This means that they didn't exist at all while he was still alive; that is, until his death, which occurred approximately in 64-65 CE, to be more precise.

What was to become the Catholic Church does not mention the Gospels by name or content until roughly 150 CE, when Justin Martyr mentions several unnamed writings on the life of Jesus, in his First Apology.

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Ignatius of Antioch (98 CE) does not mention any of the four Gospels, nor the Didache nor Clement.

Finally, the two earliest writings of Paul's Church, beyond his epistles, the First Epistle of Clement (c.

His letters held (and hold) an authority unlike any other theological writings of the day.

Hence, convincing the Priestly Elite that a specific letter was written by Paul increased its likelihood of being included in the formal and final Canon (3rd Century CE).

The Gospels are not mentioned by name until 180 CE in Irenaeus of Lyons's book On Heresies.

Moreover neither Paleographic or Carbon-14 is precise enough to demonstrate that there are any fragments before our earliest references to the Gospels.

So if Jews especially in the large cities didn't even know Hebrew, why in the name of sanity would anyone with a brain in their head write a Gospel in Hebrew for them?

For instance, while Papal encyclicals are still written in Latin, they are not only written in Latin and they're especially targeting a Catholic clergy which does know Latin and is able to spread the message further in the vernacular.

Scholars also look for confirming or dis-confirming records in other sources that would list the writing in question.