So I'm to believe in a God who is one and three at the same time, with one of the three killing another of the three and then sending another to console humans? Why not just Allah instead?

The sentence in the objection is not the doctrine, and it is worth saying that plainly before answering. What Christians confess is stranger and more careful than “one and three at the same time.”

1. The doctrine is one essence, three persons. God is one in being and three in person — one divine “what,” three divine “whos.” The Father is not the Son, and the Son is not the Spirit, and each is fully God. That is a mystery, but it is not the claim that 1 = 3.

2. A contradiction needs the same sense. P and not-P is a contradiction only when the terms mean the same thing in the same respect. Christians deny that “one” and “three” refer to the same thing in the same way. Whatever else that is, it is not a logical impossibility.

3. The creed summarises earlier texts. Matthew 28:19 baptises into the “name” — singular — of Father, Son, and Spirit. Paul splits the Shema of Deuteronomy 6:4 around Jesus (1 Corinthians 8:6). John calls the Word God (John 1:1). Peter tells Ananias he has lied to the Holy Spirit and then says he has lied to God (Acts 5:3–4). The fourth-century formula is a summary of first-century practice.

4. The cross is not the Father killing the Son. “No one takes my life from me, but I lay it down of my own accord” (John 10:18). The Father “did not spare his own Son but gave him up for us all” (Romans 8:32) — the giving is love, not the sacrifice of a victim to a wrathful deity. The Son suffers in his human nature, and the persons act together.

5. Mystery is not the same as nonsense. A God a finite mind could fully map would be a God we had mastered, which is an odd thing to worship. “How unsearchable are his judgments and how inscrutable his ways!” (Romans 11:33). Christians claim to know God truly, not exhaustively.

6. Turn it around: Islam has its own central mystery. Classical Islamic theology holds that God's speech is eternal and uncreated, which is why the Qur'an is not a creature. That raises the same kind of question the objection presses: how does an eternal attribute relate to a temporal world and a human prophet? The Trinity is not the only doctrine with a difficult centre.

7. The real difference is historical, not conceptual. Surah 4:157 says Jesus was not crucified; the Gospels say he was crucified under Pontius Pilate. Tacitus, writing in the early second century, records that “Christus” suffered the extreme penalty under Pilate. One of these claims is about a datable public event, and it can be investigated.

8. The two faiths answer guilt differently. In the Islamic account God forgives by sovereign decree; in the Christian account he forgives at cost to himself. The question is which better fits a God who is both holy and merciful — a decree that costs nothing, or a pardon that costs everything.

9. Love is eternal in the Trinity, not added later. “God is love” (1 John 4:8). If God is a solitary unit, love becomes something he does once he creates, not something he is. The Trinity says love is eternal inside God's own life, which is why the Christian God is not a lonely monarch.

10. Honesty about what this does not settle. This argument does not prove the Trinity; it clears away the charge of incoherence and shows the doctrine is grounded in the texts. Whether Jesus rose is the question that decides between the two faiths, and no amount of conceptual tidiness substitutes for it.

The objection is aimed at a doctrine nobody holds, and once the doctrine is stated correctly the charge of absurdity loses its grip. The remaining disagreement with Islam is not about arithmetic but about an event in Jerusalem. That is the question worth arguing, and it is answerable.

Sources: James White; The Forgotten Trinity; Nabeel Qureshi; Seeking Allah, Finding Jesus; Michael L. Brown; Wesley Huff.

Related challenges:
• If I were raised in India, I’d most likely be a Hindu. You would be a Muslim if raised in Saudi Arabia. Is it ‘fair and just’ of God to have billions of people’s eternal destinies determined by “God’s Divinely ordained” place of birth?
• Truth is relative. Only narrow-minded bigots believe in absolute truth!
• How do Christians respond to eastern systems of thought such as Buddhism and Hinduism?