The Ternary Logic Escape Hatch: Why It Doesn't Save the Islamic Dilemma

By Gavin G.

A while back I ran into an atheist who was less interested in an actual conversation and more interested in winning an argument. What made the exchange strange was that he was defending Islam without believing in any form of theism himself. When I pressed the Islamic Dilemma, he pushed back using a move that caught me off guard at first. Once I worked through what he was actually doing, I realized the objection was more of an escape hatch than a real rebuttal.

The Islamic Dilemma

The Islamic Dilemma is a straightforward argument built on the Qur'an's own claims about prior Scripture. It runs like this:

The Qur'an affirms both the Gospel (Injil) and the Torah (Tawrat) as genuine revelation from God.
The Qur'an denies the crucifixion of Jesus, the deity of Christ, and the Trinity.
The New Testament — the Injil Muslims claim was given to Jesus — affirms all three of those things.
Therefore, the Qur'an both affirms and contradicts the same body of revelation.

Since the Qur'an presents itself as the perfect, uncorrupted word of God, internal contradiction is fatal to that claim. The structure here is standard modus ponens:

P1: If the Qur'an affirms the Injil and Torah as genuine revelation, then it cannot contradict them without self-refuting. P2: The Qur'an does contradict them on central doctrinal points. C: Therefore, the Qur'an is self-refuting.

Formula: P → Q; P; ∴ Q

This is a valid argument. The question is whether the objection my interlocutor raised does anything to undermine it.

The Ternary Logic Move

His counter was to invoke ternary logic. Standard logic operates on the Law of Excluded Middle: any proposition is either true or false. Formula: P ∨ ¬P. There is no third option.

Ternary logic, by contrast, introduces a third truth value alongside true and false. Depending on the system, that third value might represent "unknown," "indeterminate," "possible," or something similar. His argument was that the Islamic Dilemma only works if you commit to classical binary logic, and that ternary logic opens up a third option that breaks the dilemma.

In practice, what this looks like in Muslim-Christian dialogue is familiar. I have debated Muslims who, when pressed on what the Injil actually was — what it said, what it contained — respond only that it was a book given to Jesus. When you ask them to describe its content, they deflect. The Injil becomes an undefined placeholder rather than a real document they are prepared to defend. The ternary logic move formalizes that deflection: rather than saying "I don't know," it dresses up the same non-answer in philosophical language and calls it a legitimate third option.

Why It Fails

The ternary escape hatch does not defeat P ∨ ¬P — it sidesteps it. Introducing an "unknown" or "possible" value does not show that the contradiction between the Qur'an's affirmation of prior Scripture and its denial of Christian doctrine is false. It simply declines to engage whether that contradiction is true. That is not a rebuttal. It is a suspension of the question.

More importantly, the move collapses under the Qur'an's own self-description. Surah Yusuf 12:1 describes the Qur'an as "the clear Book." The Qur'an presents itself as perspicuous — not as a document whose core claims sit in some indeterminate state between true and false. If a Muslim has to appeal to ternary logic and say "it's unknown" or "it's possible," they are conceding that their own scripture fails to provide the clarity it claims to have.

That concession circles right back to the original dilemma. A book that cannot determine whether its own affirmations are consistent with its own denials is not a clear book. It is a self-refuting one.

What This Means for the Argument

Denying the Law of Excluded Middle is a significant philosophical move, and it is not one made lightly in formal logic. My interlocutor wanted the benefits of that denial without acknowledging what it costs. If you abandon P ∨ ¬P in order to escape the Islamic Dilemma, you have not saved the Qur'an's coherence — you have undermined the logical framework you need to defend any claim at all, including Islam's own truth claims.

The burden of proof does not disappear when someone invokes ternary logic. If a Muslim cannot provide a positive account of what the Injil contained and why the Qur'an's denials are consistent with affirming it, the dilemma stands. Saying "it's unknown" is not a defense of Islam. It is an admission that the defense has run out.

Gavin G. is a contributor to Apologetics Unchained. This article reflects his engagement with live apologetic encounters and the logical analysis he developed in response.