Surah 4.82 of the Quran appears to contain at least one logical fallacy. This is the relevant verse: “Do they not then meditate on the Quran? And if it were from any other than Allah, they would have found in it many a discrepancy.” (Surah 4.82)

SUBJECTING SURAH 4.82 TO THE TESTS OF LOGIC

Here is how we can use the rules of logic in simple steps to test the logicality of Surah 4.82

Where
A = Had it been from other than Allah,
then
B = they surely would have found therein contradictions in abundance

This is the only statement we have to work with, the source statement from the Quran. This conditional statement is our assumption.

If A then B

This is our one and only axiom (assumed truth).

Now we can use the rules of logic, that allow us to move with certainty and without error to other statements.

The premise is that:

"If it has Contradictions it definitely is from something Base."

Right away this is the mistake of affirming the consequent.

We cannot form any statement like:

"If B then such and such follows"

Now we can apply the rules of logic in simple steps to prove the illogicality of Surah 4.82

Where A is true (that Allah dictated the Quran) then it follows that B is true (that the Quran is without error) Thus if A is true, we know B is true. But if all we know is that B is true (that the Quran is without error) we still don't know anything about the truth value of A. It may be true, it may not be true, we don't know.

We cannot use the truth of B to prove anything about A. All we know is if A is true then B is true. The Quran being error free or not tells us nothing about its divine authorship.

But its worse than this, because Surah 4.82 starts with the premise “If it were not from Allah”.This in the jargon, is negating the antecedent, and to conclude for B that it has or doesn't have errors is an invalid and meaningless conclusion. By starting from a negative premise 4.82 actually breaks a fallacy of formal logic.

I wish to have the above analysis tested and verified.

First, this is just a claim being made without adequate justification (e.g., "If it's not from Allah, then there would be contradictions"). Logically (formally), this would be fine. For example, we can say "If a fair coin lands on one side and that size is not heads (NOT X), then it must be tails (Y)." This works because there are only two possibilities. Once we exclude one, it must be the other. The claim is presenting a binary choice... it can only be one or the other. We can move into informal fallacies (and reason) and suggest that this (the Allah example) is a false dichotomy , because there are other options to explain a book free from contradictions (assuming it is) besides "God did it."

If we plug our coin example in the following possibilities, we see that all of the following also work:

If not Y, then X. If the coin does not land on tails, then it landed on heads.
If Y, then not X. If the coin does land on tails, then it did not land on heads.
If X, then not Y. If the coin does land on heads, then it did not land on tails.

Again, the initial claim sets up the dichotomy: "If it's not from Allah, then there would be contradictions." This means if anyone except for Allah wrote/dictated the book, contradictions would necessarily have to be in the book. Consider this example:

If I am not at school, then I am (necessarily) at home. I am not at home. Because of the claim made I can't be anywhere else (e.g., the library, the bank, a brothel) besides school. This goes against our sense of reason because we know there are many places we can be... it sets up a clear false dichotomy . It makes more sense when we use an intuitive binary such as "If I am not alive, then I am dead." I'm not dead, therefore, I must be alive" or the coin example above.

Hope this helps. Let me know if I missed your question.

Well, firstly, I must say that matters of religion can and should not be put to the scrutiny of logic. Much greater minds have tried and failed... but here we go anyway... ;-)

So, the statement is "if it were from any other than Allah, they would have found in it many a discrepancy", then the proper formal expression is:

¬ A ≡ B

wherein A is "it is from Allah", and B stands for "discrepancies can be found".

You also noticed the ≡, which stands for "material equivalence" (rather than an "if ... then"-statement, which suggests a "material implication" that should be expressed by → ), because the sentence implies that the reverse is true, too, i.e. if it is from Allah, then no discrepancies can be found, or at least that's the only way this sentence would make any sense.

This already points out that indeed one can deduct the following from the above statement:

A ≡ ¬B

However, we're not done yet, as the quote does - as I wrote - only make sense in this interpretation. There is a risk that we re-define the term in order to make it fit the logical system. But in the end, that doesn't matter, as long as there is a valid, believable interpretation of the statement that isn't too far-fetched; and that fits the case here.

Still: it's a religious statement and shouldn't be interpreted with too strict logical view. Otherwise you'd also need to look long and critically at the Bible and you may not like the results of that... :-/