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’).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. 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.Edwin Gent­zler and Maria Tymoczko, Trans­la­tion and Pow­er (Uni­ver­si­ty of Mass­a­chu­setts Press, 2002), p. xviii

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’) Willard Van Orman Quine, Math­e­mat­i­cal Log­ic (Har­vard Uni­ver­si­ty Press, 1981), p. 48 defines the basic bicon­di­tion­al propo­si­tion as follows :

(f º y) for ((f É y) . (y É f))

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 definesSee 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 the bicon­di­tion­al as :

p º q . = . É 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. 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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