@ JoC

While Ireneus, Clement and the Muratorian Fragment give evidence of authorship in the 2nd century, we have two more sources which were writing in different parts of the Roman empire and during different times.

Attestations and ascribing authorship of anonymous writings some 100 years and more after circulation is not evidence of anything except the early Pauline church seeking authority for its versions of the gospels.

Lets look at Irenaeus: He wrote his two surviving works as a polemic against the Gnostics. He maintained that the Gnosts (although in possession of their own supportive texts) were not preaching the true message. Irenaeus was arguing that the Roman sponsored Pauline version of christianity was the true path despite the success of Marcion and the Gnostics. To bolster his scriptural argument he assigned authorship in about 180 CE...let that sink in JoC, 180 CE....see your problem? there is no unbroken line of gospel attestation from the first, In fact nothing until the 2nd Century as you so cleverly have discovered and written about. Nothing. You are confounding your own claims every time you research.

Irenaeus is also the earliest attestation that the Gospel of John was written by John the Apostle, and that the Gospel of Luke was written by Luke, the companion of Paul.Wiki. Citations available on the page.

Muratorian Fragment: Is just a (partial) list of texts accepted by the early church. The earliest date for its writing is set at about 170CE the same time as all the gospels were ascribed authorship. The only comment in the Muratorian Fragment about authorship is that of the gospel of John. It is not evidence as the Fragment is late 2nd century and not contemporary to the actual writing of the gospel of John.
What is interesting about this list is that it does not contain 1 or 2 Peter, Hebrews or James suggesting that their 2nd or 3rd century origin is very likely as I have said in previous threads. ..

Clement: well if you read anything of his you would, as a good catholic, be stopping your eyes and running away. His beliefs were, shall we say eccentric? and definitely not mainstream Early Church.

Tertullian of Carthage: Funny you should cite this person. Yes , like you he believed in the authorship of the gospels....because it gave him the authority to attack the Marcionites (are you seeing a common thread in the mid to late 2nd Century yet? ) but he produces no evidence just a bare assertion. Oh, BTW did you know he was a Montanist ,JoC, that should give your good orthodox catholic soul a shudder every time you write his name!

Papias of Hierapolis: unfortunately his works have not survived except in a couple of short extracts. You have quoted him as someone who ascribed authorship of the gospels to the apostles. That is not the case. You should do some in depth reading before you start waving your flags and doing a silly dance. There is no evidence, and scholars are divided, on what texts Papias was writing about. Read more.

Keep researching JoC, even though you only skim to find confirmation of your own bias, then get debunked when the whole books or writings are researched. If you keep it up then the conclusions that nearly every scholar has come to about the authorship of the Gospels and the life of the jesus figure will solidify in your mind and you can abandon your stance of historical authority for your beliefs.

The gospels are anonymous. There is no contemporary evidence for a jesus figure as described in the gospels. None.
If you want to find evidence of the authorship of the gospels then you need solid third party corroboration from the 1st century. Otherwise you are only producing historical evidence of the start of a tradition. An erroneous tradition that persists to this day.

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Tertullian of Carthage (AD 180) : Writing 160 years after the imagined death of Jesus. What in the fuck would anyone care what he wrote. He was a Christian apologist who wrote extensively condemning the Gnostic faiths and trying to justify the trinarian point of view. (The life of Tertullian is based almost wholly on information written by men living over a century after him and from obscure references in his own works. ) WE KNOW LITTLE TO NOTHING ABOUT THE MAN. We do know he CREATED HIS OWN RELIGION AND WAS NOT A MAINSTREAM CHRISTIAN OF HIS TIME - "He eventually broke with them to found his own sect, a group that existed until the 5th century in Africa."
http://www.ntcanon.org/Tertullian.shtml

What you need to do is get back on track and prove the Gospels were written by Matthew, Mark, Luke and John. Still waiting for evidence.