proposition. The article also invited readers to consider Quine’s Mathematical Logic. In that work, Quine’s fifth definition (‘D5’) 3 defines the basic biconditional proposition as follows:

(f º y) for4

Here the biconditional, represented by the symbol referred to as a “triple bar” (‘?’), is equated with both versions of the conditional. The article also made mention of Russell’s Principia Mathematica, which similarly defines5 the biconditional as:

p º q . = . p É q . q É p

While both definitions may seem foreign to the lay reader not acquainted with logic, the point is that this particular logical connective treats the variables as equivalent. For example, let ‘Q’ stand for “I am in al-Quds,” and let ‘J’ stand for “I am in Jerusalem.” Being that Jerusalem and al-Quds are the same place: if I am in Jerusalem, then I am in al-Quds, which as a conditional proposition would be translated:


But with the conditional connective you are not allowed to affirm the consequent; i.e. you cannot conclude based on the above that if I am in al-Quds, then I am in Jerusalem, yet we also want to be able to say precisely that:


We want to say both ‘J ? Q’ and ‘Q ? J’, and these two conditional propositions can be brought together by employing the biconditional proposition ‘J ? Q’. Now, with the verse in Sura 4:82, we argued earlier this is applying specifically to the Qur’an in light of the numerous claims that the text is from God. In such a case, if the Qur’an has errors, then it is not from God, and just the same it should be noted that if it the Qur’an is not from God it has errors. What this means is that under this model the verse is stating both ‘E ? ~A’ and ‘~A ? E’. It only makes sense, therefore, that the verse be translated into logical form as follows:

~A º E

When the verse is rendered as a biconditional proposition, Muslims are given back the challenge. The above states that finding errors in the Qur’an is equivalent to demonstrating the Qur’an is not from Allah. This is exactly how Muslims have interpreted the verse for centuries.


So in conclusion, there is no error in Sura 4:82, as special pleading on behalf of the Qur’an is justified. Had one considered the Qur’an, they would have noticed that on several occasions it claims to be from God, and if the Qur’an was not from God all these claims would count as errors. While nothing in this particular article proves that the Qur’an is from God, we have established that the verse in question can be logically defended.

And only God knows best.


  1. The reader may be confused here in light of what has been stated previously, and thus should note that while ‘~A ? E’ is equivalent to ‘~E ? A’, neither is equivalent to ‘E ? ~A’. While the sentences look the same, the placement of the negation ‘~’ makes a huge difference. []
  2. Edwin Gentzler and Maria Tymoczko, Translation and Power (University of Massachusetts Press, 2002), p. xviii []
  3. Willard Van Orman Quine, Mathematical Logic (Harvard University Press, 1981), p. 48 []
  4. f É y) . (y É f []
  5. See Principia Mathematica, definition *4.01; in the abridged version made for Philosophy students, it would be found in Alfred North Whitehead and Bertrand Russell, Principia Mathematica to * 56, (Cambridge, 1962), p. 115 []


  1. Qur’an is the word of Allah – True book – pure book – Without any error – That’s true.

  2. Qur’an is not in error in any way. People brig false charges on Qur’an just because they are illiterate.

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